. [. Bibliography, T. Assémat, D. Chambrion, and . Sugny, On the control by electromagnetic fields of quantum systems with infinite dimensional hilbert space, Journal of Mathematical Chemistry, vol.53, issue.1, pp.374-385, 2015.

]. R. Acsr17a, F. Azouit, A. Chittaro, P. Sarlette, and . Rouchon, Structure-preserving adiabatic elimination for open bipartite quantum systems, IFAC World Congress on Automatic Control, 2017.

]. R. Acsr17b, F. Azouit, A. Chittaro, P. Sarlette, and . Rouchon, Towards generic adiabatic elimination for composite open quantum systems, In Quantum Science and Technology, 2017.

I. [. Abramowitz and . Stegun, Handbook of Mathematical Functions, American Journal of Physics, vol.34, issue.2, 1965.
DOI : 10.1119/1.1972842

A. [. Azouit, P. Sarlette, and . Rouchon, Convergence and adiabatic elimination for a driven dissipative quantum harmonic oscillator, 2015 54th IEEE Conference on Decision and Control (CDC), 2015.
DOI : 10.1109/CDC.2015.7403235

URL : https://hal.archives-ouvertes.fr/hal-01245092

]. R. Asr16a, A. Azouit, P. Sarlette, and . Rouchon, Adiabatic elimination for open quantum systems with effective lindblad master equations, 55th IEEE Conference on Decision and Control, p.2016, 2016.

]. R. Asr16b, A. Azouit, P. Sarlette, and . Rouchon, Well-posedness and convergence of the lindblad master equation for a quantum harmonic oscillator with multiphoton drive and damping. ESAIM: Control, Optimisation and Calculus of Variations, pp.1353-1369, 2016.

. H. Bbc-+-93-]-c, G. Bennett, C. Brassard, R. Crépeau, A. Jozsa et al., Teleporting an unknown quantum state via dual classical and Einstein-Podolsky-Rosen channels, Physical Review Letters, issue.13, pp.701895-1899, 1993.

]. R. Bha07 and . Bhatia, Positive Definite Matrices, 2007.

J. [. Bacon, D. A. Kempe, K. B. Lidar, and . Whaley, Universal Fault-Tolerant Quantum Computation on Decoherence-Free Subspaces, Physical Review Letters, vol.95, issue.8, p.851758, 2000.
DOI : 10.1103/PhysRevLett.85.194

URL : http://arxiv.org/pdf/quant-ph/9909058

H. [. Baumgartner and . Narnhofer, Analysis of quantum semigroups with GKS???Lindblad generators: II. General, Journal of Physics A: Mathematical and Theoretical, vol.41, issue.39, p.41, 2008.
DOI : 10.1088/1751-8113/41/39/395303

H. [. Baumgartner, W. Narnhofer, and . Thirring, Analysis of quantum semigroups with GKS???Lindblad generators: I. Simple generators, Journal of Physics A: Mathematical and Theoretical, vol.41, issue.6, p.41065201, 2008.
DOI : 10.1088/1751-8113/41/6/065201

[. Breuer and F. Petruccione, The Theory of Open Quantum Systems, 2006.
DOI : 10.1093/acprof:oso/9780199213900.001.0001

[. Brion, L. H. Pedersen, and K. Mølmer, Adiabatic elimination in a lambda system, Journal of Physics A: Mathematical and Theoretical, vol.40, issue.5, p.1033, 2007.
DOI : 10.1088/1751-8113/40/5/011

A. [. Bouten and . Silberfarb, Adiabatic Elimination in Quantum Stochastic Models, Communications in Mathematical Physics, vol.137, issue.1, pp.491-505, 2008.
DOI : 10.1007/978-3-642-79504-6

D. [. Brodutch and . Terno, Why Should We Care About Quantum Discord?, Lectures on General Quantum Correlations and their Applications, pp.183-199, 2017.
DOI : 10.1038/nphys3653

URL : http://arxiv.org/pdf/1608.01920

]. L. Bvhs08, R. Bouten, A. Van-handel, and . Silberfarb, Approximation and limit theorems for quantum stochastic models with unbounded coefficients, Journal of Functional Analysis, vol.254, issue.12, pp.3123-3147, 2008.

]. J. Car81 and . Carr, Application of Center Manifold Theory, 1981.

]. H. Car93a and . Carmichael, An Open Systems Approach to Quantum Optics, 1993.

]. H. Car93b and . Carmichael, Quantum trajectory theory for cascaded open systems, Phys. Rev. Lett, vol.70, issue.15, pp.2273-2276, 1993.

]. Cho75 and . Choi, Completely positive linear maps on complex matrices, Linear Algebra and its Applications, vol.10, issue.3, pp.285-290, 1975.

