13 research outputs found
Supercatalysis
We show that entanglement-assisted transformations of bipartite entangled
states can be more efficient than catalysis [D. Jonathan and M. B. Plenio,
Phys. Rev. Lett. 83, 3566 (1999)}, i.e., given two incomparable bipartite
states not only can the transformation be enabled by performing collective
operations with an auxiliary entangled state, but the entanglement of the
auxiliary state itself can be enhanced. We refer to this phenomenon as
supercatalysis. We provide results on the properties of supercatalysis and its
relationship with catalysis. In particular, we obtain a useful necessary and
sufficient condition for catalysis, provide several sufficient conditions for
supercatalysis and study the extent to which entanglement of the auxiliary
state can be enhanced via supercatalysis.Comment: Latex, 5 page
Classification of multipartite entangled states by multidimensional determinants
We find that multidimensional determinants "hyperdeterminants", related to
entanglement measures (the so-called concurrence or 3-tangle for the 2 or 3
qubits, respectively), are derived from a duality between entangled states and
separable states. By means of the hyperdeterminant and its singularities, the
single copy of multipartite pure entangled states is classified into an onion
structure of every closed subset, similar to that by the local rank in the
bipartite case. This reveals how inequivalent multipartite entangled classes
are partially ordered under local actions. In particular, the generic entangled
class of the maximal dimension, distinguished as the nonzero hyperdeterminant,
does not include the maximally entangled states in Bell's inequalities in
general (e.g., in the qubits), contrary to the widely known
bipartite or 3-qubit cases. It suggests that not only are they never locally
interconvertible with the majority of multipartite entangled states, but they
would have no grounds for the canonical n-partite entangled states. Our
classification is also useful for the mixed states.Comment: revtex4, 10 pages, 4 eps figures with psfrag; v2 title changed, 1
appendix added, to appear in Phys. Rev.
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
Schrodinger's cat meets Einstein's twins: A superposition of different clock times
The phenomenon of quantum superposition, which allows a physical system to exist in different states 'simultaneously', is one of the most bizarre notions in physics. Here we illustrate an even more bizarre example of it: a superposed state of a physical system consisting of both an 'older' version and a 'younger' version of that system. This can be accomplished by exploiting the special relativistic effect of time dilation featuring in Einstein's famous twin paradox. © 2007 Springer Science+Business Media, LLC
Error exponents for entanglement concentration
Consider entanglement concentration schemes that convert n identical copies
of a pure state into a maximally entangled state of a desired size with success
probability being close to one in the asymptotic limit. We give the distillable
entanglement, the number of Bell pairs distilled per copy, as a function of an
error exponent, which represents the rate of decrease in failure probability as
n tends to infinity. The formula fills the gap between the least upper bound of
distillable entanglement in probabilistic concentration, which is the
well-known entropy of entanglement, and the maximum attained in deterministic
concentration. The method of types in information theory enables the detailed
analysis of the distillable entanglement in terms of the error rate. In
addition to the probabilistic argument, we consider another type of
entanglement concentration scheme, where the initial state is deterministically
transformed into a (possibly mixed) final state whose fidelity to a maximally
entangled state of a desired size converges to one in the asymptotic limit. We
show that the same formula as in the probabilistic argument is valid for the
argument on fidelity by replacing the success probability with the fidelity.
Furthermore, we also discuss entanglement yield when optimal success
probability or optimal fidelity converges to zero in the asymptotic limit
(strong converse), and give the explicit formulae for those cases.Comment: 28 pages, 4 figures, LaTeX2e, iopart.cls, minor correction