84 research outputs found
Hierarchy of efficiently computable and faithful lower bounds to quantum discord
Quantum discord expresses a fundamental non-classicality of correlations more
general than quantum entanglement. We combine the no-local-broadcasting
theorem, semidefinite-programming characterizations of quantum fidelity and
quantum separability, and a recent breakthrough result of Fawzi and Renner
about quantum Markov chains to provide a hierarchy of computationally efficient
lower bounds to quantum discord. Such a hierarchy converges to the surprisal of
measurement recoverability introduced by Seshadreesan and Wilde, and provides a
faithful lower bound to quantum discord already at the lowest non-trivial
level. Furthermore, the latter constitutes by itself a valid discord-like
measure of the quantumness of correlations.Comment: 7 pages, 2 figures; comments -- also about "extendable" Vs
"extendible" -- welcom
The problem with the geometric discord
We argue that the geometric discord introduced in [B. Dakic, V. Vedral, and
C. Brukner, Phys. Rev. Lett. 105, 190502 (2010)] is not a good measure for the
quantumness of correlations, as it can increase even under trivial local
reversible operations of the party whose classicality/non-classicality is not
tested. On the other hand it is known that the standard, mutual-information
based discord does not suffer this problem; a simplified proof of such a fact
is given.Comment: 5 pages. Changes in ver 2: typos corrected, added short proof of
monotonicity of standard quantum discord under one-side action. This note is
meant to stimulate discussion in the community: comments are welcom
Einstein-Podolsky-Rosen steering provides the advantage in entanglement-assisted subchannel discrimination with one-way measurements
Steering is the entanglement-based quantum effect that embodies the "spooky
action at a distance" disliked by Einstein and scrutinized by Einstein,
Podolsky, and Rosen. Here we provide a necessary and sufficient
characterization of steering, based on a quantum information processing task:
the discrimination of branches in a quantum evolution, which we dub subchannel
discrimination. We prove that, for any bipartite steerable state, there are
instances of the quantum subchannel discrimination problem for which this state
allows a correct discrimination with strictly higher probability than in
absence of entanglement, even when measurements are restricted to local
measurements aided by one-way communication. On the other hand, unsteerable
states are useless in such conditions, even when entangled. We also prove that
the above steering advantage can be exactly quantified in terms of the steering
robustness, which is a natural measure of the steerability exhibited by the
state.Comment: 10 pages, 2 figures, comments welcom
Improved entropic uncertainty relations and information exclusion relations
The uncertainty principle can be expressed in entropic terms, also taking
into account the role of entanglement in reducing uncertainty. The information
exclusion principle bounds instead the correlations that can exist between the
outcomes of incompatible measurements on one physical system, and a second
reference system. We provide a more stringent formulation of both the
uncertainty principle and the information exclusion principle, with direct
applications for, e.g., the security analysis of quantum key distribution,
entanglement estimation, and quantum communication. We also highlight a
fundamental distinction between the complementarity of observables in terms of
uncertainty and in terms of information.Comment: 11 pages, 1 figure, v2: close to published versio
Role of correlations in the two-body-marginal problem
Quantum properties of correlations have a key role in disparate fields of
physics, from quantum information processing, to quantum foundations, to
strongly correlated systems. We tackle a specific aspect of the fundamental
quantum marginal problem: we address the issue of deducing the global
properties of correlations of tripartite quantum states based on the knowledge
of their bipartite reductions, focusing on relating specific properties of
bipartite correlations to global correlation properties. We prove that strictly
classical bipartite correlations may still require global entanglement and that
unentangled---albeit not strictly classical---reductions may require global
genuine multipartite entanglement, rather than simple entanglement. On the
other hand, for three qubits, the strict classicality of the bipartite
reductions rules out the need for genuine multipartite entanglement. Our work
sheds new light on the relation between local and global properties of quantum
states, and on the interplay between classical and quantum properties of
correlations.Comment: 10 pages, 1 figure, close to final published versio
Simple class of bound entangled states based on the properties of the antisymmetric subspace
We provide a simple construction of bipartite entangled states that are positive under partial transposition, and hence undistillable. The construction makes use of the properties of the projectors onto the symmetric and antisymmetric subspaces of the Hilbert space of two identical systems. The resulting states can be considered as generalizations of the celebrated Werner states
- …