CN110971406B - 一种两光子六量子位超纠缠Bell态并发度测量方法 - Google Patents
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Abstract
本发明公开了一种两光子六量子位超纠缠Bell态并发度测量方法,具体步骤如下:S1:构造两光子六量子位超纠缠Bell态,将超纠缠Bell态作为输入;S2:对超纠缠Bell态并发度进行测量:超纠缠Bell态在两个纵向动量和偏振组成的三个自由度中被编码,使用由弱交叉克尔非线性、分束器和偏振分束器来构造的QND测量,对超纠缠Bell态的第一纵向动量自由度、第二纵向动量自由度以及偏振自由度进行独立地测量。本发明的超纠缠Bell态并发度的测量方法,对不同纠缠态之间的纠缠程度的差别给出更具体直观的比较;仅需要交叉克尔非线性来构建QND测量,不需要精密、复杂的CNOT门操作,在很大程度上降低了实验的复杂度,对未来信息处理打下很好的基础。
Description
技术领域
本发明涉及量子信息处理领域,特别涉及一种两光子六量子位超纠缠Bell态并发度测量方法。
背景技术
量子纠缠作为几乎不可缺少的关键资源,在过去几十年里,已经在量子通信和量子计算中得到广泛应用,例如量子隐性传态、量子密钥分发、量子密集编码、量子密钥共享、量子安全直接通信,在现阶段,许多量子物理模型被用于量子信息处理QIP方面,其中光子成为了有力的竞争者,主要是光子的多个自由度能携带量子信息,如偏振、空间模式、时间片段等,并且这些纠缠态也被证实在实验中成功产生。
在许多量子信息处理的方案中,需要部分纠缠态和最大纠缠态,因此许多确定纠缠度的协议被提出,如部分熵纠缠度、相对熵纠缠度、生成纠缠度、负值度、几何纠缠度、纠缠并发度、Three-tangle,其中生成纠缠度由Bennett等人提出:对于两个量子纯态|Ψ>,纠缠程度通过并发度来量化[Charles H.Bennett,David P.DiVincenzo,John A.Smolin,andWilliam K.Wootters.Mixed-state entanglement and quantum errorcorrection.Phys.Rev.A,54:3824–3851,Nov 1996]。
Walborn等人报道了两光子纠缠纯态并发度直接测量的实验,利用光子的两个自由度的超纠缠,测量时只需要用到单光子测量器的局域操作,就可以得到初始纠缠态的纠缠并发度,但在实验中还需要用到光子控制非门(CNOT),使得实验的实现变得更加困难[S.P.Walborn,P.H.Souto Ribeiro,L.Davidovich,F.Mintert,andA.Buchleitner.Experimental determination of entanglement with a singlemeasurement.Nature,440(7087):1022–4,2006];Romero等人提出了两离子纠缠纯态系统的并发度直接测量方案,在方案中需要用到腔模来存储纠缠态,使得方案对于腔的衰减十分敏感[G.Romero,C.E.L′opez,F.Lastra,E.Solano,and J.C.Retamal.Directmeasurement of concurrence for atomic two-qubit pure states.Phys.Rev.A,75:032303,Mar 2007]。
发明内容
发明目的:针对以上问题,本发明目的是提供一种两光子六量子位超纠缠Bell态并发度测量方法,对每个自由度的并发度进行单独的测量,降低实验复杂度。
技术方案:本发明提出了一种两光子六量子位超纠缠Bell态并发度测量方法,具体步骤如下:
S1:构造两光子六量子位超纠缠Bell态,将超纠缠Bell态作为输入;
