The Theory of Open Quantum Systems
Abstract
Abstract This book treats the central physical concepts and mathematical techniques used to investigate the dynamics of open quantum systems. To provide a self-contained presentation, the text begins with a survey of classical probability theory and with an introduction to the foundations of quantum mechanics, with particular emphasis on its statistical interpretation and on the formulation of generalized measurement theory through quantum operations and effects. The fundamentals of density matrix theory, quantum Markov processes, and completely positive dynamical semigroups are developed. The most important master equations used in quantum optics and condensed matter theory are derived and applied to the study of many examples. Special attention is paid to the Markovian and non-Markovian theory of environment induced decoherence, its role in the dynamical description of the measurement process, and to the experimental observation of decohering electromagnetic field states. The book includes the modern formulation of open quantum systems in terms of stochastic processes in Hilbert space. Stochastic wave function methods and Monte Carlo algorithms are designed and applied to important examples from quantum optics and atomic physics. The fundamentals of the treatment of non-Markovian quantum processes in open systems are developed on the basis of various mathematical techniques, such as projection superoperator methods and influence functional techniques. In addition, the book expounds the relativistic theory of quantum measurements and the density matrix theory of relativistic quantum electrodynamics.
Integrity signals
Registry
Cites
Statistics
Claims the paper makes
Claims other papers make about this one
Each is checked against this paper’s own text: does it say what the citing paper says it does?
H_LS always commutes with H_S.
“Moreover, it always commutes with H S [8].”
From Fundamentals of quantum mechanics in Liouville space (2020) · cites this paper as [8]
The equations of motion for the density matrix for relaxation processes are often linear but often not amenable to easy resolution.
“the equations of motion for the density matrix for such relaxation processes are often linear in the former, they are often not amenable to easy resolution.”
From Fundamentals of quantum mechanics in Liouville space (2020) · cites this paper as [8]
For ρ(t) defined on a finite-dimensional state space of dimension d, the GKSL equation reads [5,6,7,8] (191).
“For ρ ( t ) defined on a finite-dimensional state space of dimension d , the GKSL equation reads [5, 6, 7, 8]”
From Fundamentals of quantum mechanics in Liouville space (2020) · cites this paper as [8]
The solution to a quantum Markovian master equation like the quantum optical master equation (237) may be written in the Kraus operator sum form (289) for ρS ∈ Hd.
“It is known that the solution to a quantum Markovian master equation like the quantum optical master equation under consideration, (237), may be written in the form (for ρ S ∈ H d )[6, 8, 58, 59, 60, 61]:”
From Fundamentals of quantum mechanics in Liouville space (2020) · cites this paper as [8]
Equation (237) has the properties of a quantum Markovian master equation: the time-evolution of the system is independent of its past history.
“Equation (237) has the properties of what is called quantum Markovian master equation : these are master equations where - among other properties which are beyond our scope here - the time-evolution of the system is independent of its past history.”
From Fundamentals of quantum mechanics in Liouville space (2020) · cites this paper as [8]
After a chain of algebraic manipulations, approximations, and tracing out radiation, one arrives at equation (237) for TLS density matrix.
“What interests us is that, after a chain of algebraic manipulations, introduction of some approximations and assumptions, and tracing out of the radiation field's degrees of freedom, one arrives at the following equation of motion for the TLS' density matrix ρ S ( t ) ∈ H S (in the Schr¨ odinger picture) [8, 57]:”
From Fundamentals of quantum mechanics in Liouville space (2020) · cites this paper as [8]
The second term in (237) describes the TLS' relaxation due to its interaction with the radiation field.
“The second term in (237) describes the TLS' relaxation due to its interaction with the radiation field, and it is given by the expression [8, 57]”
From Fundamentals of quantum mechanics in Liouville space (2020) · cites this paper as [8]
Non-Markovian effects become important when the relaxation time of the system is comparable to the relaxation time of the environment.
“Non-Markovian (or memory) effects become important when the relaxation time of the system is comparable to the relaxation time of the environment [25,26].”
From Quantum Speed Limit for Non-Markovian Dynamics (2013) · cites this paper as [25]
The actual dynamics of any real open quantum system is expected to deviate to some extent from the idealized Markovian evolution that arises from weak or singular coupling to a memoryless reservoir.
“The actual dynamics of any real open quantum system is expected to deviate to some extent from the idealized Markovian evolution that arises from the conditions of weak (or singular) coupling to a memoryless reservoir [1, 2].”
From Entanglement and Non-Markovianity of Quantum Evolutions (2010) · cites this paper as [2]
The conclusion is not only restricted to the above physical model; it can also be used to explain the phenomenon illustrated in Ref. [16].
“We note that our conclusion is not only restricted to the above physical model, it can also be used to explain the phenomenon illustrated in Ref. [16], where the optimal trace distance for non-Markovianity of a two-level atom resonantly coupled to a leaky single model cavity is found to be D t = | b t | = √ P t [25].”
From Quantum speedup in a memory environment (2014) · cites this paper as [25]
For a two-level atom resonantly coupled to a leaky single mode cavity, the optimal trace distance for non-Markovianity is D_t = |b_t| = √P_t.
“where the optimal trace distance for non-Markovianity of a two-level atom resonantly coupled to a leaky single model cavity is found to be D t = | b t | = √ P t [25].”
From Quantum speedup in a memory environment (2014) · cites this paper as [25]
Cites
Still being checked.
