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Separability Criterion for all bipartite Gaussian States [article]

G. Giedke, B. Kraus, M. Lewenstein, J. I. Cirac
2001 arXiv   pre-print
We provide a necessary and sufficient condition 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] .  ... 
arXiv:quant-ph/0104050v1 fatcat:jfspp2cpqfc2dadgferzea442u

Detecting the Inseparability and Distillability of Continuous Variable States in Fock Space

Xiang-Bin Wang, Matsumoto Keiji, Tomita Akihisa
2001 Physical Review Letters  
This formula, together with the known results 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.  ... 
doi:10.1103/physrevlett.87.137903 pmid:11580628 fatcat:visruqyvfzgqvgctzkp5mvprte

Entangled qubits in a non-Gaussian quantum state

T. Kiesel, W. Vogel, B. Hage, R. Schnabel
2011 Physical Review A. Atomic, Molecular, and Optical Physics  
We experimentally generate and tomographically characterize a mixed, genuinely non-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.  ... 
doi:10.1103/physreva.83.062319 fatcat:zmygjtdm2vevridcq3couz57mq

Gaussian entanglement revisited

Ludovico Lami, Alessio Serafini, Gerardo Adesso
2018 New Journal of Physics  
We show that: (iv) 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.  ... 
doi:10.1088/1367-2630/aaa654 fatcat:na5xonodrrbfzpdok6dew3d4ge

Entanglement in continuous-variable systems: recent advances and current perspectives

Gerardo Adesso, Fabrizio Illuminati
2007 Journal of Physics A: Mathematical and Theoretical  
We review the most important results on the separability and 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.  ... 
doi:10.1088/1751-8113/40/28/s01 fatcat:2ynwoc4xevcufcwpwrfjc2q5xy

Minkowski structure for purity and entanglement of Gaussian bipartite states

Marcos C. de Oliveira, Fernando Nicacio, Salomon S. Mizrahi
2013 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 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] .  ... 
doi:10.1103/physreva.88.052324 fatcat:os4dtsjqencpvpicyfp3tv7uom

Multipartite entanglement in three-mode Gaussian states of continuous-variable systems: Quantification, sharing structure, and decoherence

Gerardo Adesso, Alessio Serafini, Fabrizio Illuminati
2006 Physical Review A. Atomic, Molecular, and Optical Physics  
We analytically determine the residual contangle 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.  ... 
doi:10.1103/physreva.73.032345 fatcat:jfzkmayzejcf3jipaiu6iruuke

Continuous-variable multipartite unlockable bound entangled Gaussian states

Jing Zhang
2011 Physical Review A. Atomic, Molecular, and Optical Physics  
CV multipartite unlockable bound-entangled 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.  ... 
doi:10.1103/physreva.83.052327 fatcat:ecku24yx55ghxfusrmwvmeglpi

Entanglement sharing with separable states

Ladislav Mišta
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  ... 
doi:10.1103/physreva.87.062326 fatcat:u2b5bnqcsne3bfvgnpqewoj3ia

Separability properties of three-mode Gaussian states

G. Giedke, B. Kraus, M. Lewenstein, J. I. Cirac
2001 Physical Review A. Atomic, Molecular, and Optical Physics  
We derive a necessary and sufficient condition 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.  ... 
doi:10.1103/physreva.64.052303 fatcat:iqa4hfc2pbfa7ez2efhpbpn3ji

Numerical detection of Gaussian entanglement and its application to the identification of bound entangled Gaussian states

Shan Ma, Shibei Xue, Yu Guo, Chuan-Cun Shu
2020 Quantum Information Processing  
We present a numerical method 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 stateρ 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.  ... 
doi:10.1007/s11128-020-02726-1 fatcat:cpmdmpfwpjcz5cioeo5zdrozpm

Relativity and Lorentz Invariance of Entanglement Distillability

L. Lamata, M. A. Martin-Delgado, E. Solano
2006 Physical Review Letters  
We study entanglement 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.  ... 
doi:10.1103/physrevlett.97.250502 pmid:17280335 fatcat:ef4iefkwtbbsbfvpe2w7d7f4xm

Entanglement bounds for squeezed non-symmetric thermal state [article]

Li-zhen Jiang
2003 arXiv   pre-print
I study the three parameters 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.  ... 
arXiv:quant-ph/0309156v2 fatcat:pqxzrm6ktvdcre26bmd3mqupoy

Quantum entanglement

Ryszard Horodecki, Paweł Horodecki, Michał Horodecki, Karol Horodecki
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.  ... 
doi:10.1103/revmodphys.81.865 fatcat:6ahjbb4iyzfn5jgsocbeodmsqm

Gaussian multipartite bound information

Ladislav Mišta, Natalia Korolkova
2012 Physical Review A. Atomic, Molecular, and Optical Physics  
We construct a tripartite 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.  ... 
doi:10.1103/physreva.86.040305 fatcat:7yygz7hymrcs3fcvrracgxwjbi
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