Existence and construction of simultaneous cloning machines for mixed states

GUO ZhiHua 已出版文章查询
GUO ZhiHua
1 2 CAO HuaiXin 已出版文章查询
CAO HuaiXin
1 * QU ShiXian 已出版文章查询
QU ShiXian

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1College of Mathematics and Information Science Shaanxi Normal University Xi'an 710062 China

2 College of Physics and Information Technology Shaanxi Normal University Xi'an 710062 China

3College of Physics and Information Technology Shaanxi Normal University Xi'an 710062 China

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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 ρ1, ρ2,..., ρk of the n-dimensional quantum system Cn can be cloned simultaneously, that is, there exists a quantum channel Φ on MnMn and a state ∑ in Mn, such that Φ (ρi ⊗ ∑) = ρiρi for all i, if and only if ρiρj= 0 (i≠j). Also, the constructing procedure of the desired simultaneous cloning machine is given.

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DOI: http://dx.doi.org/10.1007/s11433-014-5619-6

语种: 英文   

基金This work was supported by the National Natural Science Fo...

关键词simultaneous cloning machine quantum channel mixed state

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