Quantum Information Theory with Gaussian Systems

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Bibliography [7] M. Reed and B. Simon, Methods of modern mathematical physics, Vol. I and II (Academic Press, New York, 1972/1975). [8] R. Werner,Quantum harmonic analysis on phase space, J. Math. Phys. 25, 1404 (1984). [9] E. P.Wigner,On the Quantum Correction For Thermodynamic Equilibrium, Phys.Rev. 40, 749 (1932). [10] A. Grossmann,Parity operator and quantization of delta-functions, Comm. Math. Phys. 48, 191 (1976). [11] Arvind, B. Dutta, N. Mukunda and R. Simon,The real symplectic groups in quantum mechanics and optics, Pramana 45, 471 (1995); quant-ph/9509002 (1995). [12] Arvind, B. Dutta, N. Mukunda and R. Simon,Two-mode quantum systems: Invariant classification of squeezing transformations and squeezed states, Phys.Rev. A 52, 1609 (1995). [13] R. Simon, N. Mukunda and B. Dutta,Quantum-noise matrix for multimode systems: U(n) invariance, squeezing, and normal forms, Phys.Rev. A 49, 1567 (1994). [14] R. F. Werner,Quantum state with Einstein-Podolsky-Rosen correlations admitting a hidden-variable model, Phys.Rev. A 40, 4277 (1989). [15] M. M. Wolf, Partial Transposition in Quantum Information Theory, Doctoral thesis (TU Braunschweig, 2003); www.imaph.tu-bs.de/qi/papers.html. [16] A. Peres,Separability Criterion for Density Matrices, Phys.Rev. Lett. 77, 1413 (1996). [17] M. Horodecki, P.Horodecki and R. Horodecki,Separability of mixed states: necessary and sufficient conditions, Phys.Lett. A 223, 1 (1996). [18] R. F. Werner and M. M. Wolf,Bound Entangled Gaussian States, Phys.Rev. Lett. 86, 3658 (2001). [19] M. Takesaki, Theory of Operator Algebras, Vol. I (Springer, New York, 1979). [20] B. Demoen, P. Vanheuverzwijn and A. Verbeure,Completely positive maps on the CCR-algebra, Lett. Math.Phys. 2, 161 (1977). [21] B. Demoen, P. Vanheuverzwijn and A. Verbeure,Completely positive quasi-free maps of the CCR-algebra, Rep. Math. Phys. 15, 27 (1979). [22] A. S. Holevo and R. F. Werner,Evaluating capacities of bosonic Gaussian channels, Phys.Rev. A 63, 032312 (2001). 118
Bibliography [23] J. Eisert and M. B. Plenio,Conditions for the Local Manipulation of Gaussian States, Phys.Rev.Lett. 89, 097901 (2002). [24] J. Fiuráˇsek,Gaussian Transformations and Distillation of Entangled Gaussian States, Phys.Rev. Lett. 89, 137904 (2002). [25] K. Kraus, States, Effects and Operations, edited by A. Bohm, J. D. Dollard and W. H. Wootters (Springer, Berlin, 1983). [26] W. K. Wooters and W. H. Zurek,A single quantum cannot be cloned, Nature (London) 299, 802 (1982). [27] H. Barnum, C. M. Caves, C. A. Fuchs, R. Josza and B. Schumacher, Noncommuting Mixed States Cannot Be Broadcast, Phys.Rev.Lett. 76, 2818 (1996). [28] R. F. Werner,Quantum information theory – an invitation, in Quantum Information – An Introduction to Basic Theoretical Concepts and Experiments, by G. Alber et al., Springer Tracts in Modern Physics Vol. 173 (Springer, Berlin, 2001). [29] R. F. Werner,The Uncertainty Relation for Joint Measurement of Position and Momentum, in Quantum Information, Statistics, Probability, edited by O. Hirota (Rinton, Princeton/NJ, 2004). [30] F. Grosshans and N. J.Cerf,Continuous-Variable Quantum Cryptography is Secure against Non-Gaussian Attacks, Phys.Rev.Lett. 92, 047905 (2004). [31] F. Grosshans, G. Van Assche, J.Wenger, R. Brouri, N. J. Cerf and P. Grangier, Quantum key distribution using gaussian-modulated coherent states, Nature (London) 421, 238 (2003). [32] S. Iblisdir, G. Van Assche and N. J.Cerf,Security of Quantum Key Distribution with Coherent States and Homodyne Detection, Phys.Rev. Lett. 93, 170502 (2004). [33] V. Buˇzek and M. Hillery,Quantum copying: Beyond the no-cloning theorem, Phys.Rev. A 54, 1844 (1996). [34] N. Gisin and S. Massar,Optimal Quantum Cloning Machines, Phys.Rev. Lett. 79, 2153 (1997). [35] D. Bruss, D. P. DiVincenzo, A. Ekert, C.A. Fuchs, C. Macchiavello and J. A. Smolin,Optimal universal and state-dependent quantum cloning, Phys.Rev. A 57, 2368 (1998). [36] V. Buˇzek and M. Hillery,Universal optimal cloning of qubits and quantum registers, in Proceedings of the 1st nasa Int.Conf.on Quantum Computing and Communications (1998) and quant-ph/9801009 (1998);Universal optimal cloning of arbitrary quantum states: from qubits to quantum registers, Phys.Rev. Lett 81, 5003 (1998). 119
