CN108365955B - Device-independent high-channel-capacity quantum communication system and method - Google Patents
Device-independent high-channel-capacity quantum communication system and method Download PDFInfo
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Abstract
The invention belongs to the technical field of information processing, and discloses a device-independent quantum communication system with high channel capacity and a method thereof, wherein the communication method adopts a super-entangled state under multiple degrees of freedom as a quantum carrier, establishes a device-independent super-entangled quantum communication model, and carries out dense coding; verifying the channel capacity by calculating the amount of information each particle can transmit and comparing with the amount of information in other protocols; meanwhile, the invention discloses a device-independent high-channel-capacity quantum communication system. According to the invention, two particles are distributed to complete the distribution of the two-bit device independent key, and the quantum efficiency reaches 1; if a common entangled state such as a Bell state is used as a quantum carrier, only one device-independent key can be distributed by distributing two particles, and the quantum efficiency is only 0.5.
Description
Technical Field
The invention belongs to the technical field of information processing, and particularly relates to a device-independent high-channel-capacity quantum communication system and method.
Background
Currently, the current state of the art commonly used in the industry is such that:
in order to promote the practicability of quantum communication, the improvement of the channel capacity under the safety and safety premises is two key problems which need to be solved urgently. In previous researches, the safety of quantum communication is guaranteed by the principle of quantum mechanics, and a quantum state preparation source and measuring equipment are perfect by default. However, in real conditions, it is difficult to realize perfect preparation of the source and the measurement device, and thus, real quantum communication systems may have various safety hazards. Various attack schemes exist for equipment imperfection, which cause secret information to be leaked, such as time displacement attack, dead time attack, strong light blinding attack and the like. That is, a quantum communication protocol that is absolutely secure in theory, may be very insecure in practice. Therefore, under the premise that the device is not trusted, the research on the safe quantum communication protocol is the first step to promote the practicability of quantum communication and ensure the safety. In addition, under the premise that the device is not trusted, the actual channel capacity can be greatly reduced, and if the channel capacity in communication is too low, a practical quantum security communication protocol cannot be really realized. Therefore, the safe quantum communication protocol with higher capacity has theoretical significance and practical value under the untrusted condition of research equipment. At present, the theory and technical research on quantum communication under the premise of equipment untrustworthiness mainly focuses on the following five aspects: and 4, the research of device-independent quantum secure communication shields the side channel attack vulnerability caused by the untrustworthiness of a preparation source and a measuring device. And (3) quantum secure communication research irrelevant to the measuring equipment is carried out, and only side channel attack loopholes caused by the untrustworthiness of the measuring equipment are shielded. And carrying out entanglement state measurement on the particles sent by the two communication parties by the untrusted third party and publishing the result, wherein the two communication parties generate a secret key by judging the relevance of respective input data, so that the channel loophole at the side of the detector is removed. However, a side channel attack vulnerability caused by an untrustworthy preparation source cannot be shielded, and only a decoy state method can be used for avoiding the security problem caused by a non-ideal light source. A semi-device independent quantum key distribution study that assumes that neither the provisioning source nor the measurement device are trusted, but requires the communicating party to prepare a quantum system of known Hilbert space dimensions. The quantum key distribution research irrelevant to unilateral equipment mainly researches the side channel attack vulnerability caused by the untrustworthy measurement equipment of one party by utilizing the violation judgment of an EPR-steeling inequality under the condition that only one device of two communication parties is untrusty. However, in the research of quantum secure communication under the premise that the above devices are not trusted, a problem indispensable in any communication is not considered: the problem of coding efficiency is not considered, the actual channel capacity can be greatly reduced on the premise that the equipment is not trustable, and if the channel capacity in communication is too low, a practical quantum security communication protocol cannot be really realized.
In summary, the problems of the prior art are as follows:
the prior art is very insecure in actual communication. Most of the prior art does not consider the potential safety hazard caused by the untrustworthy equipment, and even if a few technologies consider the untrustworthy equipment factors, the problem of low coding efficiency caused by the untrustworthy equipment is not considered.
Therefore, the prior art is theoretically very safe, practically unsafe and inefficient.
The difficulty and significance for solving the technical problems are as follows:
the method can prevent (shield) information leakage caused by the fact that the preparation source equipment or the measuring equipment is not trustable (controlled or provided by an eavesdropper), resists common side channel attack loopholes such as 'time displacement attack', 'dead time attack', 'strong light blinding attack' and the like, and provides safe and reliable communication; meanwhile, the channel capacity of the device irrelevant quantum communication is also improved, and the quantum efficiency is improved by 1 time by taking key distribution as an example. At present, the key distribution is carried out by utilizing the prior art, the theoretical value of the quantum efficiency can only reach 0.5 at most, and the theoretical value of the quantum efficiency can reach 1 at most by utilizing the technology provided by the invention.
Disclosure of Invention
Aiming at the problems in the prior art, the invention provides a device-independent high-channel-capacity quantum communication system and a device-independent high-channel-capacity quantum communication method.
