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Quantum Information Processing

Optimal probabilistic cloning of two linearly independent states with arbitrary probability distribution

Wen Zhang, Pinshu Rui, Ziyun Zhang, Yan-Lin Liao

Published Dec 10, 2015• 4 citations
Publisher
DOI
10.1007/s11128-015-1170-2

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From Ref. [Phys. Rev. Lett. 80(1998)4999] one knows that the quantum states secretly chosen from a certain set can be probabilistically cloned with positive cloning efficiencies if and only if all the states in the set are linearly independent. In this paper, we focus on the probabilistic quantum cloning (PQC) of linearly dependent states with nonnegative cloning efficiencies. We show that a linearly independent subset of the linearly dependent quantum states can be probabilistically cloned if and only if any one state in the subset can not be expressed as the linear superposition of the other states in the set. The optimal possible cloning efficiencies are also investigated.
We study the 1→ N faithful telecloning of two linear-independent states of a one-qubit system. Based on the analysis of the probabilistic cloning machine, we construct a multiparticle entangled state, and present a telecloning scheme under local operations and classical communication (LOCC). The success probability is greater than half of the optimal probability of the probabilistic cloning machine. Specifically, we show how to prepare the three-particle entangled state needed by 1→2 telecloning under LOCC using the Greenberger-Horne-Zeilinger state as a resource. All the operations in 1→2 telecloning are within the reach of current technology.
We study the 1→N faithful telecloning of two linear-independent states of a one-qubit system.Based on the analysis of the probabilistic cloning machine,we construct a multiparticle entangled state,and present a telecloning scheme under local operations and classical communication (LOCC).The success probability is greater than half of the optimal probability of the probabilistic cloning machine.Specifically,we show how to prepare the three-particle entangled state meeded by 1→2 telecloning under LOCC using the Greenberger-Horne-Zeilinger state as a resource.All the operations in 1→2 telecloning are within the reach of current technology.