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Quantum Information Theory with Gau
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Vorveröffentlichungen der Disserta
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Contents Quantum Cellular Automata
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List of Figures viii
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List of Theorems x
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Summary mum is reached by a measure
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Summary 4
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1 Introduction electromagnetic fiel
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1 Introduction 8
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2 Basics of Gaussian systems Since
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2 Basics of Gaussian systems Theore
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2 Basics of Gaussian systems For a
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2 Basics of Gaussian systems for co
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2 Basics of Gaussian systems 2.2 Ga
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2 Basics of Gaussian systems As pur
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2 Basics of Gaussian systems unitar
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2 Basics of Gaussian systems In pha
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2 Basics of Gaussian systems Remark
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2 Basics of Gaussian systems 28
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3 Optimal cloners for coherent stat
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3.1 Setup 3.1 Setup A deterministic
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f2(T) 1 0 (a) 1 f1(T) f2(T) 1 0 (
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the expectation value of an arbitra
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3.3 Covariance clone). A more gener
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3.3 Covariance In the case of joint
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3.3 Covariance where the second ide
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3.4 Optimization search to covarian
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3.4 Optimization Hence for the case
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1 2 3 1 2 0 f2 1 2 (a) 2 3 1 f1 0.0
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3.4 Optimization tained without app
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= π R 2 0 dt ǫ + R2 = π log , ǫ
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3.4 Optimization where the bound is
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3.4 Optimization wheren is the matr
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3.4 Optimization Lemma 3.10: The ou
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3.5 Optical implementation The wei
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3.6 Teleportation criteria can be t
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3.6 Teleportation criteria carry th
Page 77: Quantum Cellular Automata
Page 80 and 81: 4 Gaussian quantum cellular automat
Page 111 and 112: 5 Gaussian private quantum channels
Page 113 and 114: p Figure 5.1: Illustrating the encr
Page 115 and 116: characteristic function χrand(ξ)
Page 117 and 118: = − 1 2 2Nf i,j=1 where M ′ =
Page 119 and 120: p δ ξk ξ x 5.2 Security estimati
Page 121 and 122: 5.2 Security estimation where in th
Page 123 and 124: 5.3 Result and outlook 5.3 Result a
Page 125: Bibliography
Page 130 and 131: Bibliography [37] R. F. Werner,Opti
Page 132 and 133: Bibliography [69] N. Takei, H. Yone
Page 134 and 135: Bibliography 124
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Quantum Information Theory with Gaussian Systems

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