arXiv subjects

Cheng Zu Li

Publications and source records attributed to Cheng Zu Li.

4 recordsLinked to original sources

arXiv2004

A Geometric Diagram of Separable States

This paper present a geometric diagram of a separable state: If a mixed state $σ$ is separable, there are $2^{nS(σ)}$ linearly independant product vectors which span the same Hilbert space as the $2^{nS(σ)}$ ``likely'' strings of $σ^{\otimes n}$ do. This diagram results in a criterion for separability which is strictly stronger than the inorder criterion in [M.A. Nielsen and J. Kempe, Phys. Rev. Lett. 86, 5184 (2001)]. This means that the number of product bases of states of a system has close link to the nonlocality of the system.

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arXiv2003

Distinguishing a set of full product bases needs only projective measurements and classical communication

Nonlocality without entanglement is an interesting field. A manifestation of quantum nonlocality without entanglement is the local indistinguishability of a set of orthogonal product states. In this paper we analyze the character of operators to distinguish a set of full product bases in a multi-partite system, and show that distinguishing perfectly a set of full product bases needs only local projective measurements and classical communication, and these measurements cannot damage each product basis. Employing these conclusions one can discuss local distinguishability of full product bases easily. Finally we discuss the generalization of these results to the locally distinguishability of a set of incomplete product bases.

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arXiv2003

Orthogonality And Distinguishability: Criterion For Local Distinguishability of Arbitrary Orthogonal States

We consider deeply the relation between the orthogonality and the distinguishability of a set of arbitrary states (including multi-partite states). It is shown that if a set of arbitrary states can be distinguished by local operations and classical communication (LOCC), \QTR{it}{\}each of the states can be written as a linear combination of product vectors such that all product vectors of one of the states are orthogonal to the other states. With this result we then prove a simple necessary condition for LOCC distinguishability of a class of orthogonal states. These conclusions may be useful in discussing the distinguishability of orthogonal quantum states further, understanding the essence of nonlocality and discussing the distillation of entanglement.

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arXiv2003

Distilling multipartite pure states from a finite number of copies of multipartite mixed states

This paper will address the question of the distillation of entanglement from a finite number of multi-partite mixed states. It is shown that if one can distill a pure entangled state from n copies of a mixed state $σ_{ABC...}$ there must be at least a subspace in whole Hilbert space of the all copies such that the projection of $σ_{ABC...}^{\otimes n}$ onto the subspace is a pure entangled state. We also show that the purification of entanglement or distillation of entanglement can be carried out by local joint projective measurements with the help of classical communication and local general positive operator valued measurements on a single particle, in principle. Finally we discuss experimental realizability of the entanglement purification.

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