The invention is realized in such a way that a device-independent quantum communication method with high channel capacity comprises the following steps:
establishing a quantum communication model irrelevant to a quantum state preparation source: in the worst case, preparing an entangled quantum state density function model by an eavesdropper; then when a quantum protocol is designed under the quantum state density function description model, non-entangled states are removed according to the principle of violation of Bell inequality, super-entangled states are reserved, and on the basis of super-entangled state communication, an eavesdropper cannot acquire any secret information by controlling a preparation source according to entangled monotonicity and non-super-speed of light principles;
establishing a quantum communication model independent of equipment: the device independence comprises preparation source independence and measurement device independence; only analyzing whether the statistical probability relation between the measurement input result and the measurement output result violates the Bell inequality, taking the result as a judgment condition for considering whether an eavesdropper exists in the quantum communication, and constructing a quantum communication model unrelated to the measurement equipment; the quantum state distributed to the user for communication is in the maximum entangled state, and according to the entangled monodispersity principle and the principle of not exceeding the speed of light, an eavesdropper cannot acquire the secret information of a legal user through a measuring device by any means;
establishing a high-channel capacity quantum communication model independent of equipment: and a super-entangled state under multiple degrees of freedom is used as a quantum carrier, and an equipment-independent super-entangled quantum communication model is established for carrying out dense coding.
Further, the establishing of the quantum communication model independent of the quantum state preparation source comprises:
assuming that the entangled state is prepared by an eavesdropper Eve and then distributed to a sending end and a receiving end for the next communication; an eavesdropper Eve acquires secret information of a transmitting end and a receiving end as much as possible, and the Eve does not prepare a perfect super-entangled Bell state; on the contrary, an eavesdropper Eve prepares a mixed state of a super-entangled state and a non-entangled state, and confuses a sending end and a receiving end to ensure that the sending end and the receiving end do not find the eavesdropping behavior of the sending end and the receiving end and acquire the secret information of the sending end and the receiving end;
the super-entangled Bell states prepared by the eavesdropper Eve are represented by the following density function model:
the density function model represents: the state prepared by the eavesdropper Eve is a super-entangled state
And a mixed state of non-entangled state I/4, in which a super-entangled state is present
The visibility of (a) is p, and the visibility of the non-entangled state I/4 is 1-p;
according to the principle of entanglement monodispersity, if an eavesdropper Eve prepares an entangled state, any secret information of a sending end and a receiving end cannot be acquired; if the eavesdropper Eve prepares the non-entangled state, acquiring partial secret information of the sending end and the receiving end;
transmitting terminal and receivingThe terminal accepts the original noise when analyzing the influence of various possible noises in the channel
Is transformed into
If the non-entangled state is removed according to the principle of violation of Bell inequality in communication, the super-entangled state is reserved, and based on the super-entangled state communication, an eavesdropper Eve cannot acquire any secret information of a transmitting end and a receiving end according to the principle of entangled monotony and non-super light speed.
Further, the establishing of the device-independent quantum communication model includes:
if the eavesdropper Eve sends the A particles to the sending end, and the B particles are sent to the receiving end; the transmitting end and the receiving end respectively randomly select measurement input x and y epsilon {0,1} to measure respective particles, wherein x is 0 to represent Z firstSBase measurement of ZPBase measurement, x ═ 1 denotes Z firstSBase measurement of XPBase measurement; wherein y-0 denotes first ZSBase measurement
Base measurement, y ═ 1 denotes Z firstSBase measurement
Base measurement;
the measurement results of the sending end and the receiving end are respectively expressed as a and b belonging to {0l,0u,1l,1u };
definitions of the CHSH inequality
P(a0＝b0)+P(a0＝b1)+P(a1＝b0)+P(a1≠b1) Less than or equal to 3, wherein
P(aj＝bk)＝P(a＝b＝0l|x＝j,y＝k)+P(a＝b＝0u|x＝j,y＝k)
+P(a＝b＝1l|x＝j,y＝k)+P(a＝b＝1u|x＝j,y＝k)。
The sending end and the receiving end select some particles to calculate the conditional probability P (a, b | x, y), and judge whether the CHSH inequality is violated, if the CHSH inequality is violated, the particles distributed to the sending end and the receiving end by the eavesdropper Eve are in a super-entangled state.
Further, the original text
The super-entangled Bell state is a polarization state degree of freedom and a path mode degree of freedom;
wherein |0> and |1> represent the horizontal and vertical polarization states, respectively, of the photon; subscripts a and B represent the two photons in the super-entangled state, respectively; l and u represent different path modes of photons A and B; subscript P represents the polarization state degree of freedom, and subscript S represents the path mode degree of freedom; an ultraviolet light pump pulse passes through a barium borate beta crystal BBO to generate a photon pair which is related to each other in a mode u; after being reflected, the crystal passes through the crystal for the second time and generates mutually related photon pairs in a mode I;
for a two-photon super-entangled Bell-state quantum system with one degree of freedom of polarization state and one degree of freedom of path mode, 16 Bell states are provided and are expressed as follows:
wherein | Θ>PRepresents one of four Bell states in the freedom of polarization:
wherein | xi>SRepresents one of four Bell states in the path mode degree of freedom:
adopting CHBSA to distinguish 16 super-entangled Bell states;
two non-orthogonal measurement bases under the polarization state freedom are selected as follows: zP＝{|0>,|1>And
two non-orthogonal measurement bases under the path mode freedom are selected as follows: zS＝{|l>,|u>And
super-entangled state in two degrees of freedom of polarization state and path mode
eve prepares the quantum state:
wherein
Represents: the Eve prepared state is a super-entangled state
And a mixed state of non-entangled state I/4 in which a super-entangled state is present
Has a visibility of p, a non-entangled state I/4Is 1-p.
