. Dans-le-troisème-chapitre-on-avait-choisi, |1, |0) comme base d'un élement de la chaîne. Ici on préfère inverser l'ordre et prendre la même base (|0, |1) que dans l'article [4] pour que le lecteur intéressé puisse s'y référer facilement, En effet on répète qu'on va ici reprendre sans démonstrations les résultats de

A. Aspect, J. Dalibard, and G. Roger, Experimental Test of Bell's Inequalities Using Time- Varying Analyzers, Physical Review Letters, vol.49, issue.25, pp.1804-1807, 1982.
DOI : 10.1103/PhysRevLett.49.1804

A. Aspect, P. Grangier, and G. Roger, : A New Violation of Bell's Inequalities, Physical Review Letters, vol.49, issue.2, pp.91-94, 1982.
DOI : 10.1103/PhysRevLett.49.91

S. Attal and A. Joye, The Langevin equation for a quantum heat bath, Journal of Functional Analysis, vol.247, issue.2, pp.253-288, 2007.
DOI : 10.1016/j.jfa.2006.09.019
URL : https://hal.archives-ouvertes.fr/hal-00348741

S. Attal and A. Joye, Weak Coupling and Continuous Limits for Repeated Quantum Interactions, Journal of Statistical Physics, vol.85, issue.6, pp.1241-1283, 2007.
DOI : 10.1007/s10955-006-9085-z
URL : https://hal.archives-ouvertes.fr/hal-00348746

S. Attal, A. Joye, and C. Pillet, Open Quantum Systems, Volume I : The Hamiltonian Approach, Volume II : The Markovian Approach, Volume III : Recent Developments, volume 1880-1881-1882 of Lecture Notes in Mathematics, 2006.

S. Attal and Y. Pautrat, From Repeated to Continuous Quantum Interactions, Annales Henri Poincar??, vol.7, issue.1, pp.59-104, 2006.
DOI : 10.1007/s00023-005-0242-8

L. E. Ballentine, Quantum Mechanics, 1990.

J. S. Bell, On the einstein-poldolsky-rosen paradox, Physics, vol.1, pp.195-200, 1964.

O. Brattelli and D. Robinson, Operator Algebras and Quantum Statistical Mechanics II. Texts and Monograph in Physics, 1981.

D. Braun, Creation of Entanglement by Interaction with a Common Heat Bath, Physical Review Letters, vol.89, issue.27, p.277901, 2002.
DOI : 10.1103/PhysRevLett.89.277901
URL : https://hal.archives-ouvertes.fr/hal-00123796

H. Breuer and F. Petruccione, The Theory of Open Quantum Systems, 2002.
DOI : 10.1093/acprof:oso/9780199213900.001.0001

L. Bruneau, A. Joye, and M. Merkli, Random Repeated Interaction Quantum Systems, Entanglement and Decoherence, pp.553-581, 2008.
DOI : 10.1007/s00220-008-0580-8
URL : https://hal.archives-ouvertes.fr/hal-00348736

D. E. Browne, C. Lu, T. Yang, and J. Pan, Demonstration of shor's quantum factoring algorithm using photonic qubits, Phys. Rev. Lett, vol.99, p.250504, 2007.

H. J. Carmichael, An open system approach to quantum optics, Lectures Notes in Physics, volume Series M18, 1993.

A. R. Carvalho, M. Busse, O. Brodier, C. Viviescas, and A. Buchleitner, Optimal Dynamical Characterization of Entanglement, Physical Review Letters, vol.98, issue.19, 2007.
DOI : 10.1103/PhysRevLett.98.190501

A. R. Carvalho and J. J. Hope, Stabilizing entanglement by quantum-jump-based feedback, Physical Review A, vol.76, issue.1, p.10301, 2007.
DOI : 10.1103/PhysRevA.76.010301
URL : http://hdl.handle.net/1885/18366

A. R. Carvalho and M. F. Santos, Distant entanglement protected through artificially increased local temperature, New Journal of Physics, vol.13, issue.1, p.13010, 2011.
DOI : 10.1088/1367-2630/13/1/013010
URL : http://doi.org/10.1088/1367-2630/13/1/013010

C. Cohen-tannoudji, J. Dupont-roc, and G. Grynberg, Photons et atomes-Introduction à l'électrodynamique quantique, EDP Sciences- CNRS Éditions, 2001.