S2:对超纠缠Bell态并发度进行测量:超纠缠Bell态在两个纵向动量和偏振组成的三个自由度中被编码,使用由弱交叉克尔非线性、分束器和偏振分束器来构造的量子非破坏(QND)测量,对超纠缠Bell态的第一纵向动量自由度、第二纵向动量自由度以及偏振自由度进行独立地测量。
所述步骤S1中超纠缠Bell态为部分纠缠态或任意纠缠态,进一步,当为部分纠缠态时,满足下列关系式:
其中两光子分别分配给Alice和Bob,6个参数满足归一化条件:
|α1|2+|β1|2=1 (2)
|α2|2+|β2|2=1 (3)
|α3|2+|β3|2=1 (4)
进一步,所述步骤S1中超纠缠Bell态为任意纠缠态时,满足下列关系式:
其中12个参数满足归一化条件:
|α1|2+|β1|2+|γ1|2+|δ1|2=1 (6)
|α2|2+|β2|2+|γ2|2+|δ2|2=1 (7)
|α3|2+|β3|2+|γ3|2+|δ3|2=1 (8)
其中下角标P为偏振纠缠,F为第一纵向动量自由度纠缠,S为第二纵向动量自由度纠缠,δ、γ分别为各个态出现的概率。
所述步骤S2中三个自由度之间是相互独立的,因此第一纵向动量自由度的测量不会影响偏振自由度和第二纵向动量自由度。
所述步骤S2中第一纵向动量自由度的并发度测量:对于部分纠缠Bell态|Ψ>=α|00>+β|11>,它的并发度为:
C(|Ψ>)=2|αβ| (9)
且满足
|α|2+|β|2=1 (10)
此部分纠缠Bell态通过QND测量从而挑选出相干态没有相移的态,得到并发度为:
所述步骤S2中第二纵向动量自由度的并发度测量:动量自由度r/l和I/E是线性动量,所以第二纵向动量自由度的测量方法与第一纵向动量自由度的方法相同,并发度为:
所述步骤S2中偏振自由度的并发度测量:通过QND测量后,挑选出相干态都有±θ相移的态,得到并发度为:
两光子六量子位部分纠缠Bell态的并发度为:
所述步骤S1超纠缠Bell态为任意纠缠态时,步骤S2中任意纠缠态并发度测量为:在QND基础上进行一个Hadamard门操作,经过计算挑选出需要的态,然后计算需要态纠缠度的并发度,具体为:
第一纵向动量自由度的并发度为:
第二纵向动量自由度的并发度为:
偏振自由度的并发度为:
两光子六量子位任意纠缠Bell态的并发度为:
有益效果:本发明与现有技术相比,其显著优点是:
(1)本发明的超纠缠态并发度的测量,对不同纠缠态之间的纠缠程度的差别给出更具体直观的比较;
(2)依赖于各个自由度之间的相互独立,确保了对每一个自由度的并发度进行单独的测量;
(3)仅需要交叉克尔非线性来构建QND测量,不需要精密、复杂的CNOT门操作,在很大程度上降低了实验的复杂度,对未来信息处理打下很好的基础。
附图说明
图1为本发明超纠缠并发度测量方法流程图;
图2为本发明两光子六量子位超纠缠Bell态的示意图;
图3为本发明部分纠缠态中测量第一纵向动量纠缠的原理示意图;
图4为本发明部分纠缠态中测量第二纵向动量纠缠的原理示意图;
图5为本发明部分纠缠态中测量偏振纠缠的原理示意图;
图6为本发明任意纠缠态中测量动量纠缠的原理示意图。
具体实施方式
如图1,本发明的一种两光子六量子位超纠缠Bell态并发度测量方法,包含如下步骤:
S1:构造两光子六量子位超纠缠Bell态,将超纠缠Bell态作为输入;
S2:对超纠缠Bell态并发度进行测量:超纠缠Bell态在两个纵向动量和偏振组成的三个自由度中被编码,使用由弱交叉克尔非线性、分束器和偏振分束器来构造的量子非破坏(QND)测量,对超纠缠Bell态的第一纵向动量自由度、第二纵向动量自由度以及偏振自由度进行独立地测量。
实施例1:部分纠缠态并发度测量
步骤S1中超纠缠Bell态为部分纠缠态,满足下列关系式:
其中两光子分别分配给Alice和Bob,6个参数满足归一化条件:
|α1|2+|β1|2=1 (2)
|α2|2+|β2|2=1 (3)
|α3|2+|β3|2=1 (4)
如图2,其中H和V为水平偏振和垂直偏振,l、r、I、E为线性动量,α、β分别为各个态出现的概率,下角标A、B为Alice和Bob简写。
从上式中选取相干态没有相移的态,得到:
