Existence and construction of simultaneous cloning machines for mixed states

Autor: Shixian Qu, Zhihua Guo, Huaixin Cao
Rok vydání: 2014
Předmět:
Zdroj: Science China Physics, Mechanics & Astronomy. 58:1-5
ISSN: 1869-1927
1674-7348
DOI: 10.1007/s11433-014-5619-6
Popis: 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 Mn ⊗ Mn and a state Σ in Mn, such that Φ(ρi ⊗ Σ) = 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.
Databáze: OpenAIRE
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