C. Cormick and J. P. Paz, Observing different phases for the dynamics of entanglement in an ion trap, Physical Review A, vol.81, issue.2, p.22306, 2010.
DOI : 10.1103/PhysRevA.81.022306

J. Dalibard, Y. Castin, and K. Mølmer, Wave-function approach to dissipative processes in quantum optics, Physical Review Letters, vol.68, issue.5, pp.580-583, 1992.
DOI : 10.1103/PhysRevLett.68.580

E. B. Davies, Markovian master equations, Communications in Mathematical Physics, vol.46, issue.2, pp.91-110, 1974.
DOI : 10.1007/BF01608389

E. B. Davies, Markovian master equations. II, Mathematische Annalen, vol.13, issue.2, pp.147-158, 1976.
DOI : 10.1007/BF01351898

L. Diosí, Irreversible quantum dynamics, Lectures Notes in Physics, 2003.

P. J. Dodd and J. J. Halliwell, Disentanglement and decoherence by open system dynamics, Physical Review A, vol.69, issue.5, p.52105, 2004.
DOI : 10.1103/PhysRevA.69.052105
URL : http://arxiv.org/abs/quant-ph/0312068

L. Duan, G. Giedke, J. I. Cirac, and P. Zoller, Inseparability Criterion for Continuous Variable Systems, Physical Review Letters, vol.84, issue.12, pp.2722-2725, 2000.
DOI : 10.1103/PhysRevLett.84.2722

A. Einstein, B. Podolsky, and N. Rosen, Can quantum-mechanical description of physical reality be considere complete ? Physical Review, pp.777-780, 1935.

B. Englert and N. Metwally, Remarks on 2???q-bit states, Applied Physics B, vol.72, issue.1, pp.35-42, 2001.
DOI : 10.1007/s003400000502

A. Furusawa, Unconditional Quantum Teleportation, Science, vol.282, issue.5389, pp.706-709, 1998.
DOI : 10.1126/science.282.5389.706

B. P. Lanyon, Experimental Demonstration of a Compiled Version of Shor???s Algorithm with Quantum Entanglement, Physical Review Letters, vol.99, issue.25, p.250505, 2007.
DOI : 10.1103/PhysRevLett.99.250505

C. Langer, Long-Lived Qubit Memory Using Atomic Ions, Physical Review Letters, vol.95, issue.6, p.60502, 2005.
DOI : 10.1103/PhysRevLett.95.060502

D. Leibfried, Experimental demonstration of a robust, high-fidelity geometric two ion-qubit phase gate, Nature, vol.272, issue.6930, pp.412-415, 2003.
DOI : 10.1103/PhysRevA.62.042305

H. Häffner, Robust entanglement, Applied Physics B, vol.36, issue.2-3, pp.151-153, 2005.
DOI : 10.1007/s00340-005-1917-z

L. Mazolla, Sudden death and sudden birth of entanglement in common structured reservoirs, Physical Review A, vol.79, issue.4, p.42302, 2009.
DOI : 10.1103/PhysRevA.79.042302

M. P. Almeida, Environment-Induced Sudden Death of Entanglement, Science, vol.316, issue.5824, pp.579-582, 2007.
DOI : 10.1126/science.1139892

S. Fasel, N. Gisin, G. Ribordy, and H. Zbinden, Quantum key distribution over 30 km of standard fiber using energy-time entangled photon pairs: a comparison of two chromatic dispersion reduction methods, The European Physical Journal D, vol.85, issue.1, pp.143-148, 2004.
DOI : 10.1140/epjd/e2004-00080-8

R. P. Feynman, THE PRINCIPLE OF LEAST ACTION IN QUANTUM MECHANICS, 1942.
DOI : 10.1142/9789812567635_0001

R. P. Feynman and F. L. Vernon, The theory of a general quantum system interacting with a linear dissipative system, Annals of Physics, vol.24, pp.118-173, 1963.
DOI : 10.1016/0003-4916(63)90068-X

Z. Ficek and R. Tanas, Dark periods and revivals of entanglement in a two-qubit system, Physical Review A, vol.74, issue.2, p.24304, 2006.
DOI : 10.1103/PhysRevA.74.024304

M. C. Fischer, B. Gutierez-medina, and M. G. Raizen, Observation of the Quantum Zeno and Anti-Zeno Effects in an Unstable System, Physical Review Letters, vol.87, issue.4, p.40402, 2001.
DOI : 10.1103/PhysRevLett.87.040402

S. J. Freedman and J. F. Clauser, Experimental Test of Local Hidden-Variable Theories, Physical Review Letters, vol.28, issue.14, pp.938-941, 1972.
DOI : 10.1103/PhysRevLett.28.938

L. Gallardo, Mouvement Brownien Et Calcul D'itô. Hermann , Collection : Méthodes, 2008.

I. M. Gelfand and M. A. Naimark, On the imbedding of normed rings into the ring of operators on a hilbert space [47] F. Haake and R. Reibold. Strong damping and low-temperature anomalies for the harmonic oscillator, Math. Sbornik Phys. Rev. A, vol.12, issue.32, pp.197-2172462, 1943.