Another object of the present invention is to provide a key distribution method of the device-independent high channel capacity quantum communication method, where the key distribution method includes:
eve sends the A particles to a sending end, and the B particles to a receiving end; the transmitting end and the receiving end respectively randomly select measurement input x and y epsilon {0,1} to measure respective particles, wherein x is 0 to indicate that Z is firstSBase measurement of ZPBase measurement, x ═ 1 denotes Z firstSBase measurement of XPBase measurement; wherein y-0 denotes first ZSBase measurement
Base measurement, y ═ 1 denotes Z firstSBase measurement
Base measurement; the measurement results of the sending end and the receiving end are respectively expressed as a and b belonging to {0l,0u,1l,1u };
definitions of the CHSH inequality
P(a0＝b0)+P(a0＝b1)+P(a1＝b0)+P(a1≠b1) Less than or equal to 3, wherein
P(aj＝bk)＝P(a＝b＝0l|x＝j,y＝k)+P(a＝b＝0u|x＝j,y＝k)
+P(a＝b＝1l|x＝j,y＝k)+P(a＝b＝1u|x＝j,y＝k)；
The sending end and the receiving end select some particles to calculate conditional probability P (a, b | x, y), judge whether the CHSH inequality is violated, and if the CHSH inequality is violated, the particles distributed to the sending end and the receiving end by Eve are in a super-entangled state; based on a super-entangled state, the sending end and the receiving end share two secure keys 0l,0u,1l or 1 u.
It is a further object of the invention to provide a computer program for implementing said device-independent high channel capacity quantum communication method.
Another object of the present invention is to provide an information processing terminal loaded with the computer program.
It is another object of the present invention to provide a computer-readable storage medium comprising instructions which, when run on a computer, cause the computer to perform the device-independent high channel capacity quantum communication method as described
It is another object of the present invention to provide a device independent high channel capacity quantum communication system, comprising:
the quantum communication model unit is irrelevant to a quantum state preparation source and is used for preparing an entangled quantum state density function model by an eavesdropper under the worst condition; then when a quantum protocol is designed under the quantum state density function description model, non-entangled states are removed according to the principle of violation of Bell inequality, super-entangled states are reserved, and on the basis of super-entangled state communication, an eavesdropper cannot acquire any secret information by controlling a preparation source according to entangled monotonicity and non-super-speed of light principles;
a device-independent quantum communication model unit, the device-independence including preparation source independence and measurement device independence; the method is used for analyzing whether the statistical probability relation between the measurement input result and the measurement output result violates the Bell inequality or not, taking the result as a judgment condition for considering whether the quantum communication has an eavesdropper or not, and constructing a quantum communication model irrelevant to the measurement equipment; the quantum state distributed to the user for communication is in the maximum entangled state, and according to the entangled monodispersity principle and the principle of not exceeding the speed of light, an eavesdropper cannot acquire the secret information of a legal user through a measuring device by any means;
and the device-independent quantum communication model unit with high channel capacity is used for adopting a super-entangled state under multiple degrees of freedom as a quantum carrier and establishing a device-independent super-entangled quantum communication model for dense coding.
Another object of the present invention is to provide an information processing terminal equipped with the quantum communication system having a high channel capacity independent of the above-mentioned devices.
In summary, the advantages and positive effects of the invention are:
the method can prevent (shield) information leakage caused by the fact that the preparation source equipment or the measuring equipment is not trustable (controlled or provided by an eavesdropper), resists common side channel attack loopholes such as 'time displacement attack', 'dead time attack', 'strong light blinding attack' and the like, and provides safe and reliable communication; meanwhile, the channel capacity of the device irrelevant quantum communication is also improved, and the quantum efficiency is improved by 1 time by taking key distribution as an example. Most of the existing quantum communication technologies have the problem of information leakage caused by the fact that a preparation source device or a measuring device is not trusted, and even though a few technologies provide methods for preventing information leakage caused by the fact that the preparation source device or the measuring device is not trusted, the channel capacity cannot be guaranteed, mainly because the method does not consider that the equipment is not trusted and is also a main reason for reducing the channel capacity. At present, the key distribution is carried out by utilizing the prior art, the theoretical value of the quantum efficiency can only reach 0.5 at most, and the theoretical value of the quantum efficiency can reach 1 at most by utilizing the technology provided by the invention.
Aiming at the problem of how to improve the channel capacity (quantum efficiency) of the device-independent quantum communication, the invention adopts the super-entangled state under multiple degrees of freedom as a quantum carrier, establishes a device-independent super-entangled quantum communication model and realizes dense coding. The information quantity which can be transmitted by each particle is calculated and compared with the information quantity in other protocols, and the method provided by the invention is proved to be capable of achieving higher channel capacity (quantum efficiency). The invention completes the distribution of the two-bit device independent key by distributing two particles, and the quantum efficiency reaches 1. If a common entangled state such as Bell state | φ is adopted+>ABAs a quantum carrier, only one device independent key can be distributed by distributing two particles, and the quantum efficiency is only 0.5.
