6,607 research outputs found
A reversible theory of entanglement and its relation to the second law
We consider the manipulation of multipartite entangled states in the limit of
many copies under quantum operations that asymptotically cannot generate
entanglement. As announced in [Brandao and Plenio, Nature Physics 4, 8 (2008)],
and in stark contrast to the manipulation of entanglement under local
operations and classical communication, the entanglement shared by two or more
parties can be reversibly interconverted in this setting. The unique
entanglement measure is identified as the regularized relative entropy of
entanglement, which is shown to be equal to a regularized and smoothed version
of the logarithmic robustness of entanglement.
Here we give a rigorous proof of this result, which is fundamentally based on
a certain recent extension of quantum Stein's Lemma proved in [Brandao and
Plenio, Commun. Math. 295, 791 (2010)], giving the best measurement strategy
for discriminating several copies of an entangled state from an arbitrary
sequence of non-entangled states, with an optimal distinguishability rate equal
to the regularized relative entropy of entanglement. We moreover analyse the
connection of our approach to axiomatic formulations of the second law of
thermodynamics.Comment: 21 pages. revised versio
On circulant states with positive partial transpose
We construct a large class of quantum "d x d" 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 way 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.Comment: 15 pages; minor correction
- …