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Separability Criterion for all bipartite Gaussian States
[article]

2001
*
arXiv
*
pre-print

We provide a necessary and sufficient condition

arXiv:quant-ph/0104050v1
fatcat:jfspp2cpqfc2dadgferzea442u
*for*separability of*Gaussian**states*of*bipartite*systems of arbitrarily many modes. ... The condition provides an operational*criterion*since it can be checked by simple computation. Moreover, it allows us to find a pure product-*state*decomposition of any given separable*Gaussian**state*. ... It is also worth mentioning that our*criterion*can be used to study the separability properties with respect to*bipartite*splitting of multipartite systems in*Gaussian**states*[15] . ...##
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Detecting the Inseparability and Distillability of Continuous Variable States in Fock Space

2001
*
Physical Review Letters
*

This formula, together with the known results

doi:10.1103/physrevlett.87.137903
pmid:11580628
fatcat:visruqyvfzgqvgctzkp5mvprte
*for**Gaussian**states*, gives the*criterions**for*the inseparability and*distillability*in a subspace of the global*Gaussian**state*. ... Based on this, a number of creterions on the inseparability and*distillability**for*the multimode*Gaussian**states*are naturally drawn. ... Imai Hiroshi*for*support. We thank Dr. M. Hachimori and Dr. W. Y. Hwang*for*helpful discussions. ...##
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Entangled qubits in a non-Gaussian quantum state

2011
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Physical Review A. Atomic, Molecular, and Optical Physics
*

We experimentally generate and tomographically characterize a mixed, genuinely non-

doi:10.1103/physreva.83.062319
fatcat:zmygjtdm2vevridcq3couz57mq
*Gaussian**bipartite*continuous-variable entangled*state*. ... By testing entanglement in 2×2-dimensional two-qubit subspaces, entangled qubits are localized within the density matrix, which, firstly, proves the*distillability*of the*state*and, secondly, is useful ... Samblowski*for*fruitful discussions and their assistance. ...##
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Gaussian entanglement revisited

2018
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New Journal of Physics
*

We show that: (iv)

doi:10.1088/1367-2630/aaa654
fatcat:na5xonodrrbfzpdok6dew3d4ge
*Gaussian**states*that are invariant under partial transposition are necessarily separable; (v) the PPT*criterion*is necessary and sufficient*for*separability*for**Gaussian**states*of m ... We derive a simplified necessary and sufficient separability*criterion**for*arbitrary*Gaussian**states*of m vs n modes, which relies on convex optimisation over marginal covariance matrices on one subsystem ... The PPT*criterion*is necessary and sufficient*for*separability of*all*isotropic*Gaussian**states*of an arbitrary number of modes. ...##
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Entanglement in continuous-variable systems: recent advances and current perspectives

2007
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Journal of Physics A: Mathematical and Theoretical
*

We review the most important results on the separability and

doi:10.1088/1751-8113/40/28/s01
fatcat:2ynwoc4xevcufcwpwrfjc2q5xy
*distillability*of*Gaussian**states*and discuss the main properties of*bipartite*entanglement. ... 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*... Giampaolo, and especially Alessio Serafini,*for*sharing with us the joy of working together on some important topics covered by the present review. ...##
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Minkowski structure for purity and entanglement of Gaussian bipartite states

2013
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Physical Review A. Atomic, Molecular, and Optical Physics
*

The relation between the symplectic and Lorentz groups is explored to investigate entanglement features in a two-mode

doi:10.1103/physreva.88.052324
fatcat:os4dtsjqencpvpicyfp3tv7uom
*bipartite**Gaussian**state*. ... The second distance allows us to define a measure*for*entanglement in terms of the invariant interval between the given*state*and its closest separable*state*, given in a natural manner without the requirement ... The discriminance requirement*states*that δs 2 = 0 if and only ifρ is separable, and this is true*for**all**bipartite*GS, since there is no*bipartite*GS with bound entanglement [22] . ...##
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Multipartite entanglement in three-mode Gaussian states of continuous-variable systems: Quantification, sharing structure, and decoherence

2006
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Physical Review A. Atomic, Molecular, and Optical Physics
*

We analytically determine the residual contangle

doi:10.1103/physreva.73.032345
fatcat:jfzkmayzejcf3jipaiu6iruuke
*for*arbitrary pure three-mode*Gaussian**states*and study the distribution of quantum correlations*for*such*states*. ... Quantum correlations will be quantified by a proper convex roof extension of the squared logarithmic negativity (the contangle), satisfying a monogamy relation*for*multimode*Gaussian**states*, whose proof ...*for**all*multimode*Gaussian**state*, using the (*Gaussian*) contangle as a measure of*bipartite*entanglement. ...##
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Continuous-variable multipartite unlockable bound entangled Gaussian states

2011
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Physical Review A. Atomic, Molecular, and Optical Physics
*