Under the condition that an eavesdropper controls or provides preparation source equipment, mathematical modeling or mathematical description is carried out on the super-entangled Bell state prepared by the preparation source, and aiming at the problem that the preparation source of the quantum state (particularly the entangled state and the super-entangled state) is not trustable, a quantum state density function description model of the entangled state prepared by the eavesdropper under the worst condition is provided, then a quantum communication protocol is designed under the model, the security of quantum communication is analyzed, and the eavesdropper is ensured not to be capable of obtaining secret information by controlling the preparation source.
Drawings
Fig. 1 is a schematic structural diagram of a device-independent high-channel-capacity quantum communication system according to an embodiment of the present invention.
In the figure: 1. a quantum communication model unit unrelated to the quantum state preparation source; 2. a device-independent quantum communication model unit; 3. a device-independent high channel capacity quantum communication model unit.
Fig. 2 is a flow chart of a device-independent high-capacity quantum communication method provided by an embodiment of the invention.
Detailed Description
In order to make the objects, technical solutions and advantages of the present invention more apparent, the present invention is further described in detail with reference to the following embodiments. It should be understood that the specific embodiments described herein are merely illustrative of the invention and are not intended to limit the invention.
The prior art is very insecure in actual communication. Most of the prior art does not consider the potential safety hazard caused by the untrustworthy equipment, and even if a few technologies consider the untrustworthy equipment factors, the problem of low coding efficiency caused by the untrustworthy equipment is not considered.
As shown in fig. 1, the device-independent high-channel-capacity quantum communication system provided by the embodiment of the present invention includes:
the quantum communication model unit 1 is irrelevant to a quantum state preparation source and is used for preparing an entangled quantum state density function model by an eavesdropper under the worst condition; then when a quantum protocol is designed under the quantum state density function description model, non-entangled states are removed according to the principle of violation of Bell inequality, super-entangled states are reserved, and on the basis of super-entangled state communication, an eavesdropper cannot acquire any secret information by controlling a preparation source according to entangled monotonicity and non-super-speed of light principles;
a device-independent quantum communication model unit 2, the device-independence including preparation source independence and measurement device independence; the method is used for analyzing whether the statistical probability relation between the measurement input result and the measurement output result violates the Bell inequality or not, taking the result as a judgment condition for considering whether the quantum communication has an eavesdropper or not, and constructing a quantum communication model irrelevant to the measurement equipment; the quantum state distributed to the user for communication is in the maximum entangled state, and according to the entangled monodispersity principle and the principle of not exceeding the speed of light, an eavesdropper cannot acquire the secret information of a legal user through a measuring device by any means;
and the device-independent quantum communication model unit 3 with high channel capacity is used for adopting a super-entangled state under multiple degrees of freedom as a quantum carrier and establishing a device-independent super-entangled quantum communication model for dense coding.
The invention is further described below with reference to specific assays.
As shown in fig. 2, the device-independent high-capacity quantum communication method provided in the embodiment of the present invention includes:
establishing a quantum communication model irrelevant to a quantum state preparation source: in the worst case, preparing an entangled quantum state density function model by an eavesdropper; then when a quantum protocol is designed under the quantum state density function description model, non-entangled states are removed according to the principle of violation of Bell inequality, super-entangled states are reserved, and on the basis of super-entangled state communication, an eavesdropper cannot acquire any secret information by controlling a preparation source according to entangled monotonicity and non-super-speed of light principles;
establishing a quantum communication model independent of equipment: the device independence comprises preparation source independence and measurement device independence; only analyzing whether the statistical probability relation between the measurement input result and the measurement output result violates the Bell inequality, taking the result as a judgment condition for considering whether an eavesdropper exists in the quantum communication, and constructing a quantum communication model unrelated to the measurement equipment; the quantum state distributed to the user for communication is in the maximum entangled state, and according to the entangled monodispersity principle and the principle of not exceeding the speed of light, an eavesdropper cannot acquire the secret information of a legal user through a measuring device by any means;
establishing a high-channel capacity quantum communication model independent of equipment: and a super-entangled state under multiple degrees of freedom is used as a quantum carrier, and an equipment-independent super-entangled quantum communication model is established for carrying out dense coding.
(1) Establishing a quantum communication model irrelevant to a quantum state preparation source, wherein the functional principle is as follows:
aiming at the problem that a preparation source of a quantum state (particularly an entangled state) is not trusted, a quantum state density function description model of the entangled state is prepared by an eavesdropper under the worst condition is constructed, then a quantum communication protocol is designed under the model, the security of quantum communication is analyzed, and the eavesdropper is guaranteed not to be capable of obtaining secret information by controlling the preparation source.
Super-entangled Bell state with one degree of freedom of polarization state and one degree of freedom of path mode
For example, assuming that an eavesdropper Eve prepares the entangled state and then distributes the entangled state to a transmitting end (Alice) and a receiving end (Bob) for further communication, in order to obtain secret information of the transmitting end and the receiving end as much as possible, Eve will not prepare a perfect super-entangled Bell state, and conversely, Eve prepares a mixed state of the super-entangled state and the non-entangled state as much as possible, so that the transmitting end and the receiving end can be confused to avoid finding out eavesdropping behaviors of themselves, and can help themselves obtain the secret information of the transmitting end and the receiving end. The invention can represent the super-entangled Bell states that Eve may produce with the following density function model:
the density function represents: the Eve prepared state is a super-entangled state
And a mixed state of non-entangled state I/4, in which a super-entangled state is present
Has a visibility of p and a visibility of 1-p in the non-entangled state I/4. According to the principle of monodentation of entanglement, if Eve prepares the entangled state (including hyper-entanglement)Entangled state), he will not be able to obtain any secret information of the sender and receiver, whereas if Eve prepares a non-entangled state, he can obtain partial secret information of the sender and receiver. For the transmitting end and the receiving end, the transmitting end and the receiving end can accept the original signals by considering the influence of various possible noises in the channel
The state changes into a state due to the influence of noise
If the invention eliminates the non-entangled state according to the principle of the violation of the Bell inequality in communication, reserves the super-entangled state, and is based on the super-entangled state communication, Eve cannot acquire any secret information of the transmitting end and the receiving end according to the principle of entangled singleness and non-super speed of light.
