χ 型纠缠相干态的产生及贝尔型不等式的研.doc
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1、精品论文 型纠缠相干态的产生及贝尔型不等式的研究宋思谕1,2 , 王书浩1,2, 龙桂鲁1,21 清华大学物理学院低维量子物理国家重点实验室,北京1000842 清华大学清华信息科学技术国家实验室,北京100084 摘要:我们提出了一种新的纠缠相干态 - 型纠缠相干态的产生方案。这个过程是通过克尔介 质和线性光学器件来实现的。基于光子对称性测量和光子阈值测量,我们研究了 型纠缠相 干态的量子非局域性。对于贝尔型不等式,它显示出强的违背。 关键词:纠缠相干态,态产生,贝尔型不等式中图分类号: O43Generation of the -type entangled coherent state
2、and violations of Bell-type inequalitySi Yu Song1,2, Shuhao Wang1,2, Gui Lu Long1,21 State Key Laboratory of Low-Dimensional Quantum Physics and Department of Physics, Tsinghua University, Beijing, 1000842 Tsinghua National Laboratory For Information Science and Technology, TsinghuaUniversity, Beiji
3、ng, 100084Abstract: We propose a protocol to generate a new type of state, called the -type entangled coherent state. The process is realized by using one -cross-Kerr medium and linear optical components. The quantum non-locality of the -type entangled coherent state is investigated based on photon-
4、parity and photon-threshold measurements. We show that stronger violations of Bell-type inequality appear in the -type entangled state.Key words: entangled coherent states, state generation, Bell-type inequality0 INTRODUCTIONEntanglement is a key feature in quantum mechanics, which contributes to th
5、e non-local and non-classical behavior of quantum systems. Entanglement has great potential in quantum information processing, including quantum cryptography 1, 2, 3, 4, superdose coding 5, 6, 7,基金项目: National Natural Science Foundation (11175094),National Basic Research Program (2009CB929402), Na-
6、tional Basic Research Program (2011CB9216002), the SRFDP under Grant (20110002110007)作者简介: Song Si Yu(1986-),female,PHD,major research direction:quantum information. Correspondence author:Long Gui Lu (1962-),male,professor,major research direction:quantum information.- 14 -quantum teleportation 8, 9
7、, 10, 11, 12, 18, 19, 20, 17, 22, 13, 14, 21, 16, 15, and quantum computation 28, 23, 24, 25, 26, 27. The Bell inequality was rst proposed in 1964 29, and violations of this inequality can be regard as evidence of entanglement in two-qubit systems 30. The Bell-Merman inequality 31 is the multi-qubit
8、 version of the Bell inequality in Ref. 29. This inequality is based on the assumption that every party is allowed to choose between two measurement settings. The Bell-type inequality for continuous variable entangled states of two-mode electromagnetic elds are given by Banaszek and Wdkiewicz, who s
9、how that such inequality can be obtained through a Wigner distribution function 32. The multi-mode continuous variable states have been thoroughly investigated thereafter 33, 26.Entangled photons are important information carriers. The discrete degree of freedoms of photons, for instance, the polari
10、zation, are typically used for information processing. Such entangled photons can be generated through parametric down conversion. However, another realization of information carriers is facilitated by coherent superposed states (CSSs)|CSSEven/Odd = N (| | ),(1)where the subscript Even/Odd correspon
11、ds to the even and odd CSSs, and N is a normalization21constant equal to N = 2(1 + e2| ) 2 . The encoding method of entangled coherent states(ECSs) 23 using CSSs as qubits is similar to that of entangled discrete photon system. Themethod has the advantage of being robust against decoherence 34, thus
12、 the state has been widely used 18, 19, 20, 22, 21, 23, 24, 25, 26.The coherent states are the eigenstates of the annihilation operator a, i.e., a| = |, where is the eigenvalue corresponding to |, which is complex. The coherent states can beexpressed as |2 n| = e 2 |n = D()|0 (2)n=0 n! with the numb
13、er state is |n = (a)n/n!|0, and the displacement operator isD () =exp(a a). The coherent states | and | are encoded as 0 and 1, respectively, where we assume that is real. Given that |0|1|2 = | |2 = exp(4|2 ), the coherent statesare orthogonal when is suciently large.If the multiples of annihilation
14、 operators are involved in the coherent state, such state is called a multi-mode coherent state. Multi-mode ECSs have several types: the GHZ-type ECS 19, 20, 26, 21, the W-type ECS 22, 26, 35, 36, the cluster-type ECS 37, etc. These ECSs can be constructed by using beam splitters (BSs), phase shifte
15、rs (PSs), and nonlinear Kerr media 26, 37, which have been used in numerous proposed schemes.! # % & $(图 1: Schematic diagram of ECS generation, where BS denotes beamsplitter. (a) Input-outputthrough the -cross-Kerr media; (b) Generation of the GHZ state (| , , , + | 1/2 22 2 2222 , , )/22; (c) Gene
16、ration of the -type ECS, its input state is the outputstate in process (b).|1,2,3,4=N(|, , , |, , , |, , , + |, , , +| , , , + | , , , +| , , , + | , , , )1,2,3,4 ,In this paper, another type of multi-mode ECS, i.e., the -type ECS(3)21where N = 8(1 + e4| ) 2 , is generated by using one -cross-Kerr m
17、edium and linearoptical components. The entanglement performance is investigated based on photon-parityand photon-threshold measurements. The Bell-Mermin inequality 31 is applied to |, suchthat violations appear in the range of small amplitude of .The remainder of this paper is organized as follows:
18、 In Sec. 1, the generation scheme for| is given, and the eciency and the delity are discussed. In Sec. 2, the non-locality of| is discussed by means of the Bell Mermin inequality based upon two measurements. InSec. 3, we give a short summary.1 ENTANGLED STATES GENERATIONTo demonstrate the generation
19、 process of -type ECSs, we rst give a brief review of the interaction between the two-mode elds in a -cross-Kerr medium as well as of the process of generating a GHZ-type four-mode ECS in free-traveling elds from a CSS. When two-modecoherent states |(1)sa and |(1)tn are sent to the -cross-Kerr mediu
20、m (see Fig. 1(a),they become entangled as a result of the interaction between the two modes 40, 41K an|(1)sa|(1)tn = |(1)sa(| + | )n + (1)t|(1)s+1 a(| | )n/2 (4)with s, t 0, 1. The four-mode GHZ-type ECS |GHZ =1 (| , , , 42 2 22 2+ | 2, 2, 2, 2 )1,2,3,4 (5)can be generated by inputting the coherent
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