278 Bibliography [140] J. Laurat, T. Coudreau, N. Treps, A. Maître, and C. Fabre, Phys. Rev. Lett. 91, 213601 (2003). [141] J. Laurat, L. Longchambon, T. Coudreau, G. Keller, N. Treps, and C. Fabre, Phys. Rev. A 71, 022313 (2005). [142] S. Lee, D. P. Chi, S. D. Oh, and J. Kim, Phys. Rev. A 68, 062304 (2003). [143] G. Leuchs and T. Beth eds., Quantum Information Processing (Wiley–VCH, Berlin, 2003). [144] M. Lewenstein, D. Bruß, J. I. Cirac, B. Kraus, M. Kuś, J. Samsonowicz, A. Sanpera, and R. Tarrach, J. Mod. Opt. 47, 2841 (2000). [145] M. Lewenstein, B. Kraus, J. I. Cirac, and P. Horodecki, Phys. Rev. A 62, 052310 (2000). [146] N. Linden, S. Popescu, and A. Sudbery, Phys. Rev. Lett. 83, 243 (1999). [147] L. Longchambon, J. Laurat, T. Coudreau, and C. Fabre, Eur. Phys. J. D 30, 279 (2004). [148] C.-Y. Lu, X.-Q. Zhou, O. Gühne, W.-B. Gao, J. Zhang, Z.-S. Yuan, A. Goebel, T. Yang, and J.-W. Pan, e–print quant-ph/0609130 (2006). [149] A. Marshall and I. Olkin, Inequalities: Theory of Majorization and Its Applications (Academic Press, San Diego, 1979). [150] L. Masanes, e–print quant-ph/0510188 (2005). [151] L. Masanes, Phys. Rev. Lett. 96, 150501 (2006). [152] E. J. Mason and N. C. Wong, Opt. Lett. 23, 1733 (1998). [153] D. McHugh, M. Ziman, and V. Bu˘zek, Phys. Rev. A 74, 042303 (2006). [154] D. McHugh, M. Ziman, and V. Bu˘zek, Phys. Rev. A 74, 050306(R) (2006). [155] N. C. Menicucci, P. van Loock, M. Gu, C. Weedbrook, T. C. Ralph, and M. A. Nielsen, Phys. Rev. Lett. 97, 110501 (2005). [156] F. Mintert, M. Kuś, and A. Buchleitner, Phys. Rev. Lett. 92, 167902 (2004). [157] A. Miranowicz, M. Piani, P. Horodecki, and R. Horodecki, e–print quantph/0605001 (2006). [158] W. J. Munro, D. F. V. James, A. G. White, and P. G. Kwiat, Phys. Rev. A 64, 030302(R) (2001). [159] M. Murao, D. Jonathan, M. B. Plenio, and V. Vedral, Phys. Rev. A 59, 156 (1999). [160] M. Navascues and A. Acin, Phys. Rev. Lett. 94, 020505 (2005). [161] R. Neigovzen and A. Sanpera, e–print quant-ph/0507249 (2005). [162] H. Nha and J. Kim, Phys. Rev. A 74, 012317 (2006). [163] M. A. Nielsen and I. L. Chuang, Quantum Computation and Quantum Information (Cambridge University Press, Cambridge, 2000). [164] M. A. Nielsen and J. Kempe, Phys. Rev. Lett. 86, 5184 (2001). [165] D. K. L. Oi and J. Åberg, e–print quant-ph/0603157 (2006). [166] R. Oliveira, O. C. O. Dahlsten, and M. B. Plenio, e–print quant-ph/0605126 (2006). [167] T. J. Osborne, e–print quant-ph/0402055 (2004). [168] T. J. Osborne and M. A. Nielsen, Phys. Rev. A 66, 032110 (2002).