Therefore, if a quantum carrier used for communication is described as a quantum state density function model prepared by an eavesdropper (in the worst case), then when a quantum protocol is designed, non-entangled states are removed according to the violation principle of Bell inequality, super-entangled states are reserved, and based on super-entangled state communication, the eavesdropper can be ensured not to obtain any secret information by controlling a preparation source according to the principle of entangled monodentation and non-super-speed of light.
(2) Establishing a quantum communication model independent of equipment (including preparation source independence and measurement equipment independence), and realizing a functional principle:
on the basis of independence of a preparation source, the problem that a measuring device is untrustworthy is shielded, a device-independent (including independence of the preparation source and independence of the measuring device) quantum communication model is established, internal implementation and operation details of the measuring device are not considered (namely, the measuring device is treated as a black box), whether a statistical probability relation between a measurement input result and a measurement output result violates a Bell inequality is observed only, the statistical probability relation is used as a judgment condition for considering whether an eavesdropper exists in quantum communication or not, the quantum communication model which is irrelevant to the measuring device is established, and quantum states which are distributed to users for communication are guaranteed to be in a maximum entangled state (non-local relation), so that the eavesdropper cannot acquire secret information of a legal user through the measuring device by any means according to an entangled monodispersity principle and a non-over-speed principle.
Eve sends A particles to the sending end and B particles to the receiving end. The transmitting end and the receiving end respectively randomly select measurement input x and y epsilon {0,1} to measure respective particles, wherein x is 0 to indicate that Z is firstSBase measurement of ZPBase measurement, x ═ 1 denotes Z firstSBase measurement of XPBase measurement; wherein y-0 denotes first ZSBase measurement
Base measurement, y ═ 1 denotes Z firstSBase measurement
And (4) base measurement. The measurement results of the transmitting end and the receiving end are respectively expressed as a and b e {0l,0u,1l,1u }.
Definitions of the CHSH inequality
P(a0＝b0)+P(a0＝b1)+P(a1＝b0)+P(a1≠b1) Less than or equal to 3, wherein
P(aj＝bk)＝P(a＝b＝0l|x＝j,y＝k)+P(a＝b＝0u|x＝j,y＝k)
+P(a＝b＝1l|x＝j,y＝k)+P(a＝b＝1u|x＝j,y＝k)。
The sending end and the receiving end select some particles to calculate the conditional probability P (a, b | x, y), judge whether the CHSH inequality is violated, and if the CHSH inequality is violated, the particles distributed to the sending end and the receiving end by Eve are in a super-entangled state.
(3) And establishing a high-channel capacity quantum communication model independent of the equipment.
Aiming at the problem of how to improve the channel capacity (quantum efficiency) of the device-independent quantum communication, the super-entangled state under multiple degrees of freedom is adopted as a quantum carrier, and a device-independent super-entangled quantum communication model is established to realize dense coding. The information quantity which can be transmitted by each particle is calculated and compared with the information quantity in other protocols, and the method provided by the invention is proved to be capable of achieving higher channel capacity (quantum efficiency).
On the basis of establishing a quantum communication model irrelevant to a quantum state preparation source and establishing a quantum communication model irrelevant to equipment (including preparation source irrelevant and measuring equipment irrelevant), a sending end and a receiving end can share a two-bit security key 0l,0u,1l or 1u based on a super-entangled state. It is apparent that in the above-described key distribution process, if the particles for CHSH inequality detection are removed, the distribution of the two-bit device independent key is completed by distributing two particles, and the quantum efficiency reaches 1. If a common entangled state such as Bell state | φ is adopted+>ABAs a quantum carrier, only one device independent key can be distributed by distributing two particles, and the quantum efficiency is only 0.5.
In the device-independent high-capacity quantum communication method provided by the embodiment of the invention, the super-entanglement is a state of simultaneously entangling at a plurality of degrees of freedom. Photons have a plurality of quantum degrees of freedom, each of which, under the appropriate conditions, has the possibility of defining a qubit, and in theory these different degrees of freedom can also form entanglements, so-called superentanglements. For example: two degrees of freedom of a photon can be entangled with two degrees of freedom of another photon at the same time, so that one photon can be treated as two qubits.
The super-entangled Bell states for one polarization state degree of freedom and path mode degree of freedom can be described as:
where |0> and |1> represent the horizontal and vertical polarization states, respectively, of the photon. The subscripts a and B represent the two photons in the super-entangled state, respectively. l and u represent different path modes of photons a and B. The subscript P represents the polarization state degree of freedom and the subscript S represents the path mode degree of freedom. An ultraviolet light pump pulse passing through a barium borate beta crystal (BBO) will generate correlated photon pairs in mode u; after reflection, the second time passes through the crystal, and then the correlated photon pairs are generated in the mode l.
