Circulant states with positive partial transpose
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In this paper, a large class of quantum dxd states which are positive under partial transposition (so called PPT states) were constructed based on certain direct sum decomposition of the total Hilbert space displaying characteristic circular structure.Abstract:
We construct a large class of quantum dxd states which are positive under partial transposition (so called PPT states). The construction is based on certain direct sum decomposition of the total Hilbert space displaying characteristic circular structure - that is why we call them circulant states. It turns out that partial transposition maps any such decomposition into another one and hence both original density matrix and its partially transposed partner share similar cyclic properties. This class contains many well-known examples of PPT states from the literature and gives rise to a huge family of completely new states.read more
Citations
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Witnessing quantum discord in 2 x N systems
TL;DR: In this paper, it was shown that 2xN states with vanishing quantum discord are necessarily separable and hence positive partial transpose (PPT) are necessarily PPTs.
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Parametrizations of density matrices
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Constructing optimal entanglement witnesses
TL;DR: In this article, a class of indecomposable entanglement witnesses, called optimal and atomic witnesses, are presented, i.e., they are able to detect the weakest quantum entanglements encoded into states with positive partial transposition.
References
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Quantum Computation and Quantum Information
TL;DR: In this article, the quantum Fourier transform and its application in quantum information theory is discussed, and distance measures for quantum information are defined. And quantum error-correction and entropy and information are discussed.
Quantum Computation and Quantum Information
TL;DR: This chapter discusses quantum information theory, public-key cryptography and the RSA cryptosystem, and the proof of Lieb's theorem.
Journal ArticleDOI
Extreme points of the set of density matrices with positive partial transpose
TL;DR: In this paper, a necessary and sufficient condition for a finite-dimensional density matrix to be an extreme point of the convex set of density matrices with positive partial transposition with respect to a subsystem is presented.