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Quantum Information and Computation

Distillation and bound entanglement

HorodeckiPaweł, HorodeckiRyszard

Published Jan 1, 2001• 1 citation
Publisher

Abstract

Quantum entanglement has been known for over sixty years, however the full significance of it as a basic resource in quantum information theory is only being discovered. The fundamental problem is ...
DOI
10.5555/2011326.2011330

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We prove the existence of bound entangled states with negative partial transpose (NPT) in any d × d(d ≥ 3) Hilbert space with a simple assumption on Schmidt rank two states. Obviously they belong to the class of conjectured to be bound entangled states by Divincenzo et.al [Phys. Rev. A, 61, 062312(2000)] and by Dür et.al [Phys. Rev. A, 61, 062313(2000)]. PACS number(s): 03.67.Hk, 03.65.Ud. The basic issue on the classification of mixed state entanglement at least on the level of bipartite systems solely depends upon whether there exist bound entangled states or not. The existence of PPT-bound (PPT means positive partial transpose) entangled states [1] and also the existence of NPT N−copy undistillable states [2, 3] for every positive integer N naturally indicates there may exist NPT-bound entangled states. In this work we are able to show the existence of NPT-bound entangled states with a simple assumption on Schmidt rank two states. We first briefly describe the issue and the importance of the problem. In recent years it is found that quantum entanglement is an useful resource in performing several tasks in quantum information theory and quantum communication [4]. Maximally entangled states shared between two parties are essential ingredients in this respect [5]. Now due to the interaction with environment, states are in practice found to be mixed. However there is a process called distillation by which we can distill sometimes maximally entangled
The quantum entanglement and nonlocality,the most miraculous feature and resource of quantum information,do not only involve basic problems of quantum theory such as reality,locality,latent variable and measurement theory,but pose a fundamental question for philosophy.With a philosophical reflection on quantum entanglement and nonlocality,the paper discusses the philosophical significance of quantum entanglement and nonlocality.It bears an important significance for recognizing and understanding the information theory and technology.
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