CV multipartite unlockable bound-entangled

doi:10.1103/physreva.83.052327
fatcat:ecku24yx55ghxfusrmwvmeglpi
*states*may serve as a useful quantum resource*for*new multiparty communication schemes. ... The experimental protocol*for*generating CV unlockable bound-entangled*states*is proposed with a setup that is at present accessible. ... [17] , they study the bound entangled*Gaussian**states**for*a*bipartite*system with an arbitrary number of modes in each party. ...##
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Entanglement sharing with separable states

2013
*
Physical Review A. Atomic, Molecular, and Optical Physics
*

*For*the

*state*shared by the players and Bob one cannot establish entanglement between any two modes even with the help of operation on the third mode provided that Bob is restricted to

*Gaussian*measurements ... We propose an entanglement sharing protocol based on separable

*states*. Initially, two parties, Alice and Bob, share a two-mode separable

*Gaussian*

*state*. ...

*For*certain families of three-mode

*Gaussian*

*states*one can find even analytically the symplectic eigenvalue (17)

*for*a two-mode

*state*obtained by

*Gaussian*measurement on the third mode minimized over

*all*...

##
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Separability properties of three-mode Gaussian states

2001
*
Physical Review A. Atomic, Molecular, and Optical Physics
*

We derive a necessary and sufficient condition

doi:10.1103/physreva.64.052303
fatcat:iqa4hfc2pbfa7ez2efhpbpn3ji
*for*the separability of tripartite three mode*Gaussian**states*, that is easy to check*for*any such*state*. ... We give a classification of the separability properties of those systems and show how to determine*for*any*state*to which class it belongs. ... B.K. and J.I.C. thank the University of Hannover*for*hospitality. M.L., B.K., and J.I.C. acknowledge the hospitality of the Erwin Schrödinger Institute. ...##
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Numerical detection of Gaussian entanglement and its application to the identification of bound entangled Gaussian states

2020
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Quantum Information Processing
*

We present a numerical method

doi:10.1007/s11128-020-02726-1
fatcat:cpmdmpfwpjcz5cioeo5zdrozpm
*for*solving the separability problem of*Gaussian*quantum*states*in continuous-variable quantum systems. ... We apply this method to the identification of bound entangled*Gaussian**states*. ...*For*a*Gaussian**state*ρ AB pertaining to an (m + n)-mode*bipartite*system A + B, a necessary and sufficient condition has been developed in Ref. [30]*for*the separability of the*state*. ...##
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Relativity and Lorentz Invariance of Entanglement Distillability

2006
*
Physical Review Letters
*

We study entanglement

doi:10.1103/physrevlett.97.250502
pmid:17280335
fatcat:ef4iefkwtbbsbfvpe2w7d7f4xm
*distillability*of*bipartite*mixed spin*states*under Wigner rotations induced by Lorentz transformations. ... We define weak and strong criteria*for*relativistic isoentangled and isodistillable*states*to characterize relative and invariant behavior of entanglement and*distillability*. ... (iii) Weak isodistillable*state*WID : A*state*that is*distillable*in*all*considered reference frames. This implies that the*state*is entangled*for*these observers. ...##
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Entanglement bounds for squeezed non-symmetric thermal state
[article]

2003
*
arXiv
*
pre-print

I study the three parameters

arXiv:quant-ph/0309156v2
fatcat:pqxzrm6ktvdcre26bmd3mqupoy
*bipartite*quantum*Gaussian**state*called squeezed asymmetric thermal*state*, calculate*Gaussian*entanglement of formation analytically and the up bound of relative entropy of ... entanglement, compare them with coherent information of the state.Based on the result obtained, one can determine the relative entropy of entanglement of the*state*with infinitive squeezing. ...*For*mixed*bipartite**states*it is usually difficult to be calculated, except*for*some specific*states*. ...##
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Quantum entanglement

2009
*
Reviews of Modern Physics
*

*All*our former experience with application of quantum theory seems to say: what is predicted by quantum formalism must occur in laboratory. ... This article reviews basic aspects of entanglement including its characterization, detection,

*distillation*and quantifying. ... ACKNOWLEDGMENTS We thank Jadwiga Horodecka

*for*help in the editing of this paper. ...

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Gaussian multipartite bound information

2012
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Physical Review A. Atomic, Molecular, and Optical Physics
*

We construct a tripartite

doi:10.1103/physreva.86.040305
fatcat:7yygz7hymrcs3fcvrracgxwjbi
*Gaussian*distribution from which no secret key can be*distilled*, but which cannot be created by local operations and public communication. ... We demonstrate the existence of*Gaussian*multipartite bound information which is a classical analog of*Gaussian*multipartite bound entanglement. ... In conclusion, we derived a tripartite*Gaussian*distribution having secret correlations across only one*bipartition*which is an example of*Gaussian*bound information. ...
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