Journal ArticleDOI

# How to Measure Squeezing and Entanglement of Gaussian States without Homodyning

06 Aug 2004-Physical Review Letters (American Institute of Physics)-Vol. 93, Iss: 6, pp 063601-063601

TL;DR: This work proposes a scheme for measuring the squeezing, purity, and entanglement of Gaussian states of light that does not require homodyne detection and needs only beam splitters and single-photon detectors.

AbstractWe propose a scheme for measuring the squeezing, purity, and entanglement of Gaussian states of light that does not require homodyne detection. The suggested setup needs only beam splitters and single-photon detectors. Two-mode entanglement can be detected from coincidences between photodetectors placed on the two beams.

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##### References
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Guifre Vidal
TL;DR: A measure of entanglement that can be computed effectively for any mixed state of an arbitrary bipartite system is presented and it is shown that it does not increase under local manipulations of the system.
Abstract: We present a measure of entanglement that can be computed effectively for any mixed state of an arbitrary bipartite system. We show that it does not increase under local manipulations of the system, and use it to obtain a bound on the teleportation capacity and on the distillable entanglement of mixed states.

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Abstract: Preface. About the Editors. Part I: Quantum Computing. 1. Quantum computing with qubits S.L. Braunstein, A.K. Pati. 2. Quantum computation over continuous variables S. Lloyd, S.L. Braunstein. 3. Error correction for continuous quantum variables S.L. Braunstein. 4. Deutsch-Jozsa algorithm for continuous variables A.K. Pati, S.L. Braunstein. 5. Hybrid quantum computing S. Lloyd. 6. Efficient classical simulation of continuous variable quantum information processes S.D. Bartlett, B.C. Sanders, S.L. Braunstein, K. Nemoto. Part II: Quantum Entanglement. 7. Introduction to entanglement-based protocols S.L. Braunstein, A.K. Pati. 8. Teleportation of continuous uantum variables S.L. Braunstein, H.J. Kimble. 9. Experimental realization of continuous variable teleportation A. Furusawa, H.J. Kimble. 10. Dense coding for continuous variables S.L. Braunstein, H.J. Kimble. 11. Multipartite Greenberger-Horne-Zeilinger paradoxes for continuous variables S. Massar, S. Pironio. 12. Multipartite entanglement for continuous variables P. van Loock, S.L. Braunstein. 13. Inseparability criterion for continuous variable systems Lu-Ming Duan, G. Giedke, J.I. Cirac, P. Zoller. 14. Separability criterion for Gaussian states R. Simon. 15. Distillability and entanglement purification for Gaussian states G. Giedke, Lu-Ming Duan, J.I. Cirac, P. Zoller. 16. Entanglement purification via entanglement swapping S. Parke, S. Bose, M.B. Plenio. 17. Bound entanglement for continuous variables is a rare phenomenon P. Horodecki, J.I. Cirac, M. Lewenstein. Part III: Continuous Variable Optical-Atomic Interfacing. 18. Atomic continuous variable processing and light-atoms quantum interface A. Kuzmich, E.S. Polzik. Part IV: Limits on Quantum Information and Cryptography. 19. Limitations on discrete quantum information and cryptography S.L. Braunstein, A.K. Pati. 20. Quantum cloning with continuous variables N.J. Cerf. 21. Quantum key distribution with continuous variables in optics T.C. Ralph. 22. Secure quantum key distribution using squeezed states D. Gottesman, J. Preskill. 23. Experimental demonstration of dense coding and quantum cryptography with continuous variables Kunchi Peng, Qing Pan, Jing Zhang, Changde Xie. 24. Quantum solitons in optical fibres: basic requisites for experimental quantum communication G. Leuchs, Ch. Silberhorn, E. Konig, P.K. Lam, A. Sizmann, N. Korolkova. Index.

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TL;DR: The Peres-Horodecki criterion of positivity under partial transpose is studied in the context of separability of bipartite continuous variable states and turns out to be a necessary and sufficient condition for separability.
Abstract: The Peres-Horodecki criterion of positivity under partial transpose is studied in the context of separability of bipartite continuous variable states. The partial transpose operation admits, in the continuous case, a geometric interpretation as mirror reflection in phase space. This recognition leads to uncertainty principles, stronger than the traditional ones, to be obeyed by all separable states. For all bipartite Gaussian states, the Peres-Horodecki criterion turns out to be a necessary and sufficient condition for separability.

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Abstract: As with discrete systems, quantum entanglement also plays the basic role in quantum information protocols with continuous variables. A problem of great importance is then to check whether a continuous variable state, generally mixed, is entangled (inseparable). For discrete systems, there is the Peres-Horodecki inseparability criterion [1,2], based on the negativity of the partial transpose of the composite density operator. This negativity provides a necessary and sufficient condition for inseparability of 2 × 2 or 2 × 3 —dimensional systems. In this section, we will describe an entirely different inseparability criterion for continuous variable states, which was first proposed in Ref. [3]. The Peres-Horodecki criterion was also successfully extended to the continuous variable systems shortly afterwards, which will be described in the next section by Simon.

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Book
13 Mar 1998
Abstract: Classical Models of Light Experiments with Photons Quantum Models of Light Basic Optical Components Photo-currents: Generation and Detection The Laser Quantum Noise: Basic Measurements Sub-Poissonian Light Squeezing Experiments Quantum Non-demolition Experiments Applications of Quantum Optics Summary and Outlook Appendices Index.

753 citations