S. Haroche, Cours et travaux du Collège de France, 2008.

S. Haroche and J. Raymond, Exploring the Quantum : Atoms, Cavities and Photons, 2006.
DOI : 10.1093/acprof:oso/9780198509141.001.0001

R. A. Horn and C. R. Johnson, Matrix Analysis, 1985.

M. Horodecki, P. Horodecki, and R. Horodecki, Separability of mixed states: necessary and sufficient conditions, Physics Letters A, vol.223, issue.1-2, pp.1-8, 1996.
DOI : 10.1016/S0375-9601(96)00706-2

P. Horodecki, Separability criterion and inseparable mixed states with positive partial transposition, Physics Letters A, vol.232, issue.5, pp.333-339, 1997.
DOI : 10.1016/S0375-9601(97)00416-7

R. Horodecki and M. Horodecki, Information-theoretic aspects of inseparability of mixed states, Physical Review A, vol.54, issue.3, pp.1838-1843, 1996.
DOI : 10.1103/PhysRevA.54.1838

L. P. Hughston, R. Jozsa, and W. K. Wootters, A complete classification of quantum ensembles having a given density matrix, Physics Letters A, vol.183, issue.1, pp.14-18, 1993.
DOI : 10.1016/0375-9601(93)90880-9

V. Jaksic and C. Pillet, From resonances to master equations, Ann. Inst. H. Poincare Phys. Theor, vol.67, pp.425-445, 1997.
URL : https://hal.archives-ouvertes.fr/hal-00129123

A. Joye, REPEATED INTERACTIONS QUANTUM SYSTEMS: DETERMINISTIC AND RANDOM, Mathematical Results in Quantum Mechanics, 2008.
DOI : 10.1142/9789812832382_0012

R. and R. Jr, Entanglement preservation on two coupled cavities, Phys. Lett. A, vol.374, pp.2331-2334, 2010.

T. Kato, Perturbation theory for linear operators, 1966.

L. Landau and E. Lifchitz, Physique théorique 3, Mécanique Quantique, Éditions Mir, 1975.

R. Vargas-le-bert, Systèmes Quantiques d'Interactions Répétées : L'approche Perturbative, 2009.

J. L. Lebowitz and H. Spohn, Irreversible thermodynamics for quantum sys-tems weakly coupled to thermal reservoirs, Advances in Chemical Physics, vol.38, pp.109-142, 1978.

G. Lindblad, On the generators of quantum dynamical semigroups, Communications in Mathematical Physics, vol.66, issue.2, pp.119-130, 1976.
DOI : 10.1007/BF01608499

S. Maniscalco, F. Francica, R. L. Zaffino, and N. Lo-gullo, Protecting Entanglement via the Quantum Zeno Effect, Physical Review Letters, vol.100, issue.9, p.90503, 2008.
DOI : 10.1103/PhysRevLett.100.090503

E. Mascarenhas, D. Cavalcanti, V. Vedral, and M. F. Santos, Physically realizable entanglement by local continuous measurements, Physical Review A, vol.83, issue.2, p.22311, 2011.
DOI : 10.1103/PhysRevA.83.022311

E. Mascarenhas, B. Marques, D. Cavalcanti, M. O. Cunha, and M. F. Santos, Protection of quantum information and optimal singlet conversion through higher-dimensional quantum systems and environment monitoring, Physical Review A, vol.81, issue.3, p.32310, 2010.
DOI : 10.1103/PhysRevA.81.032310

M. Merkli, Entanglement evolution via quantum resonances, Journal of Mathematical Physics, vol.52, issue.9, p.92201, 2011.
DOI : 10.1063/1.3637628

M. Merkli, G. P. Berman, F. Borgonovi, and K. Gebresellasie, Evolution of entanglement of two qubits interacting through local and collective environments, Quantum Information and Computation, vol.11, pp.390-419, 2011.