For a two-photon super-entangled Bell-state quantum system with one polarization state degree of freedom and one path mode degree of freedom, 16 Bell states exist, which can be expressed as:
wherein | Θ>PRepresents one of four Bell states in the freedom of polarization:
wherein | xi>SRepresents one of four Bell states in the path mode degree of freedom:
with CHBSA, 16 super-entangled Bell states can be completely distinguished.
Two non-orthogonal measurement bases in the polarization state freedom can be chosen as: zP＝{|0>,|1>And
two non-orthogonal measurement bases in the path mode degree of freedom can be selected as: zS＝{|l>,|u>And
super-entangled state with two degrees of freedom of polarization state and path mode
For example. Eve prepares the quantum state:
wherein
Represents: the Eve prepared state is a super-entangled state
(i.e., non-local relationship) and a mixed state of non-entangled state I/4 (i.e., local relationship) in which the super-entangled state is present
Has a visibility of p and a visibility of 1-p in the non-entangled state I/4.
The invention is further described below in connection with key distribution as an example.
The invention takes key distribution as an example to illustrate the process of communication by using a super-entangled state under the condition of no equipment dependence, and proves that the channel capacity (quantum efficiency) is effectively improved. Eve sends A particles to the sending end and B particles to the receiving end. The transmitting end and the receiving end respectively randomly select measurement input x and y epsilon {0,1} to measure respective particles, wherein x is 0 to indicate that Z is firstSBase measurement of ZPBase measurement, x ═ 1 denotes Z firstSBase measurement of XPBase measurement; wherein y-0 denotes first ZSBase measurement
Base measurement, y ═ 1 denotes Z firstSBase measurement
And (4) base measurement. Measurement of transmitting and receiving endsThe results are expressed as a and b ∈ {0l,0u,1l,1u }, respectively.
Definitions of the CHSH inequality
P(a0＝b0)+P(a0＝b1)+P(a1＝b0)+P(a1≠b1) Less than or equal to 3, wherein
P(aj＝bk)＝P(a＝b＝0l|x＝j,y＝k)+P(a＝b＝0u|x＝j,y＝k)
+P(a＝b＝1l|x＝j,y＝k)+P(a＝b＝1u|x＝j,y＝k)。
The sending end and the receiving end select some particles to calculate the conditional probability P (a, b | x, y), judge whether the CHSH inequality is violated, and if the CHSH inequality is violated, the particles distributed to the sending end and the receiving end by Eve are in a super-entangled state. At this time, based on a super-entangled state, the sending end and the receiving end can share two secure keys 0l,0u,1l or 1 u.
The invention proves that by adopting the communication mode, the quantum efficiency higher than that of the common entangled state can be obtained by using the key irrelevant to the super-entangled state distribution equipment. Obviously, in the key distribution process, if the particles used for CHSH inequality detection are removed, the invention completes the distribution of the two-bit device independent key by distributing two particles, and the quantum efficiency reaches 1. If a common entangled state such as Bell state | φ is adopted+>ABAs a quantum carrier, only one device independent key can be distributed by distributing two particles, and the quantum efficiency is only 0.5.
In the above embodiments, the implementation may be wholly or partially realized by software, hardware, firmware, or any combination thereof. When used in whole or in part, can be implemented in a computer program product that includes one or more computer instructions. When loaded or executed on a computer, cause the flow or functions according to embodiments of the invention to occur, in whole or in part. The computer may be a general purpose computer, a special purpose computer, a network of computers, or other programmable device. The computer instructions may be stored in a computer readable storage medium or transmitted from one computer readable storage medium to another, for example, the computer instructions may be transmitted from one website site, computer, server, or data center to another website site, computer, server, or data center via wire (e.g., coaxial cable, fiber optic, Digital Subscriber Line (DSL), or wireless (e.g., infrared, wireless, microwave, etc.)). The computer-readable storage medium can be any available medium that can be accessed by a computer or a data storage device, such as a server, a data center, etc., that includes one or more of the available media. The usable medium may be a magnetic medium (e.g., floppy Disk, hard Disk, magnetic tape), an optical medium (e.g., DVD), or a semiconductor medium (e.g., Solid State Disk (SSD)), among others.
The above description is only for the purpose of illustrating the preferred embodiments of the present invention and is not to be construed as limiting the invention, and any modifications, equivalents and improvements made within the spirit and principle of the present invention are intended to be included within the scope of the present invention.
