Existence and construction of simultaneous cloning machines for mixed states  

Existence and construction of simultaneous cloning machines for mixed states

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作  者:GUO ZhiHua CAO HuaiXin QU ShiXian 

机构地区:[1]College of Mathematics and Information Science, Shaanxi Normal University [2]College of Physics and Information Technology, Shaanxi Normal University

出  处:《Science China(Physics,Mechanics & Astronomy)》2015年第4期11-15,共5页中国科学:物理学、力学、天文学(英文版)

基  金:supported by the National Natural Science Foundation of China(Grant Nos.11401359,11371012,11171197 and 11301318);the Fundamental Research Funds for the Central Universities(Grant Nos.GK201402005 and GK201301007);the China Postdoctoral Science Foundation(Grant No.2014M552405);the Natural Science Basic Research Plan in Shaanxi Province of China(Grant No.2014JQ1010)

摘  要:It is a well-known fact that the no-cloning theorem forbids the creation of identical copies of an arbitrary unknown quantum state. In other words, there does not exist a quantum cloning machine that can clone all quantum states. However, it is possible to clone given quantum states under certain conditions, for instance, k distinct pure states |ψ1〉, |ψ2),....,|ψk) can be cloned simultaneously if and only if they are orthogonal. This paper discusses the existence and construction of simultaneous cloning machines for mixed states. It is proved that k distinct mixed states Pl,P2 Pk of the n-dimensional quantum system Cn can be cloned simultaneously, that is, there exists a quantum channel Ф on .Mn ⊙ Mn and a state ∑ in Mn, such that Ф(ρi ⊙∑) = ρi ⊙ ρi for all i, if and only if ρiρj = 0 (i ≠j). Also, the constructing procedure of the desired simultaneous cloning machine is given.It is a well-known fact that the no-cloning theorem forbids the creation of identical copies of an arbitrary unknown quantum state.In other words,there does not exist a quantum cloning machine that can clone all quantum states.However,it is possible to clone given quantum states under certain conditions,for instance,k distinct pure states|ψ1,|ψ2,...,|ψk can be cloned simultaneously if and only if they are orthogonal.This paper discusses the existence and construction of simultaneous cloning machines for mixed states.It is proved that k distinct mixed statesρ1,ρ2,...,ρkof the n-dimensional quantum system Cncan be cloned simultaneously,that is,there exists a quantum channel Φ on MnMn and a state Σ in Mn,such that Φ(ρiΣ)=ρiρi for all i,if and only ifρiρj=0(i j).Also,the constructing procedure of the desired simultaneous cloning machine is given.

关 键 词:simultaneous cloning machine quantum channel mixed state 

分 类 号:O413.1[理学—理论物理]

 

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