862 research outputs found
Bipartite and Multipartite Entanglement of Gaussian States
In this chapter we review the characterization of entanglement in Gaussian
states of continuous variable systems. For two-mode Gaussian states, we discuss
how their bipartite entanglement can be accurately quantified in terms of the
global and local amounts of mixedness, and efficiently estimated by direct
measurements of the associated purities. For multimode Gaussian states endowed
with local symmetry with respect to a given bipartition, we show how the
multimode block entanglement can be completely and reversibly localized onto a
single pair of modes by local, unitary operations. We then analyze the
distribution of entanglement among multiple parties in multimode Gaussian
states. We introduce the continuous-variable tangle to quantify entanglement
sharing in Gaussian states and we prove that it satisfies the
Coffman-Kundu-Wootters monogamy inequality. Nevertheless, we show that pure,
symmetric three-mode Gaussian states, at variance with their discrete-variable
counterparts, allow a promiscuous sharing of quantum correlations, exhibiting
both maximum tripartite residual entanglement and maximum couplewise
entanglement between any pair of modes. Finally, we investigate the connection
between multipartite entanglement and the optimal fidelity in a
continuous-variable quantum teleportation network. We show how the fidelity can
be maximized in terms of the best preparation of the shared entangled resources
and, viceversa, that this optimal fidelity provides a clearcut operational
interpretation of several measures of bipartite and multipartite entanglement,
including the entanglement of formation, the localizable entanglement, and the
continuous-variable tangle.Comment: 21 pages, 4 figures, WS style. Published as Chapter 1 in the book
"Quantum Information with Continuous Variables of Atoms and Light" (Imperial
College Press, 2007), edited by N. Cerf, G. Leuchs, and E. Polzik. Details of
the book available at http://www.icpress.co.uk/physics/p489.html . For recent
follow-ups see quant-ph/070122
Generic Entanglement and Standard Form for N-mode Pure Gaussian States
We investigate the correlation structure of pure N-mode Gaussian resources
which can be experimentally generated by means of squeezers and beam splitters,
whose entanglement properties are generic. We show that those states are
specified (up to local unitaries) by N(N-1)/2 parameters, corresponding to the
two-point correlations between any pair of modes. Our construction yields a
practical scheme to engineer such generic-entangled N-mode pure Gaussian states
by linear optics. We discuss our findings in the framework of Gaussian matrix
product states of harmonic lattices, raising connections with entanglement
frustration and the entropic area law.Comment: 4 pages, 1 EPS figure. Revised, corrected and clarified. Final
shortened version, published in PR
Determination of continuous variable entanglement by purity measurements
We classify the entanglement of two--mode Gaussian states according to their
degree of total and partial mixedness. We derive exact bounds that determine
maximally and minimally entangled states for fixed global and marginal
purities. This characterization allows for an experimentally reliable estimate
of continuous variable entanglement based on measurements of purity.Comment: 4 pages, 3 EPS figures. Final versio
Equivalence between Entanglement and the Optimal Fidelity of Continuous Variable Teleportation
We devise the optimal form of Gaussian resource states enabling continuous
variable teleportation with maximal fidelity. We show that a nonclassical
optimal fidelity of -user teleportation networks is {\it necessary and
sufficient} for -party entangled Gaussian resources, yielding an estimator
of multipartite entanglement. This {\it entanglement of teleportation} is
equivalent to entanglement of formation in the two-user protocol, and to
localizable entanglement in the multi-user one. The continuous-variable tangle,
quantifying entanglement sharing in three-mode Gaussian states, is
operationally linked to the optimal fidelity of a tripartite teleportation
network.Comment: 4 pages, 1 figure. Approved for publication in Phys. Rev. Let
Optical state engineering, quantum communication, and robustness of entanglement promiscuity in three-mode Gaussian states
We present a novel, detailed study on the usefulness of three-mode Gaussian
states states for realistic processing of continuous-variable quantum
information, with a particular emphasis on the possibilities opened up by their
genuine tripartite entanglement. We describe practical schemes to engineer
several classes of pure and mixed three-mode states that stand out for their
informational and/or entanglement properties. In particular, we introduce a
simple procedure -- based on passive optical elements -- to produce pure
three-mode Gaussian states with {\em arbitrary} entanglement structure (upon
availability of an initial two-mode squeezed state). We analyze in depth the
properties of distributed entanglement and the origin of its sharing structure,
showing that the promiscuity of entanglement sharing is a feature peculiar to
symmetric Gaussian states that survives even in the presence of significant
degrees of mixedness and decoherence. Next, we discuss the suitability of the
considered tripartite entangled states to the implementation of quantum
information and communication protocols with continuous variables. This will
lead to a feasible experimental proposal to test the promiscuous sharing of
continuous-variable tripartite entanglement, in terms of the optimal fidelity
of teleportation networks with Gaussian resources. We finally focus on the
application of three-mode states to symmetric and asymmetric telecloning, and
single out the structural properties of the optimal Gaussian resources for the
latter protocol in different settings. Our analysis aims to lay the basis for a
practical quantum communication with continuous variables beyond the bipartite
scenario.Comment: 33 pages, 10 figures (some low-res due to size constraints), IOP
style; (v2) improved and reorganized, accepted for publication in New Journal
of Physic
Quantum versus classical correlations in Gaussian states
Quantum discord, a measure of genuinely quantum correlations, is generalized
to continuous variable systems. For all two-mode Gaussian states, we calculate
analytically the quantum discord and a related measure of classical
correlations, solving an optimization over all Gaussian measurements. Almost
all two-mode Gaussian states are shown to have quantum correlations, while for
separable states, the discord is smaller than unity. For a given amount of
entanglement, it admits tight upper and lower bounds. Via a duality between
entanglement and classical correlations, we derive a closed formula for the
Gaussian entanglement of formation of all mixed three-mode Gaussian states
whose normal mode decomposition includes two vacua.Comment: 4+2 pages, 1+1 figures. Close to published version including appendi
Entanglement sharing: from qubits to Gaussian states
It is a central trait of quantum information theory that there exist
limitations to the free sharing of quantum correlations among multiple parties.
Such 'monogamy constraints' have been introduced in a landmark paper by
Coffman, Kundu and Wootters, who derived a quantitative inequality expressing a
trade-off between the couplewise and the genuine tripartite entanglement for
states of three qubits. Since then, a lot of efforts have been devoted to the
investigation of distributed entanglement in multipartite quantum systems. In
these proceedings we report, in a unifying framework, a bird's eye view of the
most relevant results that have been established so far on entanglement sharing
in quantum systems. We will take off from the domain of N qubits, graze qudits,
and finally land in the almost unexplored territory of multimode Gaussian
states of continuous variable systems.Comment: 11 pages. Proceedings of the workshop "Entanglement in physical and
information sciences", Centro Ennio de Giorgi, Pisa, December 2004. (v2)
References updated, final version published in Int. J. Quant. In
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