S. Laquelle, B. Sôaõ, and . Sôbõõ, Ceci provient directement de l'inégalité d'Araki-Lieb, selon

. Dans-la-suite-du-manuscrit, nous omettrons cette notation pour alléger les formules, en gardant à l'esprit que seules X A et P A

F. Grosshans and P. Grangier, Continuous Variable Quantum Cryptography Using Coherent States, Physical Review Letters, vol.88, issue.5, p.57902, 2002.
DOI : 10.1103/PhysRevLett.88.057902
URL : https://hal.archives-ouvertes.fr/hal-00509124

F. Grosshans, G. Van-assche, J. Wenger, R. Brouri, N. Cerf et al., Quantum key distribution using gaussian-modulated coherent states, Nature, vol.421, issue.6920, p.238, 2003.
DOI : 10.1038/nature01289
URL : https://hal.archives-ouvertes.fr/hal-00509181

F. Grosshans, Communication et cryptographie quantiques avec des variables continues, Thèse de doctorat, 2002.
URL : https://hal.archives-ouvertes.fr/tel-00002343

J. Wenger, Dispositifs impulsionnels pour la communication quantique à variables continues, Thèse de doctorat, 2004.
URL : https://hal.archives-ouvertes.fr/tel-00006926

J. Lodewyck, Dispositif de distribution quantique de clé avec des états cohérents à longueur d'onde télécom, Thèse de doctorat, 2006.

B. Schneier, Applied Cryptography, 1996.

A. Kerckhoffs, La cryptographie militaire, Journal des sciences militaires IX, vol.5, 1883.

C. Shannon, A Mathematical Theory of Communication / Communication Theory of Secrecy Systems, Bell System Technical Journal, vol.27, issue.379 623, 1948.

B. Schneier, The Blowfish Encryption Algorithm, Dr Dobbs Journal, vol.19, issue.38, 1994.

R. L. Rivest, A. Shamir, and L. Adleman, A method for obtaining digital signatures and public-key cryptosystems, Commun. ACM, vol.21, issue.120, 1978.

G. S. Vernam, Secret Signaling System, Brevet déposé aux États-Unis sous le numéro 1, p.719, 1919.

C. Bennett and G. Brassard, Quantum cryptography: Public key distribution and coin tossing, IEEE Conf. on Computers, Systems and Signal Processing, p.175, 1984.
DOI : 10.1016/j.tcs.2014.05.025

C. H. Bennett, Quantum cryptography using any two nonorthogonal states, Physical Review Letters, vol.68, issue.21, p.3121, 1992.
DOI : 10.1103/PhysRevLett.68.3121

D. Bruss, Optimal Eavesdropping in Quantum Cryptography with Six States, Physical Review Letters, vol.81, issue.14, p.3018, 1998.
DOI : 10.1103/PhysRevLett.81.3018

A. K. Ekert, Quantum cryptography based on Bell???s theorem, Physical Review Letters, vol.67, issue.6, p.661, 1991.
DOI : 10.1103/PhysRevLett.67.661

K. Inoue, E. Waks, and Y. Yamamoto, Differential Phase Shift Quantum Key Distribution, Physical Review Letters, vol.89, issue.3, p.37902, 2002.
DOI : 10.1103/PhysRevLett.89.037902

P. C. Sun, Y. Mazurenko, and Y. Fainman, Long-distance frequency-division interferometer for communication and quantum cryptography, Optics Letters, vol.20, issue.9, p.1062, 1995.
DOI : 10.1364/OL.20.001062

Y. T. Mazurenko, R. Giust, and J. P. Goedgebuer, Spectral coding for secure optical communications using refractive index dispersion, Optics Communications, vol.133, issue.1-6, 1997.
DOI : 10.1016/S0030-4018(96)00436-1

J. Mérolla, Y. Mazurenko, J. Goedgebuer, and W. T. Rhodes, Single-Photon Interference in Sidebands of Phase-Modulated Light for Quantum Cryptography, Physical Review Letters, vol.82, issue.8, p.1656, 1999.
DOI : 10.1103/PhysRevLett.82.1656

T. Debuisschert and W. Boucher, Time coding protocols for quantum key distribution, Physical Review A, vol.70, issue.4, p.42306, 2004.
DOI : 10.1103/PhysRevA.70.042306

D. Stucki, N. Brunner, N. Gisin, V. Scarani, and H. Zbinden, Fast and simple one-way quantum key distribution, Applied Physics Letters, vol.87, issue.19, p.194108, 2005.
DOI : 10.1063/1.2126792

W. Boucher and T. Debuisschert, Experimental implementation of time-coding quantum key distribution, Physical Review A, vol.72, issue.6, p.62325, 2005.
DOI : 10.1103/PhysRevA.72.062325

J. Bonneau and I. Mironov, Cache-collision timing attacks against AES " . Lecture notes in computer science 4249, p.201, 2006.