Claims (5)
1. A device independent high channel capacity quantum communication method, characterized in that the device independent high channel capacity quantum communication method comprises:
establishing a quantum communication model irrelevant to a quantum state preparation source: in the worst case, preparing an entangled quantum state density function model by an eavesdropper; then when a quantum protocol is designed under the quantum state density function model, non-entangled states are removed according to the principle of violation of Bell inequality, super-entangled states are reserved, and on the basis of super-entangled state communication, an eavesdropper cannot acquire any secret information by controlling a preparation source according to entangled monotonicity and non-super-speed of light principles;
establishing a quantum communication model independent of equipment: the device independence comprises preparation source independence and measurement device independence; only analyzing whether the statistical probability relation between the measurement input result and the measurement output result violates the Bell inequality, taking the result as a judgment condition for considering whether an eavesdropper exists in the quantum communication, and constructing a quantum communication model unrelated to the measurement equipment; the quantum state distributed to the user for communication is in the maximum entangled state, and according to the entangled monodispersity principle and the principle of not exceeding the speed of light, an eavesdropper cannot acquire the secret information of a legal user through a measuring device by any means;
establishing a high-channel capacity quantum communication model independent of equipment: adopting a super-entangled state under multiple degrees of freedom as a quantum carrier, and establishing an equipment-independent super-entangled quantum communication model for dense coding;
the establishment of the quantum communication model irrelevant to the quantum state preparation source comprises the following steps: assuming that the entangled state is prepared by an eavesdropper Eve and then distributed to a sending end and a receiving end for the next communication; an eavesdropper Eve acquires secret information of a transmitting end and a receiving end as much as possible, and the Eve does not prepare a perfect super-entangled Bell state; on the contrary, an eavesdropper Eve prepares a mixed state of a super-entangled state and a non-entangled state, and confuses a sending end and a receiving end to ensure that the sending end and the receiving end do not find the eavesdropping behavior of the sending end and the receiving end and acquire the secret information of the sending end and the receiving end;
the super-entangled Bell state prepared by the eavesdropper Eve is represented by the following density function model of the quantum state density function:
the density function model represents: the state prepared by the eavesdropper Eve is a super-entangled state
And a mixed state of non-entangled state I/4, in which a super-entangled state is present
The visibility of (a) is p, and the visibility of the non-entangled state I/4 is 1-p;
according to the principle of entanglement monodispersity, if an eavesdropper Eve prepares an entangled state, any secret information of a sending end and a receiving end cannot be acquired; if the eavesdropper Eve prepares the non-entangled state, acquiring partial secret information of the sending end and the receiving end;
the sending end and the receiving end receive the original influence of various possible noises in the channel when analyzing the influence of various possible noises in the channel
Is transformed into
If the non-entangled state is removed according to the principle of violation of Bell inequality in communication, the super-entangled state is reserved, and based on the super-entangled state communication, an eavesdropper Eve cannot acquire any secret information of a transmitting end and a receiving end according to the principle of entanglement unicity and non-super speed of light;
wherein:
is a representation of the super-entangled Bell state in one degree of freedom of polarization state and one degree of freedom of path mode, where |0>And |1>Respectively representing the horizontal polarization state and the vertical polarization state of the photon; subscripts A and B respectively represent two photons in a super-entangled state, l and u represent different path modes of the photons A and B, subscript P represents a polarization state degree of freedom, subscript S represents a path mode degree of freedom, and an ultraviolet light pump pulse passing through a barium borate beta crystal BBO generates a photon pair which is correlated with each other in the mode u; after being reflected, the crystal passes through the crystal for the second time and generates mutually related photon pairs in a mode I; the
The meaning of the formula is: the probability of two particles A and B having 1/2 in the polarization state degree of freedom is at |00>The states, namely: a particle |0>State, B particle also |0>State, 1/2, has a probability of |11>The states, namely: a particle |1>State, B particle also |1>State; in the path mode degree of freedom, the probability that two particles A and B have 1/2 is in the mode | ll>Namely: both A and B particles are in mode | l>1/2 is in mode | uu>Namely: both A and B particles are in mode | u>；
And
in contrast to this, the present invention is,
is a super-entangled Bell state, is expressed by a vector or a matrix,
is a vector
Complex conjugate transpose;
is in a super-entangled Bell state
Is represented by a matrix of densities of (a),
p in (1) indicates that the currently described state has a probability that p is in the state
In the above-mentioned manner,
a, B density matrix expression of two particles in the freedom degree of polarization state and the freedom degree of path mode, which means: they have a probability p of being in the density matrix
The probability of the state represented, remaining (1-p) is in the density matrix
The state of (a), wherein I represents a unit array;
the establishing of the quantum communication model independent of the device comprises the following steps:
if the eavesdropper Eve sends the A particles to the sending end, and the B particles are sent to the receiving end; the transmitting end and the receiving end respectively randomly select measurement input x and y epsilon {0,1} to measure respective particles, wherein x is 0 to represent Z firstSBase measurement of ZPBase measurement, x ═ 1 denotes Z firstSBase measurement of XPBase measurement; wherein y-0 denotes first ZSBase measurement
Base measurement, y ═ 1 denotes Z firstSBase measurement
Base measurement;
the measurement results of the sending end and the receiving end are respectively expressed as a and b belonging to {0l,0u,1l,1u };