N. Metropolis and S. Ulam, The Monte Carlo Method, Journal of the American Statistical Association, vol.44, issue.247, pp.335-341, 1949.
DOI : 10.1080/01621459.1949.10483310

G. L. Miller, Riemann's hypothesis and tests for primality, Journal of Computer and System Sciences, vol.13, issue.3, pp.300-317, 1976.
DOI : 10.1016/S0022-0000(76)80043-8

B. Misra and E. C. Sudarshan, The Zeno???s paradox in quantum theory, Journal of Mathematical Physics, vol.18, issue.4, pp.756-763, 1977.
DOI : 10.1063/1.523304

D. M. Mundarin and M. Orszag, Entanglement preservation by continuous distillation, Physical Review A, vol.79, issue.5, p.52333, 2009.
DOI : 10.1103/PhysRevA.79.052333

M. Mück, Thermal Relaxation for Particle Systems in Interaction with Several Bosonic Heat Reservoirs, 2004.

S. Nakajima, On Quantum Theory of Transport Phenomena, Progress of Theoretical Physics, vol.20, issue.6, pp.948-959, 1958.
DOI : 10.1143/PTP.20.948

H. Nha and H. J. Carmichael, Entanglement within the Quantum Trajectory Description of Open Quantum Systems, Physical Review Letters, vol.93, issue.12, p.120408, 2004.
DOI : 10.1103/PhysRevLett.93.120408

M. A. Nielsen and I. L. Chuang, Quantum Computation and Quantum Information, 2000.

M. Orszag and M. Hernandez, Coherence and entanglement in a two-qubit system, Advances in Optics and Photonics, vol.2, issue.2, pp.229-286, 2010.
DOI : 10.1364/AOP.2.000229

J. P. Paz and A. J. Roncaglia, Dynamical phases for the evolution of the entanglement between two oscillators coupled to the same environment, Physical Review A, vol.79, issue.3, p.32102, 2009.
DOI : 10.1103/PhysRevA.79.032102

C. Pellegrini, Existence, unicité et approximation des équations de Schrödinger stochastiques [81] A. Peres. Separability criterion for density matrices, Phys. Rev. Lett, vol.77, pp.1413-1415, 1996.

M. B. Plenio and P. L. Knight, The quantum-jump approach to dissipative dynamics in quantum optics, Reviews of Modern Physics, vol.70, issue.1, pp.101-144, 1998.
DOI : 10.1103/RevModPhys.70.101

M. O. Rabin, Probabilistic algorithm for testing primality, Journal of Number Theory, vol.12, issue.1, pp.128-138, 1980.
DOI : 10.1016/0022-314X(80)90084-0
URL : http://doi.org/10.1016/0022-314x(80)90084-0

J. M. Raymond, M. Brune, and S. Haroche, Manipulating quantum entanglement with atoms and photons in a cavity, Reviews of Modern Physics, vol.73, issue.3, pp.565-582, 2001.
DOI : 10.1103/RevModPhys.73.565

M. D. Reid and P. D. Drummond, Quantum Correlations of Phase in Nondegenerate Parametric Oscillation, Physical Review Letters, vol.60, issue.26, pp.2731-2733, 1998.
DOI : 10.1103/PhysRevLett.60.2731

F. Rouvière, Petit guide de calcul différentiel à l'usage de la licence et de l'agrégation. Cassini, 2003.

I. Sainz and G. Bjork, COMBATING ENTANGLEMENT SUDDEN DEATH WITH NON-LOCAL QUANTUM-ERROR CORRECTION, International Journal of Quantum Information, vol.07, issue.supp01, pp.245-255, 2009.
DOI : 10.1142/S0219749909004608

J. J. Sakurai, Modern Quantum Mechanics, 1994.

A. Sanpera, R. Tarrach, and G. Vidal, Local description of quantum inseparability, Physical Review A, vol.58, issue.2, pp.826-830, 1998.
DOI : 10.1103/PhysRevA.58.826

M. F. Santos, P. Milman, L. Davidovitch, and N. Zagury, Direct measurement of finite-time disentanglement induced by a reservoir, Physical Review A, vol.73, issue.4, p.40305, 2006.
DOI : 10.1103/PhysRevA.73.040305

E. Schrödinger, Discussion of Probability Relations between Separated Systems, Mathematical Proceedings of the Cambridge Philosophical Society, vol.31, issue.04, pp.555-563, 1935.
DOI : 10.1017/S0305004100013554

F. Schwalb, Quantum Mechanics, 2002.

I. E. Segal, Irreducible representations of operator algebras, Bulletin of the American Mathematical Society, vol.53, issue.2, pp.73-88, 1947.
DOI : 10.1090/S0002-9904-1947-08742-5