]. J. Coh17 and . Cohen, Autonomous quantum error correction with superconducting circuits

B. [. Cohen-tannoudji, F. Diu, and . Laloë, Mécanique Quantique, volume I& II, 1977.

J. [. Cohen-tannoudji, G. Dupont-roc, and . Grynberg, Atom-Photon interaction: Basic Processes and Applications, 1992.

D. [. ?ernotík, K. Vasilyev, and . Hammerer, Adiabatic elimination of Gaussian subsystems from quantum dynamics under continuous measurement, Physical Review A, vol.92, issue.1, p.12124, 2015.
DOI : 10.1007/BF01044716

P. [. Cirac, H. Zoller, H. J. Kimble, and . Mabuchi, Quantum State Transfer and Entanglement Distribution among Distant Nodes in a Quantum Network, Physical Review Letters, vol.77, issue.16, p.783221, 1997.
DOI : 10.1103/PhysRevLett.77.3260

P. [. Duchêne and . Rouchon, Kinetic scheme reduction via geometric singular perturbation techniques Geometric singular perturbation theory for ordinary differential equations, Chemical Engineering Science Journal of Differential Equations, vol.51, issue.31, pp.4661-467253, 1979.

[. Facchi and S. Pascazio, Quantum Zeno Subspaces, Physical Review Letters, vol.452, issue.8, p.80401, 2002.
DOI : 10.1103/PhysRevD.21.2235

URL : http://arxiv.org/pdf/quant-ph/0201115

]. C. Gar86 and . Gardiner, Inhibition of atomic phase decays by squeezed light: A direct effect of squeezing, Physical Review Letters, vol.56, issue.18, pp.1917-1920, 1986.

M. [. Gough and . James, The Series Product and Its Application to Quantum Feedforward and Feedback Networks, IEEE Transactions on Automatic Control, vol.54, issue.11, pp.2530-2544, 2009.
DOI : 10.1109/TAC.2009.2031205

A. [. Gorini, E. C. Kossakowski, and . Sudarshan, Completely positive dynamical semigroups of N-level systems, Journal of Mathematical Physics, vol.17, issue.5, pp.821-825, 1976.
DOI : 10.1063/1.522979

H. [. Gough, S. Nurdin, and . Wildfeuer, Commutativity of the adiabatic elimination limit of fast oscillatory components and the instantaneous feedback limit in quantum feedback networks, Journal of Mathematical Physics, vol.36, issue.12, p.51123518, 2010.
DOI : 10.1063/1.2354331

]. J. Gvh07, R. Gough, and . Van-handel, Singular perturbation of quantum stochastic differential equations with coupling through an oscillator mode, Journal of Statistical Physics, vol.127, issue.3, pp.575-607, 2007.

P. [. Gardiner and . Zoller, Quantum noise, 2010.

[. Horodecki, P. Horodecki, M. Horodecki, and K. Horodecki, Quantum entanglement. Reviews of modern physics, p.865, 2009.

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

]. C. Jon95 and . Jones, Geometric singular perturbation theory. Dynamical systems, pp.44-118, 1995.

]. T. Kap99 and . Kaper, Systems theory for singular perturbation problems Analyzing Multiscale Phenomena Using Singular Perturbation Methods, p.5685, 1998.

]. T. Kat66 and . Kato, Perturbation Theory for Linear Operators, 1966.

]. E. Kes12 and . Kessler, Generalized Schrieffer-Wolff formalism for dissipative systems, Physical Review A, vol.86, issue.1, p.12126, 2012.

]. H. Kha92 and . Khalil, Nonlinear Systems, 1992.

H. [. Kokotovi?, J. Khalil, and . O-'reilly, Singular perturbation methods in control: analysis and design, SIAM, 1999.
DOI : 10.1137/1.9781611971118

]. W. Klo83 and . Klonowski, Simplifying principles for chemical and enzyme reaction kinetics, Biophysical chemistry, vol.18, issue.2, pp.73-87, 1983.

I. [. Lidar, K. B. Chuang, and . Whaley, Decoherence-Free Subspaces for Quantum Computation, Physical Review Letters, vol.52, issue.12, p.812594, 1998.
DOI : 10.1103/PhysRevA.52.3457

]. G. Lin76 and . Lindblad, On the generators of quantum dynamical semigroups, Communications in Mathematical Physics, vol.48, 1976.

. Ltp-+-15-]-z, S. Leghtas, I. M. Touzard, A. Pop, B. Kou et al., Confining the state of light to a quantum manifold by engineered two-photon loss, Science, issue.6224, pp.347853-857, 2015.

K. [. Lidar and . Whaley, Decoherence-Free Subspaces and Subsystems, Irreversible Quantum Dynamics, pp.83-120, 2003.
DOI : 10.1007/3-540-44874-8_5

URL : http://arxiv.org/pdf/quant-ph/0301032

. Ma-+-14-]-m, Z. Mirrahimi, V. V. Leghtas, S. Albert, R. J. Touzard et al., Dynamically protected cat-qubits: a new paradigm for universal quantum computation, New Journal of Physics, vol.16, p.45014, 2014.