definitions of the CHSH inequality
P(a0＝b0)+P(a0＝b1)+P(a1＝b0)+P(a1≠b1) Less than or equal to 3, wherein
P(aj＝bk)＝P(a＝b＝0l|x＝j,y＝k)+P(a＝b＝0u|x＝j,y＝k)
+P(a＝b＝1l|x＝j,y＝k)+P(a＝b＝1u|x＝j,y＝k)；
The sending end and the receiving end select some particles to calculate conditional probability P (a, b | x, y), and judge whether the CHSH inequality is violated, if the CHSH inequality is violated, the particles distributed to the sending end and the receiving end by an eavesdropper Eve are in a super-entangled state; wherein: zSRefers to the Z radical in the path mode degree of freedom, ZS＝{|l>,|u>}；ZPRefers to the Z radical in the degree of freedom of the polarization state, ZP＝{|0>,|1>"the measurement results of the sending end and the receiving end are respectively expressed as a and B ∈ {0l,0u,1l,1u }", 0l means that the measurement results of the particles A and B are | l under the path mode degree of freedom>State, degree of freedom of polarization |0>State; 0u refers to | u in the degree of freedom of the path mode>State, degree of freedom of polarization |0>State; 1l refers to | l in the degree of freedom of the path mode>State, degree of freedom of polarization |1>State; 1u refers to | u in the degree of freedom of the path mode>State, degree of freedom of polarization |1>State; p (a)j＝bk) J is a value of x, k is a value of y, x and y respectively represent measurement bases selected by a transmitting end and a receiving end, P (a ═ B ═ 0l | x ═ j, y ═ k) represents a probability function, and P (a ═ B ═ 0l | x ═ j, y ═ k) + P (a ═ B ═ 0u | x ═ j, y ═ k) represents a value of y, P (…) represents a probability function, and k is a value of yj＝bk) The probability that the measurement results of the transmitting end and the receiving end are the same when the value of x is j and the value of y is k is represented, P (… | …) is a conditional probability function, and P (a ═ b ═ 0l | x ═ j, y ═ k) represents the probability that the measurement results of the transmitting end and the receiving end are both 0l when the value of x is j and the value of y is k; p (a ═ b ═ 0 | x ═ j, y ═ k) denotes the probability that the measurement results at the transmitting end and the receiving end are both 0u when the value of x is j and the value of y is k, and P (a ═ b ═ 0 | x ═ j, y ═ k) (a ═ b ═ denotes the probability that the measurement results at both the transmitting end and the receiving end are0＝b0) Denotes the probability that the measurement results of the transmitting end and the receiving end are the same when x is 0 and y is also 0, wherein x-0 denotes ZSBase measurement of ZPBase measurement, x ═ 1 denotes Z firstSBase measurement of XPBase measurement; wherein y-0 denotes first ZSBase measurement
Base measurement, y ═ 1 denotes Z firstSBase measurement
Base measurement; p (a)0＝b1) When x is 0 and y is 1, the probability that the measurement results of the sending end and the receiving end are the same is shown; p (a)1≠b1) And the probability that the measurement results of the sending end and the receiving end are different when x is 1 and y is 1 is shown.
2. A key distribution method of the device-independent high channel capacity quantum communication method of claim 1, wherein the key distribution method comprises:
eve sends the A particles to a sending end, and the B particles to a receiving end; the transmitting end and the receiving end respectively randomly select measurement input x and y epsilon {0,1} to measure respective particles, wherein x is 0 to indicate that Z is firstSBase measurement of ZPBase measurement, x ═ 1 denotes Z firstSBase measurement of XPBase measurement; wherein y-0 denotes first ZSBase measurement
Base measurement, y ═ 1 denotes Z firstSBase measurement
Base measurement; the measurement results of the sending end and the receiving end are respectively expressed as a and b belonging to {0l,0u,1l,1u };
definitions of the CHSH inequality
P(a0＝b0)+P(a0＝b1)+P(a1＝b0)+P(a1≠b1) Less than or equal to 3, wherein
P(aj＝bk)＝P(a＝b＝0l|x＝j,y＝k)+P(a＝b＝0u|x＝j,y＝k)+P(a＝b＝1l|x＝j,y＝k)+P(a＝b＝1u|x＝j,y＝k)；
The sending end and the receiving end select some particles to calculate conditional probability P (a, b | x, y), judge whether the CHSH inequality is violated, and if the CHSH inequality is violated, the particles distributed to the sending end and the receiving end by Eve are in a super-entangled state; based on a super-entangled state, the sending end and the receiving end share two secure keys 0l,0u,1l or 1 u.
3. A computer-readable storage medium comprising instructions that, when executed on a computer, cause the computer to perform the device-independent high channel capacity quantum communication method of claims 1-2.
4. A device-independent high channel capacity quantum communication system of the device-independent high channel capacity quantum communication method of claim 1, wherein the device-independent high channel capacity quantum communication system comprises:
the quantum communication model unit is irrelevant to a quantum state preparation source and is used for preparing an entangled quantum state density function model by an eavesdropper under the worst condition; then when a quantum protocol is designed under the quantum state density function model, non-entangled states are removed according to the principle of violation of Bell inequality, super-entangled states are reserved, and on the basis of super-entangled state communication, an eavesdropper cannot acquire any secret information by controlling a preparation source according to entangled monotonicity and non-super-speed of light principles;
a device-independent quantum communication model unit, the device-independence including preparation source independence and measurement device independence; the method is used for analyzing whether the statistical probability relation between the measurement input result and the measurement output result violates the Bell inequality or not, taking the result as a judgment condition for considering whether the quantum communication has an eavesdropper or not, and constructing a quantum communication model irrelevant to the measurement equipment; the quantum state distributed to the user for communication is in the maximum entangled state, and according to the entangled monodispersity principle and the principle of not exceeding the speed of light, an eavesdropper cannot acquire the secret information of a legal user through a measuring device by any means;
and the device-independent quantum communication model unit with high channel capacity is used for adopting a super-entangled state under multiple degrees of freedom as a quantum carrier and establishing a device-independent super-entangled quantum communication model for dense coding.
5. An information processing terminal incorporating a high channel capacity quantum communication system independent of the device of claim 4.
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