2,825 research outputs found
The power of symmetric extensions for entanglement detection
In this paper, we present new progress on the study of the symmetric
extension criterion for separability. First, we show that a perturbation of
order O(1/N) is sufficient and, in general, necessary to destroy the
entanglement of any state admitting an N Bose symmetric extension. On the other
hand, the minimum amount of local noise necessary to induce separability on
states arising from N Bose symmetric extensions with Positive Partial Transpose
(PPT) decreases at least as fast as O(1/N^2). From these results, we derive
upper bounds on the time and space complexity of the weak membership problem of
separability when attacked via algorithms that search for PPT symmetric
extensions. Finally, we show how to estimate the error we incur when we
approximate the set of separable states by the set of (PPT) N -extendable
quantum states in order to compute the maximum average fidelity in pure state
estimation problems, the maximal output purity of quantum channels, and the
geometric measure of entanglement.Comment: see Video Abstract at
http://www.quantiki.org/video_abstracts/0906273
Convex set of quantum states with positive partial transpose analysed by hit and run algorithm
The convex set of quantum states of a composite system with
positive partial transpose is analysed. A version of the hit and run algorithm
is used to generate a sequence of random points covering this set uniformly and
an estimation for the convergence speed of the algorithm is derived. For this algorithm works faster than sampling over the entire set of states and
verifying whether the partial transpose is positive. The level density of the
PPT states is shown to differ from the Marchenko-Pastur distribution, supported
in [0,4] and corresponding asymptotically to the entire set of quantum states.
Based on the shifted semi--circle law, describing asymptotic level density of
partially transposed states, and on the level density for the Gaussian unitary
ensemble with constraints for the spectrum we find an explicit form of the
probability distribution supported in [0,3], which describes well the level
density obtained numerically for PPT states.Comment: 11 pages, 4 figure
Entanglement in continuous variable systems: Recent advances and current perspectives
We review the theory of continuous-variable entanglement with special
emphasis on foundational aspects, conceptual structures, and mathematical
methods. Much attention is devoted to the discussion of separability criteria
and entanglement properties of Gaussian states, for their great practical
relevance in applications to quantum optics and quantum information, as well as
for the very clean framework that they allow for the study of the structure of
nonlocal correlations. We give a self-contained introduction to phase-space and
symplectic methods in the study of Gaussian states of infinite-dimensional
bosonic systems. We review the most important results on the separability and
distillability of Gaussian states and discuss the main properties of bipartite
entanglement. These include the extremal entanglement, minimal and maximal, of
two-mode mixed Gaussian states, the ordering of two-mode Gaussian states
according to different measures of entanglement, the unitary (reversible)
localization, and the scaling of bipartite entanglement in multimode Gaussian
states. We then discuss recent advances in the understanding of entanglement
sharing in multimode Gaussian states, including the proof of the monogamy
inequality of distributed entanglement for all Gaussian states, and its
consequences for the characterization of multipartite entanglement. We finally
review recent advances and discuss possible perspectives on the qualification
and quantification of entanglement in non Gaussian states, a field of research
that is to a large extent yet to be explored.Comment: 61 pages, 7 figures, 3 tables; Published as Topical Review in J.
Phys. A, Special Issue on Quantum Information, Communication, Computation and
Cryptography (v3: few typos corrected
- …