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Chinese Physics Letters

Class of Unlockable Bound Entangled States and Their Applications

刁大生, 张成杰, 张永生, 郭光灿

Published Jan 1, 2008• 0 citations
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Abstract

一个班开有能力的界限纠缠的状态和他们的应用被介绍。当伪概括了 Smolin 状态，他们能被考虑[Phys。加快。一 63 (2001 ) 032306 ] ，它是 N + N qubits 的状态。没有纯纠纷能被本地量操作和古典通讯从状态的这个班提取。然而，如果某些聚会一起组织，他们变得可由蒸馏而得。尽管他们是，纠缠的界限说，他们能被用来完成一些重要任务，例如量，秘密分享出现在学习。

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一个班开有能力的界限纠缠的状态和他们的应用被介绍。当伪概括了 Smolin 状态，他们能被考虑[Phys。加快。一 63 (2001 ) 032306 ] ，它是 N + N qubits 的状态。没有纯纠纷能被本地量操作和古典通讯从状态的这个班提取。然而，如果某些聚会一起组织，他们变得可由蒸馏而得。尽管他们是，纠缠的界限说，他们能被用来完成一些重要任务，例如量，秘密分享出现在学习。
A class of unlockable bound entangled states and their applications are presented. They can be considered as quasi generalized Smolin states [Phys. Rev. A 63 (2001) 032306], which are the states of N + N qubits. No pure entanglement can be distilled from this class of states by local quantum operations and classical communications. However, if certain parties group together, they become distillable. Although they are bound entangled states, they could be used to achieve some non-trivial tasks, such as quantum secret sharing shown in the study.
We find an interesting relationship between multipartite bound entangled states and the stabilizer formalism. We prove that, if a set of commuting operators from the generalized Pauli group on nnn qudits satisfy certain constraints, then the maximally mixed state over the subspace stabilized by them is an unlockable bound entangled state. Moreover, the properties of this state, such as symmetry under permutations of parties, undistillability, and unlockability, can be easily explained from the stabilizer formalism without tedious calculation. In particular, the four-qubit Smolin state [Smolin, Phys. Rev. A 63, 032306 (2001)] and its recent generalization to even numbers of qubits [Bandyopadhyay et al., Phys. Rev. A 71, 062317 (2005); Augusiak et al., ibid 73, 012318 (2006)] can be viewed as special examples of our results. Finally, we extend our results to arbitrary multipartite systems in which the dimensions of all parties may be different.
For efficient quantum information processing (QIP), pure and strong entanglement in qubits has been thought to be indispensable.However, it was recently pointed out that bound entangled states, which involve undistillable entanglement between qubits, also have great potential for QIP.In this paper, we report the efficient generation of a four-qubit bound entangled state referred to as the Smolin state using photon polarization qubits.We observed the unlockable bound entanglement which is the specific property of the Smolin state.