9 research outputs found
Information-theoretic temporal Bell inequality and quantum computation
An information-theoretic temporal Bell inequality is formulated to contrast
classical and quantum computations. Any classical algorithm satisfies the
inequality, while quantum ones can violate it. Therefore, the violation of the
inequality is an immediate consequence of the quantumness in the computation.
Furthermore, this approach suggests a notion of temporal nonlocality in quantum
computation.Comment: v2: 5 pages, refereces added, discussion slightly revised, main
result unchanged. v3: typos correcte
Accessibility of physical states and non-uniqueness of entanglement measure
Ordering physical states is the key to quantifying some physical property of
the states uniquely. Bipartite pure entangled states are totally ordered under
local operations and classical communication (LOCC) in the asymptotic limit and
uniquely quantified by the well-known entropy of entanglement. However, we show
that mixed entangled states are partially ordered under LOCC even in the
asymptotic limit. Therefore, non-uniqueness of entanglement measure is
understood on the basis of an operational notion of asymptotic convertibility.Comment: 8 pages, 1 figure. v2: main result unchanged but presentation
extensively changed. v3: figure added, minor correction
Mean Field Approximations and Multipartite Thermal Correlations
The relationship between the mean-field approximations in various interacting
models of statistical physics and measures of classical and quantum
correlations is explored. We present a method that allows us to bound the total
amount of correlations (and hence entanglement) in a physical system in thermal
equilibrium at some temperature in terms of its free energy and internal
energy. This method is first illustrated using two qubits interacting through
the Heisenberg coupling, where entanglement and correlations can be computed
exactly. It is then applied to the one dimensional Ising model in a transverse
magnetic field, for which entanglement and correlations cannot be obtained by
exact methods. We analyze the behavior of correlations in various regimes and
identify critical regions, comparing them with already known results. Finally,
we present a general discussion of the effects of entanglement on the
macroscopic, thermodynamical features of solid-state systems. In particular, we
exploit the fact that a dimensional quantum system in thermal equilibrium
can be made to corresponds to a d+1 classical system in equilibrium to
substitute all entanglement for classical correlations.Comment: 17 pages, 6 figure
A Concentration/Purification Scheme for Two Partially Entangled Photon Pairs
An experimental scheme for concentrating entanglement in partially entangled
photon pairs is proposed. In this scheme, two separated parties obtain one
maximally entangled photon pair from previously shared two partially entangled
photon pairs by local operations and classical communication. A practical
realization of the proposed scheme is discussed, which uses imperfect photon
detectors and spontaneous parametric down-conversion as a photon source. This
scheme also works for purifying a class of mixed states.Comment: 8 pages, 3 figure
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