4,448 research outputs found
Optimal measurements for nonlocal correlations
A problem in quantum information theory is to find the experimental setup
that maximizes the nonlocality of correlations with respect to some suitable
measure such as the violation of Bell inequalities. The latter has however some
drawbacks. First and foremost it is unfeasible to determine the whole set of
Bell inequalities already for a few measurements and thus unfeasible to find
the experimental setup maximizing their violation. Second, the Bell violation
suffers from an ambiguity stemming from the choice of the normalization of the
Bell coefficients. An alternative measure of nonlocality with a direct
information-theoretic interpretation is the minimal amount of classical
communication required for simulating nonlocal correlations. In the case of
many instances simulated in parallel, the minimal communication cost per
instance is called nonlocal capacity, and its computation can be reduced to a
convex-optimization problem. This quantity can be computed for a higher number
of measurements and turns out to be useful for finding the optimal experimental
setup. Focusing on the bipartite case, in this paper, we present a simple
method for maximizing the nonlocal capacity over a given configuration space
and, in particular, over a set of possible measurements, yielding the
corresponding optimal setup. Furthermore, we show that there is a functional
relationship between Bell violation and nonlocal capacity. The method is
illustrated with numerical tests and compared with the maximization of the
violation of CGLMP-type Bell inequalities on the basis of entangled two-qubit
as well as two-qutrit states. Remarkably, the anomaly of nonlocality displayed
by qutrits turns out to be even stronger if the nonlocal capacity is employed
as a measure of nonlocality.Comment: Some typos and errors have been corrected, especially in the section
concerning the relation between Bell violation and communication complexit
Quantum states with a positive partial transpose are useful for metrology
We show that multipartite quantum states that have a positive partial
transpose with respect to all bipartitions of the particles can outperform
separable states in linear interferometers. We introduce a powerful iterative
method to find such states. We present some examples for multipartite states
and examine the scaling of the precision with the particle number. Some
bipartite examples are also shown that possess an entanglement very robust to
noise. We also discuss the relation of metrological usefulness to Bell
inequality violation. We find that quantum states that do not violate any Bell
inequality can outperform separable states metrologically. We present such
states with a positive partial transpose, as well as with a non-positive
positive partial transpose.Comment: 6 pages including two figures + three-page supplement including two
figures using revtex 4.1, with numerically obtained density matrices as text
files; v2: published version; v3: published version, typo in the 4x4 bound
entangled state is corrected (noticed by Peng Yin
Faithful Squashed Entanglement
Squashed entanglement is a measure for the entanglement of bipartite quantum
states. In this paper we present a lower bound for squashed entanglement in
terms of a distance to the set of separable states. This implies that squashed
entanglement is faithful, that is, strictly positive if and only if the state
is entangled. We derive the bound on squashed entanglement from a bound on
quantum conditional mutual information, which is used to define squashed
entanglement and corresponds to the amount by which strong subadditivity of von
Neumann entropy fails to be saturated. Our result therefore sheds light on the
structure of states that almost satisfy strong subadditivity with equality. The
proof is based on two recent results from quantum information theory: the
operational interpretation of the quantum mutual information as the optimal
rate for state redistribution and the interpretation of the regularised
relative entropy of entanglement as an error exponent in hypothesis testing.
The distance to the set of separable states is measured by the one-way LOCC
norm, an operationally-motivated norm giving the optimal probability of
distinguishing two bipartite quantum states, each shared by two parties, using
any protocol formed by local quantum operations and one-directional classical
communication between the parties. A similar result for the Frobenius or
Euclidean norm follows immediately. The result has two applications in
complexity theory. The first is a quasipolynomial-time algorithm solving the
weak membership problem for the set of separable states in one-way LOCC or
Euclidean norm. The second concerns quantum Merlin-Arthur games. Here we show
that multiple provers are not more powerful than a single prover when the
verifier is restricted to one-way LOCC operations thereby providing a new
characterisation of the complexity class QMA.Comment: 24 pages, 1 figure, 1 table. Due to an error in the published
version, claims have been weakened from the LOCC norm to the one-way LOCC
nor
A measure of majorisation emerging from single-shot statistical mechanics
The use of the von Neumann entropy in formulating the laws of thermodynamics
has recently been challenged. It is associated with the average work whereas
the work guaranteed to be extracted in any single run of an experiment is the
more interesting quantity in general. We show that an expression that
quantifies majorisation determines the optimal guaranteed work. We argue it
should therefore be the central quantity of statistical mechanics, rather than
the von Neumann entropy. In the limit of many identical and independent
subsystems (asymptotic i.i.d) the von Neumann entropy expressions are recovered
but in the non-equilbrium regime the optimal guaranteed work can be radically
different to the optimal average. Moreover our measure of majorisation governs
which evolutions can be realized via thermal interactions, whereas the
nondecrease of the von Neumann entropy is not sufficiently restrictive. Our
results are inspired by single-shot information theory.Comment: 54 pages (15+39), 9 figures. Changed title / changed presentation,
same main results / added minor result on pure bipartite state entanglement
(appendix G) / near to published versio
Beyond the thermodynamic limit: finite-size corrections to state interconversion rates
Thermodynamics is traditionally constrained to the study of macroscopic
systems whose energy fluctuations are negligible compared to their average
energy. Here, we push beyond this thermodynamic limit by developing a
mathematical framework to rigorously address the problem of thermodynamic
transformations of finite-size systems. More formally, we analyse state
interconversion under thermal operations and between arbitrary
energy-incoherent states. We find precise relations between the optimal rate at
which interconversion can take place and the desired infidelity of the final
state when the system size is sufficiently large. These so-called second-order
asymptotics provide a bridge between the extreme cases of single-shot
thermodynamics and the asymptotic limit of infinitely large systems. We
illustrate the utility of our results with several examples. We first show how
thermodynamic cycles are affected by irreversibility due to finite-size
effects. We then provide a precise expression for the gap between the
distillable work and work of formation that opens away from the thermodynamic
limit. Finally, we explain how the performance of a heat engine gets affected
when one of the heat baths it operates between is finite. We find that while
perfect work cannot generally be extracted at Carnot efficiency, there are
conditions under which these finite-size effects vanish. In deriving our
results we also clarify relations between different notions of approximate
majorisation.Comment: 31 pages, 10 figures. Final version, to be published in Quantu
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