M. [. Macieszczak, I. Guu?, J. P. Lesanovsky, and . Garrahan, Towards a Theory of Metastability in Open Quantum Dynamics, Physical Review Letters, vol.5, issue.24, p.240404, 2016.
DOI : 10.1088/1751-8113/48/27/275304

P. [. Mirrahimi and . Rouchon, Singular Perturbations and Lindblad-Kossakowski Differential Equations, IEEE Transactions on Automatic Control, vol.54, issue.6, pp.1325-1329, 2009.
DOI : 10.1109/TAC.2009.2015542

URL : https://hal.archives-ouvertes.fr/hal-00447790

E. [. Misra and . Sudarshan, The Zeno???s paradox in quantum theory, Journal of Mathematical Physics, vol.140, issue.4, pp.756-763, 1977.
DOI : 10.1512/iumj.1972.21.21080

. H. Msb-+-16-]-m, M. Michael, R. T. Silveri, V. V. Brierley, J. Albert et al., New class of quantum error-correcting codes for a bosonic mode, Physical Review X, vol.6, issue.3, p.31006, 2016.

. W. Mwb-+-13-]-k, S. J. Murch, K. M. Weber, E. Beck, I. Ginossar et al., Reduction of the radiative decay of atomic coherence in squeezed vacuum, Nature, issue.7456, pp.49962-65, 2013.

I. [. Nielsen and . Chuang, Quantum Computation and Quantum Information, 2000.

J. [. Nurdin and . Gough, On structure-preserving transformations of the Ito generator matrix for model reduction of quantum feedback networks, Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences, vol.35, issue.1979, pp.5422-5436, 1979.
DOI : 10.1007/BF01198172

J. [. Poyatos, P. Cirac, and . Zoller, Quantum Reservoir Engineering with Laser Cooled Trapped Ions, Physical Review Letters, vol.74, issue.23, pp.4728-4731, 1996.
DOI : 10.1103/PhysRevLett.74.4091

A. [. Reiter and . Sørensen, Effective operator formalism for open quantum systems, Physical Review A, vol.85, issue.3, p.32111, 2012.
DOI : 10.1088/1751-8113/42/15/153001

URL : http://arxiv.org/pdf/1112.2806

]. J. Sak94 and . Sakurai, Quantum Mechanics, 1994.

M. [. Sarlette, J. M. Brune, P. Raimond, and . Rouchon, Stabilization of Nonclassical States of the Radiation Field in a Cavity by Reservoir Engineering, Physical Review Letters, vol.107, issue.1, p.10402, 2011.
DOI : 10.1103/PhysRevA.80.013805

URL : https://hal.archives-ouvertes.fr/hal-00638446

]. P. Sho94 and . Shor, Algorithms for quantum computation: Discrete logarithms and factoring, 35th Annual Symposium on Foundations of Computer Science, pp.124-134, 1994.

P. [. Stannigel, P. Rabl, and . Zoller, Driven-dissipative preparation of entangled states in cascaded quantum-optical networks, New Journal of Physics, vol.14, issue.6, p.63014, 2012.
DOI : 10.1088/1367-2630/14/6/063014

]. A. Ste96 and . Steane, Error correcting codes in quantum theory, Physical Review Letters, vol.77, issue.5, p.793, 1996.

]. V. Tar08 and . Tarasov, Quantum Mechanics of Non-Hamiltonian and Dissipative Systems, 2008.

]. A. Tik52 and . Tikhonov, Systems of differential equations containing small parameters in the derivatives, pp.575-586, 1952.

C. [. Tang, A. Prieur, and . Girard, Tikhonov theorem for linear hyperbolic systems, Automatica, vol.57, pp.1-10, 2015.
DOI : 10.1016/j.automatica.2015.03.028

URL : https://hal.archives-ouvertes.fr/hal-01064805

M. Ueda, Probability-density-functional description of quantum photodetection processes, Quantum Optics: Journal of the European Optical Society Part B, vol.1, issue.2, p.131, 1989.
DOI : 10.1088/0954-8998/1/2/005

]. F. Ver05 and . Verhulst, Methods and Applications of Singular Perturbations: Boundary Layers and Multiple Timescale Dynamics, 2005.

H. [. Warszawski and . Wiseman, Adiabatic elimination in compound quantum systems with feedback, Physical Review A, vol.13, issue.1, p.13803, 2000.
DOI : 10.1088/0305-4470/13/2/034

L. [. Zanardi and . Venuti, Coherent Quantum Dynamics in Steady-State Manifolds of Strongly Dissipative Systems, Physical Review Letters, vol.113, issue.24, p.240406, 2014.
DOI : 10.1103/PhysRevA.63.042307