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 qua...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.展开更多
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)+1 种基金the China Postdoctoral Science Foundation(Grant No.2014M552405)the Natural Science Basic Research Plan in Shaanxi Province of China(Grant No.2014JQ1010)
文摘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.
