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Chinese Physics Letters

Class of Unlockable Bound Entangled States and Their Applications

Diao Da-Sheng, Zhang Cheng-Jie, Zhang Yong-Sheng, Guo Guang-Can

Published Jul 1, 2008• 6 citations
Publisher

Abstract

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.

DOI
10.1088/0256-307x/25/7/010

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Chinese Physics Letters•Jan 1, 2008•0 citations
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.
I present a four-party unlockable bound entangled state, that is, a four-party quantum state which cannot be written in a separable form and from which no pure entanglement can be distilled by local quantum operations and classical communication among the parties, and yet when any two of the parties come together in the same laboratory they can perform a measurement which enables the other two parties to create a pure maximally entangled state between them without coming together. This unlocking ability can be viewed in two ways, either as a determination of which Bell state is shared in the mixture or as a kind of quantum teleportation with cancellation of Pauli operators.
Four-qubit bound entangled Smolin states are generalized with help of the Hilbert-Schmidt formalism to any even number of qubits. They are shown to maximally violate simple correlation Bell inequalities and, as such, to reduce communication complexity, although they do not admit quantum security. They are also shown to serve for remote quantum information concentration, as in the case of the original four-qubit states. It is proven that the latter effect allows us to unlock some entanglement measures and classical correlations. Also the possibility of quantum secret sharing by the considered state is pointed out.
Entanglement is one of the essential resources in quantum information and communication technology (QICT). The entanglement thus far explored and applied to QICT has been pure and distillable entanglement. Yet, there is another type of entanglement, called "bound entanglement," which is not distillable by local operations and classical communication. We demonstrate the experimental "activation" of the bound entanglement held in the four-qubit Smolin state, unleashing its immanent entanglement in distillable form, with the help of auxiliary two-qubit entanglement and local operations and classical communication. We anticipate that it opens the way to a new class of QICT applications that utilize more general classes of entanglement than ever, including bound entanglement.
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.