D. J. Bernstein, Cache-timing attacks on AES, 2004.

E. Wigner, On the Quantum Correction For Thermodynamic Equilibrium, Physical Review, vol.40, issue.5, p.749, 1932.
DOI : 10.1103/PhysRev.40.749

R. L. Hudson, When is the wigner quasi-probability density non-negative?, Reports on Mathematical Physics, vol.6, issue.2, p.249, 1974.
DOI : 10.1016/0034-4877(74)90007-X

C. Piquet, Fonctions de type positif associées à deux opérateurs hermitiens, 1974.

A. Einstein, B. Podolsky, and N. Rosen, Can Quantum-Mechanical Description of Physical Reality Be Considered Complete?, Physical Review, vol.47, issue.10, p.777, 1935.
DOI : 10.1103/PhysRev.47.777

W. H. Zurek, Decoherence, einselection, and the quantum origins of the classical, Reviews of Modern Physics, vol.75, issue.3, p.715, 2003.
DOI : 10.1103/RevModPhys.75.715

J. Williamson, On the Algebraic Problem Concerning the Normal Forms of Linear Dynamical Systems, American Journal of Mathematics, vol.58, issue.1, p.141, 1963.
DOI : 10.2307/2371062

R. García-patrón and . Sanchez, Quantum Information with Optical Continuous Variables : from Bell Tests to Key Distribution, Thèse de doctorat, 2007.

T. C. Ralph, Continuous variable quantum cryptography, Physical Review A, vol.61, issue.1, p.10303, 1999.
DOI : 10.1103/PhysRevA.61.010303

M. Hillery, Quantum cryptography with squeezed states, Physical Review A, vol.61, issue.2, p.22309, 2000.
DOI : 10.1103/PhysRevA.61.022309

N. J. Cerf, M. Lévy, and G. Van-assche, Quantum distribution of Gaussian keys using squeezed states, Physical Review A, vol.63, issue.5, p.52311, 2001.
DOI : 10.1103/PhysRevA.63.052311

C. Weedbrook, A. M. Lance, W. P. Bowen, T. Symul, T. C. Ralph et al., Quantum Cryptography Without Switching, Physical Review Letters, vol.93, issue.17, p.170504, 2004.
DOI : 10.1103/PhysRevLett.93.170504

N. J. Cerf and C. Adami, Quantum extension of conditional probability, Physical Review A, vol.60, issue.2, p.893, 1999.
DOI : 10.1103/PhysRevA.60.893

R. García-patrón and N. J. Cerf, Unconditional Optimality of Gaussian Attacks against Continuous-Variable Quantum Key Distribution, Physical Review Letters, vol.97, issue.19, p.190503, 2006.
DOI : 10.1103/PhysRevLett.97.190503

M. Navascués, F. Grosshans, and A. Acín, Optimality of Gaussian Attacks in Continuous-Variable Quantum Cryptography, Physical Review Letters, vol.97, issue.19, p.190502, 2006.
DOI : 10.1103/PhysRevLett.97.190502

A. S. Holevo, The capacity of the quantum channel with general signal states, IEEE Transactions on Information Theory, vol.44, issue.1, p.269, 1998.
DOI : 10.1109/18.651037

I. Devetak and A. Winter, Distillation of secret key and entanglement from quantum states, Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, vol.461, issue.2053, p.207, 2005.
DOI : 10.1098/rspa.2004.1372

I. Csiszár and J. Körner, Broadcast channels with confidential messages, IEEE Transactions on Information Theory, vol.24, issue.3, p.339, 1978.
DOI : 10.1109/TIT.1978.1055892

R. Renner and J. I. Cirac, de Finetti Representation Theorem for Infinite-Dimensional Quantum Systems and Applications to Quantum Cryptography, Physical Review Letters, vol.102, issue.11, p.110504, 2009.
DOI : 10.1103/PhysRevLett.102.110504

J. Lodewyck, M. Bloch, R. García-patrón, S. Fossier, E. Karpov et al., with an all-fiber continuous-variable system, Physical Review A, vol.76, issue.4, p.42305, 2007.
DOI : 10.1103/PhysRevA.76.042305

R. Ursin, F. Tiefenbacher, T. Schmitt-manderbach, H. Weier, T. Scheidl et al., Entanglement-based quantum communication over 144???km, Nature Physics, vol.39, issue.7, p.481, 2007.
DOI : 10.1103/PhysRevA.64.010102

T. Schmitt-manderbach, H. Weier, M. Fuerst, R. Ursin, F. Tiefenbacher et al., Experimental Demonstration of Free-Space Decoy-State Quantum Key Distribution over 144??km, Physical Review Letters, vol.98, issue.1, p.10504, 2007.
DOI : 10.1103/PhysRevLett.98.010504

A. Cozannet, M. Treheux, and R. Bouillie, Étude de la propagation de la lumière dans les fibres optiques à gradient d'indice, Annals of Telecommunications, vol.24, p.219, 1974.