C. E. Shannon, A Mathematical Theory of Communication, Bell System Technical Journal, vol.27, issue.3, pp.379-423, 1948.
DOI : 10.1002/j.1538-7305.1948.tb01338.x

P. W. Shor, Polynomial-Time Algorithms for Prime Factorization and Discrete Logarithms on a Quantum Computer, SIAM Journal on Computing, vol.26, issue.5, pp.1484-1511, 1997.
DOI : 10.1137/S0097539795293172

D. Spehner, Contributions à la théorie du transport électronique dissipatif dans les solides apériodiques, 2000.

D. Spehner and M. Orszag, Quantum jump dynamics in cavity QED, Journal of Mathematical Physics, vol.43, issue.7, pp.3511-3537, 2002.
DOI : 10.1063/1.1476392
URL : https://hal.archives-ouvertes.fr/hal-00381959

W. T. Strunz, F. Haake, and D. Braun, Universality of decoherence for macroscopic quantum superpositions, Physical Review A, vol.67, issue.2, p.22101, 2003.
DOI : 10.1103/PhysRevA.67.022101

P. E. Toscheck and C. Wunderlich, What does an observed quantum system reveal to its observer?, The European Physical Journal D, vol.14, issue.3, pp.387-396, 2001.
DOI : 10.1007/s100530170207

L. Van-hove, Quantum-mechanical perturbations giving rise to a statistical transport equation, Physica, vol.21, issue.1-5, pp.517-540, 1955.
DOI : 10.1016/S0031-8914(54)92646-4

L. Van-hove, The approach to equilibrium in quantum statistics, Physica, vol.23, issue.1-5, pp.441-480, 1957.
DOI : 10.1016/S0031-8914(57)92891-4

C. Viviescas, I. Guevara, A. R. Carvalho, M. Busse, and A. Buchleitner, Entanglement Dynamics in Open Two-Qubit Systems via Diffusive Quantum Trajectories, Physical Review Letters, vol.105, issue.21, p.210502, 2010.
DOI : 10.1103/PhysRevLett.105.210502

S. Vogelsberger and D. Spehner, Average entanglement for Markovian quantum trajectories, Physical Review A, vol.82, issue.5, p.52327, 2010.
DOI : 10.1103/PhysRevA.82.052327
URL : https://hal.archives-ouvertes.fr/hal-01060038

S. Vogelsberger and D. Spehner, Entanglement evolution for quantum trajectories, Journal of Physics: Conference Series, vol.306, p.12029, 2011.
DOI : 10.1088/1742-6596/306/1/012029

H. Walther, Atoms in cavities and traps Advances in atomic, molecular , and optical physics, pp.379-405, 1994.

V. Weisskopf and E. Wigner, Berechnung der natürlichen linienbreite auf grund der diracschen lichttheorie, Zeitschrift für Physik, pp.54-73, 1930.

R. F. Werner, Quantum states with Einstein-Podolsky-Rosen correlations admitting a hidden-variable model, Physical Review A, vol.40, issue.8, pp.4277-4281, 1989.
DOI : 10.1103/PhysRevA.40.4277

H. M. Wiseman and G. J. Milburn, Quantum theory of field-quadrature measurements, Physical Review A, vol.47, issue.1, pp.642-662, 1993.
DOI : 10.1103/PhysRevA.47.642

H. M. Wiseman and G. J. Milburn, Quantum Measurement and Control, 2009.
DOI : 10.1017/CBO9780511813948

W. K. Wootters, Entanglement of Formation of an Arbitrary State of Two Qubits, Physical Review Letters, vol.80, issue.10, pp.2245-2248, 1998.
DOI : 10.1103/PhysRevLett.80.2245

S. Wu, The convex sum of product states for a separable state, Physics Letters A, vol.321, issue.5-6, pp.301-307, 2004.
DOI : 10.1016/j.physleta.2003.12.046

T. Yu and J. H. Eberly, Finite-Time Disentanglement Via Spontaneous Emission, Physical Review Letters, vol.93, issue.14, p.140404, 2004.
DOI : 10.1103/PhysRevLett.93.140404

W. H. Zureck, Decoherence and the Transition from Quantum to Classical ??? Revisited, Los Alamos Science, vol.27, pp.2-25, 2002.
DOI : 10.1007/978-3-7643-7808-0_1

R. Zwanzig, Ensemble Method in the Theory of Irreversibility, The Journal of Chemical Physics, vol.33, issue.5, pp.1338-1341, 1960.
DOI : 10.1063/1.1731409