ENTANGLEMENT OF GAUSSIAN STATES Gerardo Adesso

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272 List of Publications [GA11] G. Adesso, A. Serafini, and F. Illuminati, Multipartite entanglement in threemode Gaussian states of continuous variable systems: Quantification, sharing structure, and decoherence, Phys. Rev. A 73, 032345 (2006), e–print quant-ph/0512124. [GA12] G. Adesso and F. Illuminati, Entanglement Sharing: From Qubits to Gaussian States, Int. J. Quant. Inf. 4, 383 (2006), e–print quant-ph/0506213. [GA13] G. Adesso and M. Ericsson, Entanglement in Gaussian matrix-product states, Phys. Rev. A 74, 030305(R) (2006), e–print quant-ph/0602067. [GA14] G. Adesso, Generic Entanglement and Standard Form for N-Mode Pure Gaussian States, Phys. Rev. Lett. 97, 130502 (2006), e–print quant-ph/0606190. [GA15] T. Hiroshima, G. Adesso, and F. Illuminati, Monogamy Inequality for Distributed Gaussian Entanglement, Phys. Rev. Lett. 98, 050503 (2007), e–print quant-ph/0605021. [GA16] G. Adesso, A. Serafini, and F. Illuminati, Continuous variable quantum information with three-mode Gaussian states: Quantum state engineering and communication protocols, New J. Phys. (2006), submitted, e–print quant-ph/0609071. [GA17] G. Adesso and M. Ericsson, Optical implementation and entanglement distribution in Gaussian valence bond states, submitted to Optics & Spectroscopy, Special Issue for ICQO2006, Minsk (2006). [GA18] A. Serafini and G. Adesso, Standard forms and entanglement engineering of multimode Gaussian states under local operations, submitted to J. Phys. A, Special Issue on Quantum Information (2006). [GA19] G. Adesso, M. Ericsson, and F. Illuminati, Coexistence of unlimited bipartite and multipartite continuous variable entanglement (2006), e–print quant-ph/0609178. [GA20] G. Adesso, I. Fuentes-Schuller, and M. Ericsson, Continuous variable entanglement sharing in non-inertial frames (2007), e–print quant-ph/0701074. [GA21] G. Adesso and I. Fuentes-Schuller, Loss and distribution of quantum and classical correlations in black holes (2007), e–print quant-ph/0702001. [GA22] G. Adesso and F. Illuminati, Bipartite and Multipartite Entanglement of Gaussian States, contribution to the book Quantum Information with Continuous Variables of Atoms and Light [49], edited by N. Cerf, G. Leuchs, and E. S. Polzik (Imperial College Press, London, 2007, in press), e–print quant-ph/0510052. [GA23] G. Adesso and F. Illuminati, Entanglement in continuous variable systems: Recent advances and current perspectives, invited review, submitted to J. Phys. A, Special Issue on Quantum Information (2007), e–print quant-ph/0701221.
Bibliography [1] Open Problems in Quantum Information Theory, O. Krüger and R. F. Werner eds., Institute for Mathematical Physics, Technical University of Braunschweig, http://www.imaph.tu-bs.de/qi/problems/problems.html. [2] I. Affleck, T. Kennedy, E. H. Lieb, and H. Tasaki, Commun. Math. Phys. 115, 477 (1988). [3] G. S. Agarwal and A. Biswas, New J. Phys. 7, 211 (2005). [4] D. Ahn and M. S. Kim, e–print quant-ph/0604007 (2006). [5] R. Alicki and M. Fannes, e–print quant-ph/0312081 (2003). [6] P. M. Alsing, I. Fuentes-Schuller, R. B. Mann, and T. E. Tessier, Phys. Rev. A 74, 032326 (2006). [7] P. M. Alsing and G. J. Milburn, Phys. Rev. Lett. 91, 180404 (2003). [8] T. Aoki, N. Takei, H. Yonezawa, K. Wakui, T. Hiraoka, A. Furusawa, and P. van Loock, Phys. Rev. Lett. 91, 080404 (2003). [9] H. Araki and E. H. Lieb, Comm. Math. Phys. 18, 160 (1970). [10] Arvind, B. Dutta, N. Mukunda, and R. Simon, Pramana 45, 471 (1995), e–print quant-ph/9509002. [11] K. Audenaert, J. Eisert, M. B. Plenio, and R. F. Werner, Phys. Rev. A 66, 042327 (2002). [12] K. Audenaert, M. B. Plenio, and J. Eisert, Phys. Rev. Lett. 90, 027901 (2003). [13] K. M. R. Audenaert and M. B. Plenio, New J. Phys. 8, 266 (2006). [14] J. Ball, I. Fuentes-Schuller, and F. P. Schuller, Phys. Lett. A 359, 550 (2006). [15] M. Barbieri, F. De Martini, G. Di Nepi, P. Mataloni, G. M. D’Ariano, and C. Macchiavello, Phys. Rev. Lett. 91, 227901 (2004). [16] A. M. Barnett and P. M. Radmore, Methods in Theoretical Quantum Optics (Clarendon Press, Oxford, 1997). [17] M. J. Bastiaans, J. Opt. Soc. Am. A 1, 711 (1984). [18] R. Bathia, Matrix Analysis (Springer Verlag, Berlin, 1997). [19] J. S. Bell, Physics 1, 195 (1964). [20] J. S. Bell, Speakable and Unspeakable in Quantum Mechanics (Cambridge University Press, Cambridge, 1987). [21] C. H. Bennett, H. J. Bernstein, S. Popescu, and B. Schumacher, Phys. Rev. A 53, 2046 (1996). [22] C. H. Bennett, G. Brassard, C. Crépeau, R. Jozsa, A. Peres, and W. K. Wootters, Phys. Rev. Lett. 70, 1895 (1993). 273
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ENTANGLEMENT OF GAUSSIAN STATES Ger
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Life’s Entanglement. CR Studio In
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Abstract This Dissertation collects
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x Contents 2.2.2.2. Symplectic repr