J. Lodewyck, T. Debuisschert, R. Tualle-brouri, and P. Grangier, Controlling excess noise in fiber-optics continuous-variable quantum key distribution, Physical Review A, vol.72, issue.5, p.50303, 2005.
DOI : 10.1103/PhysRevA.72.050303

S. Fossier, E. Diamanti, T. Debuisschert, A. Villing, R. Tualle-brouri et al., Field test of a continuous-variable quantum key distribution prototype, New Journal of Physics, vol.11, issue.4, p.4502314, 2009.
DOI : 10.1088/1367-2630/11/4/045023
URL : https://hal.archives-ouvertes.fr/hal-00553585

H. Haseler, T. Moroder, and N. Lütkenhaus, Testing quantum devices: Practical entanglement verification in bipartite optical systems, Physical Review A, vol.77, issue.3, p.32303, 2008.
DOI : 10.1103/PhysRevA.77.032303

G. Van-assche, Quantum Cryptography and Secret-Key Distillation, 2006.
DOI : 10.1017/CBO9780511617744

G. Brassard and L. Salvail, Secret-Key Reconciliation by Public Discussion Advances in Cryptology, pp.410-423, 1994.

C. Crépeau, Réconciliation et Distillation publiques de secret

W. T. Buttler, S. K. Lamoreaux, J. R. Torgerson, G. H. Nickel, C. H. Donahue et al., Fast, efficient error reconciliation for quantum cryptography, Physical Review A, vol.67, issue.5, p.52303, 2003.
DOI : 10.1103/PhysRevA.67.052303

C. Berrou, A. Glavieux, and P. Thitimajshima, Near Shannon limit error-correcting coding and decoding: Turbo-codes. 1, Proceedings of ICC '93, IEEE International Conference on Communications, pp.1064-1070, 1993.
DOI : 10.1109/ICC.1993.397441

R. G. Gallager, Low-density parity-check codes, IEEE Transactions on Information Theory, vol.8, issue.1, 1962.
DOI : 10.1109/TIT.1962.1057683

M. Bloch, A. Thangaraj, and S. W. Mclaughlin, Efficient Reconciliation of Correlated Continuous Random Variables using LDPC Codes " . arXiv abs, p.509041, 2005.

R. C. Bose and D. Ray-chaudhuri, On a class of error correcting binary group codes, Information and Control, vol.3, issue.1, p.68, 1960.
DOI : 10.1016/S0019-9958(60)90287-4

A. Hocquenghem, Codes correcteurs d'erreurs, Chiffres (Paris), vol.2, p.147, 1959.

U. Wachsmann, R. F. Fischer, and J. B. Huber, Multilevel codes: theoretical concepts and practical design rules, IEEE Transactions on Information Theory, vol.45, issue.5, 1999.
DOI : 10.1109/18.771140

T. Richardson, M. Shokrollahi, and R. Urbanke, Design of capacity-approaching irregular low-density parity-check codes, IEEE Transactions on Information Theory, vol.47, issue.2, p.619, 2001.
DOI : 10.1109/18.910578

P. Radosavljevic, A. De-baynast, and J. Cavallaro, Optimized Message Passing Schedules for LDPC Decoding, Conference Record of the Thirty-Ninth Asilomar Conference onSignals, Systems and Computers, 2005., p.591, 2005.
DOI : 10.1109/ACSSC.2005.1599818

C. Bennett, G. Brassard, C. Crepeau, and U. Maurer, Generalized privacy amplification, IEEE Transactions on Information Theory, vol.41, issue.6, p.1915, 1995.
DOI : 10.1109/18.476316

J. L. Carter and M. N. Wegman, Universal classes of hash functions, STOC '77 : Proceedings of the ninth annual ACM symposium on Theory of computing, pp.106-112, 1977.
DOI : 10.1016/0022-0000(79)90044-8

D. R. Stinson, Universal Hashing and Authentication Codes, CRYPTO '91 : 11th Annual International Cryptology Conference on Advances in Cryptology, p.74, 1992.