Bibliography 279 [169] T. J. Osborne and F. Verstraete, Phys. Rev. Lett. 96, 220503 (2006). [170] A. Osterloh, L. Amico, G. Falci, and R. Fazio, Nature 416, 608 (2002). [171] Z. Y. Ou, S. F. Pereira, H. J. Kimble, and K. C. Peng, Phys. Rev. Lett. 68, 3663 (1992). [172] A. Ourjoumtsev, A. Dantan, R. Tualle-Brouri, and Ph. Grangier, Phys. Rev. Lett. 98, 030502 (2007). [173] M. Owari, S. L. Braunstein, K. Nemoto, and M. Murao, e–print quantph/0609167. [174] M. G. A. Paris, Quantum filtering by two-photocurrent devices, Proc. of the 7th International Conference on Squeezed States and Uncertainty Relations, (Boston University, Boston, 2001). [175] M. Paternostro, M. S. Kim, and G. M. Palma, e–print quant-ph/0612045 (2006). [176] M. Paternostro, W. Son, M. S. Kim, G. Falci, and G. M. Palma, Phys. Rev. A 70, 022320 (2004). [177] A. Peres, Quantum Theory: Concepts and Methods (Kluwer Achademic Publishers, Dordrecht, 1993). [178] A. Peres, Phys. Rev. Lett. 77, 1413 (1996). [179] A. Peres and D. R. Terno, Rev. Mod. Phys. 76, 93 (2004). [180] D. Perez-Garcia, F. Verstraete, M. M. Wolf, and J. I. Cirac, e–print quantph/0608197 (2006). [181] S. Pirandola, Int. J. Quant. Inf. 3, 239 (2005). [182] S. Pirandola and S. Mancini, Laser Physics 16, 1418 (2006). [183] S. Pirandola, S. Mancini, and D. Vitali, Phys. Rev. A 71, 042326 (2005), erratum ibid. 72, 059901 (2005). [184] S. Pirandola, S. Mancini, D. Vitali, and P. Tombesi, Phys. Rev. A 68, 062317 (2003). [185] S. Pirandola, D. Vitali, P. Tombesi, and S. Lloyd, Phys. Rev. Lett. 97, 150403 (2006). [186] M. B. Plenio, Phys. Rev. Lett. 95, 090503 (2005). [187] M. B. Plenio, J. Eisert, J. Dreißig, and M. Cramer, Phys. Rev. Lett. 94, 060503 (2005). [188] M. B. Plenio and S. Virmani, Quant. Inf. Comp. 7, 1 (2007). [189] S. Popescu and D. Rohrlich, Found. Phys. 24, 379 (1994). [190] S. Popescu and D. Rohrlich, Phys. Rev. A 56, 3319(R) (1997). [191] J. Preskill, Quantum Information and Computation (Lecture Notes for Physics 229, California Institute of Technology, 1998). [192] R. Raussendorf and H. J. Briegel, Phys. Rev. Lett. 86, 5188 (2001). [193] M. Reck, A. Zeilinger, H. J. Bernstein, and P. Bertani, Phys. Rev. Lett. 73, 58 (1994). [194] A. Rényi, Probability Theory (North Holland, Amsterdam, 1970). [195] G. Rigolin and M. C. de Oliveira, e–print quant-ph/0608184 (2006). [196] G. Rigolin and C. O. Escobar, Phys. Rev. A 69, 012307 (2004). [197] H. P. Robertson, Phys. Rev. 34, 163 (1929).
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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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2.4. Standard forms of Gaussian cov
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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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4.3. Entanglement versus Entropic m
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Μ Μ1Μ2 3 2 1 1 4.3. Entanglemen
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4.3. Entanglement versus Entropic m
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4.3. Entanglement versus Entropic m
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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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4.5. Gaussian entanglement measures
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4.5. Gaussian entanglement measures
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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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96 5. Multimode entanglement under
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98 5. Multimode entanglement under
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100 5. Multimode entanglement under
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102 5. Multimode entanglement under
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104 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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112 6. Gaussian entanglement sharin
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114 6. Gaussian entanglement sharin
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116 6. Gaussian entanglement sharin
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118 6. Gaussian entanglement sharin
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120 6. Gaussian entanglement sharin
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122 7. Tripartite entanglement in t
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124 7. Tripartite entanglement in t
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126 7. Tripartite entanglement in t
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128 7. Tripartite entanglement in t
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130 7. Tripartite entanglement in t
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132 7. Tripartite entanglement in t
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134 7. Tripartite entanglement in t
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136 7. Tripartite entanglement in t
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138 7. Tripartite entanglement in t
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140 7. Tripartite entanglement in t
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142 7. Tripartite entanglement in t
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144 7. Tripartite entanglement in t
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146 7. Tripartite entanglement in t
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148 8. Unlimited promiscuity of mul
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150 8. Unlimited promiscuity of mul
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152 8. Unlimited promiscuity of mul
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154 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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162 9. Two-mode Gaussian states in
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164 9. Two-mode Gaussian states in
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166 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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CHAPTER 11 Efficient production of
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11.2. Generic entanglement and stat
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11.2. Generic entanglement and stat
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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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196 12. Multiparty quantum communic
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198 12. Multiparty quantum communic
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200 12. Multiparty quantum communic
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202 12. Multiparty quantum communic
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204 12. Multiparty quantum communic
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206 12. Multiparty quantum communic
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208 12. Multiparty quantum communic
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210 12. Multiparty quantum communic
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212 12. Multiparty quantum communic
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214 12. Multiparty quantum communic
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216 12. Multiparty quantum communic
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CHAPTER 13 Entanglement in Gaussian
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13.1. Gaussian valence bond states
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Eq. (13.3) thus takes the form 13.1
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13.2. Entanglement distribution in
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- Page 286 and 287: 272 List of Publications [GA11] G.
- Page 288 and 289: 274 Bibliography [23] C. H. Bennett
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