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xii Contents 7.2.3. Tripartite enta
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xiv Contents Chapter 13. Entangleme
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Introduction About eighty years aft
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Introduction 5 Gaussian states. Imp
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Introduction 7 The companion Part V
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10 1. Characterizing entanglement a
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12 1. Characterizing entanglement w
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14 1. Characterizing entanglement W
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16 1. Characterizing entanglement F
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18 1. Characterizing entanglement a
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20 1. Characterizing entanglement i
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22 1. Characterizing entanglement e
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24 1. Characterizing entanglement n
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26 1. Characterizing entanglement p
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CHAPTER 2 Gaussian states: structur
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2.1. Introduction to continuous var
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2.2. Mathematical description of Ga
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2.2. Mathematical description of Ga
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2.3. Degree of information encoded
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2.3. Degree of information encoded
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2.4. Standard forms of Gaussian cov
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Part II Bipartite entanglement of G
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52 3. Characterizing entanglement o
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54 3. Characterizing entanglement o
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CHAPTER 4 Two-mode entanglement Thi
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4.2. Entanglement and symplectic ei
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4.3. Entanglement versus Entropic m
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1 0.75 0.5 SL1 0.25 0 (a) 4.3. Enta
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Μ Μ1Μ2 3 2 1 1 4.3. Entanglemen
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global generalized entropy S3 globa
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4.4. Quantifying entanglement via p
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4.4. Quantifying entanglement via p
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4.5. Gaussian entanglement measures
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Ν p Σopt 1 0.8 0.6 0.4 0.2 0 4.5
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GEF GEF 4 3 2 1 0 4.6. Summary and
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4.6. Summary and further remarks 91
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94 5. Multimode entanglement under
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Part III Multipartite entanglement
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110 6. Gaussian entanglement sharin
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122 7. Tripartite entanglement in t
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148 8. Unlimited promiscuity of mul
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Part IV Quantum state engineering o
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160 9. Two-mode Gaussian states in
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CHAPTER 10 Tripartite and four-part
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10.1. Optical production of three-m
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(out) (in) TRITTER 10.1. Optical pr
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10.2. How to produce and exploit un
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CHAPTER 11 Efficient production of
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11.2. Generic entanglement and stat
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11.3. Economical state engineering
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Part V Operational interpretation a
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CHAPTER 13 Entanglement in Gaussian
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Page 288 and 289: 274 Bibliography [23] C. H. Bennett
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Page 296: 282 Bibliography [258] J. Von Neuma
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ENTANGLEMENT OF GAUSSIAN STATES Gerardo Adesso

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