从式(20)得到|l>A1|r>A2|l>B1|r>B2的概率是PF=|α2β2|2,得到第一纵向动量自由度并发度为:
本发明中超纠缠Bell态的动量自由度是线性的,第二纵向动量纠缠的并发度测量与第一纵向动量纠缠并发度的测量相同,原理如图4所述,第二纵向动量自由度的并发度为:
经过纵向动量纠缠态并发度测量之后,得到的态为:
从式(21)已知每个光子的纵向动量是明确的,通过图5,测量偏振自由度并发度,图5中包括了交叉克尔非线性和偏振分束器(PBS),其中PBS传输|H>偏振光子反射|V>偏振光子,得到:
从式(22)中挑选出相干态都有±θ相移的态,得到:
所以两光子六量子位超纠缠Bell态的并发度为:
实施例2:任意纠缠态并发度测量
任意纠缠态为:
首先测量第一纵向动量自由度的并发度,初始态被写成:
通过图3后挑选出相干态没有相移的态,得到:
概率为P1F=2(|α2β2|2+|γ2δ2|2),如图6所示:每一个分束器BS作用为Hadamard门操作,让B1通过分束器BS1,B2通过分束器BS2,
则|φ>1将变为:
如果相干态的相移为θ1+θ4,得到:
如果相干态的相移为θ2+θ3,得到:
与上述第一纵向动量自由度的并发度原理相同,得到第二纵向动量自由度的并发度为:
偏振自由度的并发度为:
因此任意纠缠态并发度为:
Claims (5)
1.一种两光子六量子位超纠缠Bell态并发度测量方法,其特征在于,具体步骤如下:
S1:构造两光子六量子位超纠缠Bell态,将超纠缠Bell态作为输入;超纠缠Bell态为部分纠缠态或任意纠缠态;
当超纠缠Bell态为部分纠缠态时,满足下列关系式:
其中为初始态,H和V为水平偏振和垂直偏振,l、r、I、E为线性动量,α、β分别为各个态出现的概率,下角标A、B为Alice和Bob简写;两光子分别分配给Alice和Bob,6个参数满足归一化条件:
|α1|2+|β1|2=1 (2)
|α2|2+|β2|2=1 (3)
|α3|2+|β3|2=1 (4)
当超纠缠Bell态为任意纠缠态时,满足下列关系式:
|α1|2+|β1|2+|γ1|2+|δ1|2=1 (6)
|α2|2+|β2|2+|γ2|2+|δ2|2=1 (7)
|α3|2+|β3|2+|γ3|2+|δ3|2=1 (8)
其中下角标P为偏振纠缠,F为第一纵向动量自由度纠缠,S为第二纵向动量自由度纠缠,γ、δ为各个态出现的概率;
S2:对超纠缠Bell态并发度进行测量:超纠缠Bell态在两个纵向动量和偏振组成的三个自由度中被编码,使用由弱交叉克尔非线性、分束器和偏振分束器来构造的量子非破坏测量,对超纠缠Bell态的第一纵向动量自由度、第二纵向动量自由度以及偏振自由度进行独立地测量。
2.根据权利要求1所述的一种两光子六量子位超纠缠Bell态并发度测量方法,其特征在于,所述步骤S2中第一纵向动量自由度的并发度测量:对于部分纠缠Bell态|ψ>=α|00>+β|11>,它的并发度为:C(|ψ>)=2|αβ|且满足|α|2+|β|2=1,此部分纠缠Bell态通过QND测量从而挑选出相干态没有相移的态,得到并发度为:
3.根据权利要求1所述的一种两光子六量子位超纠缠Bell态并发度测量方法,其特征在于,所述步骤S2中第二纵向动量自由度的并发度测量:动量自由度r/l和I/E是线性动量,并发度为:
4.根据权利要求1所述的一种两光子六量子位超纠缠Bell态并发度测量方法,其特征在于,所述步骤S2中偏振自由度的并发度测量:通过QND测量后,挑选出相干态都有±θ相移的态,得到并发度为:
5.根据权利要求1所述的一种两光子六量子位超纠缠Bell态并发度测量方法,其特征在于,所述步骤S1超纠缠Bell态为任意纠缠态时,步骤S2中任意纠缠态并发度测量为:在QND基础上进行一个Hadamard门操作,经过计算挑选出所需要的态,然后计算需要态纠缠度的并发度。
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