A. J. Sharpe, D. Shields, M. Stucki, C. Suda, T. Tamas et al., The SECOQC quantum key distribution network in Vienna, New Journal of Physics, vol.11, p.75001, 2009.
URL : https://hal.archives-ouvertes.fr/hal-00559693

J. Dynes, Z. Yuan, A. Sharpe, and A. Shields, Decoy pulse quantum key distribution for practical purposes, IET Optoelectronics, vol.2, issue.5, p.195, 2008.
DOI : 10.1049/iet-opt:20070091

H. Hübel, M. R. Vanner, T. Lederer, B. Blauensteiner, T. Lorünser et al., High-fidelity transmission of polarization encoded qubits from an entangled source over 100 km of fiber, Optics Express, vol.15, issue.12, p.7853, 2007.
DOI : 10.1364/OE.15.007853

H. Weier, T. Schmitt-manderbach, N. Regner, C. Kurtsiefer, and H. Weinfurter, Free space quantum key distribution: Towards a real life application, Fortschritte der Physik, p.840, 2006.
DOI : 10.1002/prop.200610322

A. Leverrier and P. Grangier, Unconditional Security Proof of Long-Distance Continuous-Variable Quantum Key Distribution with Discrete Modulation, Physical Review Letters, vol.102, issue.18, p.180504, 2009.
DOI : 10.1103/PhysRevLett.102.180504
URL : https://hal.archives-ouvertes.fr/hal-00459177

T. Richardson and R. Urbanke, Multi-Edge Type LDPC Codes, Workshop honoring Prof. Bob McEliece on his 60th birthday, 2002.

A. Zavatta, S. Viciani, and M. Bellini, Quantum-to-Classical Transition with Single-Photon-Added Coherent States of Light, Science, vol.306, issue.5696, p.660, 2004.
DOI : 10.1126/science.1103190

H. Briegel, W. Dür, J. I. Cirac, and P. Zoller, Quantum Repeaters: The Role of Imperfect Local Operations in Quantum Communication, Physical Review Letters, vol.81, issue.26, p.5932, 1998.
DOI : 10.1103/PhysRevLett.81.5932

W. Dür, H. Briegel, J. I. Cirac, and P. Zoller, Quantum repeaters based on entanglement purification, Physical Review A, vol.59, issue.1, p.169, 1999.
DOI : 10.1103/PhysRevA.59.169

M. Fleischhauer and M. D. Lukin, Quantum memory for photons: Dark-state polaritons, Physical Review A, vol.65, issue.2, p.22314, 2002.
DOI : 10.1103/PhysRevA.65.022314

B. Julsgaard, J. Sherson, J. Cirac, J. Fiurá?-sek, and E. Polzik, Experimental demonstration of quantum memory for light, Nature, vol.6, issue.7016, p.482, 2004.
DOI : 10.1103/PhysRevLett.85.5639

T. C. Ralph and A. P. Lund, Nondeterministic Noiseless Linear Amplification of Quantum Systems, AIP Conference Proceedings, p.326, 2008.
DOI : 10.1063/1.3131295

J. A. Levenson, I. Abram, T. Rivera, and P. Grangier, Reduction of quantum noise in optical parametric amplification, Journal of the Optical Society of America B, vol.10, issue.11, p.2233, 1993.
DOI : 10.1364/JOSAB.10.002233
URL : https://hal.archives-ouvertes.fr/hal-00870996

R. Mears, L. Reekie, I. Jauncey, and D. Payne, Low-noise erbium-doped fibre amplifier operating at 1.54??m, Electronics Letters, vol.23, issue.19, p.1026, 1987.
DOI : 10.1049/el:19870719

E. Desurvire, J. R. Simpson, and P. C. Becker, High-gain erbium-doped traveling-wave fiber amplifier, Optics Letters, vol.12, issue.11, p.888, 1987.
DOI : 10.1364/OL.12.000888

C. M. Caves, Quantum limits on noise in linear amplifiers, Physical Review D, vol.26, issue.8, p.1817, 1982.
DOI : 10.1103/PhysRevD.26.1817

D. T. Pegg, L. S. Phillips, and S. M. Barnett, Optical State Truncation by Projection Synthesis, Physical Review Letters, vol.81, issue.8, p.1604, 1998.
DOI : 10.1103/PhysRevLett.81.1604

A. Ourjoumtsev, ??tude th??orique et exp??rimentale de superpositions quantiques coh??rentes et d'??tats intriqu??s non-gaussiens de la lumi??re, Thèse de doctorat, 2007.
DOI : 10.1051/anphys:2008045
URL : https://pastel.archives-ouvertes.fr/tel-00200715/document

J. Lodewyck and P. Grangier, Tight bound on the coherent-state quantum key distribution with heterodyne detection, Physical Review A, vol.76, issue.2, p.22332, 2007.
DOI : 10.1103/PhysRevA.76.022332

J. Sudjana, L. Magnin, R. Garcia-patron, and N. J. Cerf, Tight bounds on the eavesdropping of a continuous-variable quantum cryptographic protocol with no basis switching, Physical Review A, vol.76, issue.5, p.52301, 2007.
DOI : 10.1103/PhysRevA.76.052301