Cited by
Sorted by citations
Theory of open quantum systems
Xu, R., & Yan, Y. (2002) · The Journal of Chemical Physics · doi:10.1063/1.1474579 · Cited by 6,622 · see citing works
QuTiP: An open-source Python framework for the dynamics of open quantum systems
Johansson, J. R., Nation, P. D., & Nori, F. (2012) · Computer Physics Communications · doi:10.1016/j.cpc.2012.02.021 · Cited by 2,126 · see citing works
Carusotto, I., & Ciuti, C. (2013) · Reviews of Modern Physics · doi:10.1103/revmodphys.85.299 · Cited by 2,029 · see citing works
Circuit quantum electrodynamics
Blais, A., Grimsmo, A. L., Girvin, S. M., & Wallraff, A. J. (2021) · Reviews of Modern Physics · doi:10.1103/revmodphys.93.025005 · Cited by 1,981 · see citing works
Colloquium : Quantum coherence as a resource
Streltsov, A., Adesso, G., & Plenio, M. B. (2017) · Reviews of Modern Physics · doi:10.1103/revmodphys.89.041003 · Cited by 1,787 · see citing works
Exceptional topology of non-Hermitian systems
Bergholtz, E. J., Budich, J. C., & Kunst, F. K. (2021) · Reviews of Modern Physics · doi:10.1103/revmodphys.93.015005 · Cited by 1,742 · see citing works
Noisy intermediate-scale quantum algorithms
Bharti, K., Cervera-Lierta, A., Kyaw, T. H., Haug, T., Alperin-Lea, S., Anand, A., Degroote, M., Heimonen, H., Kottmann, J. S., Menke, T., et al. (2022) · Reviews of Modern Physics · doi:10.1103/revmodphys.94.015004 · Cited by 1,726 · see citing works
Measure for the Degree of Non-Markovian Behavior of Quantum Processes in Open Systems
Breuer, H.-P., Laine, E.-M., & Piilo, J. (2009) · Physical Review Letters · doi:10.1103/physrevlett.103.210401 · Cited by 1,480 · see citing works
Self-citationNonequilibrium fluctuations, fluctuation theorems, and counting statistics in quantum systems
Esposito, M., Harbola, U., & Mukamel, S. (2009) · Reviews of Modern Physics · doi:10.1103/revmodphys.81.1665 · Cited by 1,414 · see citing works
Colloquium : Non-Markovian dynamics in open quantum systems
Breuer, H., Laine, E.-M., Piilo, J., & Vacchini, B. (2016) · Reviews of Modern Physics · doi:10.1103/revmodphys.88.021002 · Cited by 1,386 · see citing works
Self-citationMicrowave photonics with superconducting quantum circuits
Gu, X. Q., Kockum, A. F., Miranowicz, A., Liu, Y.-X., & Nori, F. (2017) · Physics Reports · doi:10.1016/j.physrep.2017.10.002 · Cited by 1,294 · see citing works
Environment-assisted quantum walks in photosynthetic energy transfer
Mohseni, M., Rebentrost, P., Lloyd, S., & Aspuru-Guzik, A. (2008) · The Journal of Chemical Physics · doi:10.1063/1.3002335 · Cited by 1,189 · see citing works
On-chip quantum simulation with superconducting circuits
Houck, A. A., Türeci, H. E., & Koch, J. (2012) · Nature Physics · doi:10.1038/nphys2251 · Cited by 1,069 · see citing works
Entanglement and Non-Markovianity of Quantum Evolutions
Rivas, Á., Huelga, S. F., & Plenio, M. B. (2010) · Physical Review Letters · doi:10.1103/physrevlett.105.050403 · Cited by 1,037 · see citing works
PSEUDO-HERMITIAN REPRESENTATION OF QUANTUM MECHANICS
MOSTAFAZADEH, A. (2010) · International Journal of Geometric Methods in Modern Physics · doi:10.1142/s0219887810004816 · Cited by 951 · see citing works
Vinjanampathy, S., & Anders, J. (2016) · Contemporary Physics · doi:10.1080/00107514.2016.1201896 · Cited by 940 · see citing works
Weimer, H., Müller, M., Lesanovsky, I., Zoller, P., & Büchler, H. P. (2010) · Nature Physics · doi:10.1038/nphys1614 · Cited by 867 · see citing works
Quantum trajectories and open many-body quantum systems
Daley, A. J. (2014) · Advances In Physics · doi:10.1080/00018732.2014.933502 · Cited by 840 · see citing works
Ma, J., Wang, X., Sun, C. P., & Nori, F. (2011) · Physics Reports · doi:10.1016/j.physrep.2011.08.003 · Cited by 843 · see citing works
Non-Markovian Effects on the Dynamics of Entanglement
Bellomo, B., Franco, R. L., & Compagno, G. (2007) · Physical Review Letters · doi:10.1103/physrevlett.99.160502 · Cited by 818 · see citing works
Dynamics of Light Harvesting in Photosynthesis
Cheng, Y., & Fleming, G. R. (2008) · Annual Review of Physical Chemistry · doi:10.1146/annurev.physchem.040808.090259 · Cited by 784 · see citing works
Concepts and Methods in the Theory of Open Quantum Systems
Breuer, H.-P., & Petruccione, F. (2003) · Lecture Notes in Physics · doi:10.1007/3-540-44874-8_4 · Cited by 746 · see citing works
Self-citationThe quest for a Quantum Neural Network
Schuld, M., Sinayskiy, I., & Petruccione, F. (2014) · Quantum Information Processing · doi:10.1007/s11128-014-0809-8 · Cited by 671 · see citing works
Self-citationCaruso, F., Chin, A. W., Datta, A., Huelga, S. F., & Plenio, M. B. (2009) · The Journal of Chemical Physics · doi:10.1063/1.3223548 · Cited by 655 · see citing works
A Survey on quantum computing technology
Gyongyosi, L., & Imre, S. (2019) · Computer Science Review · doi:10.1016/j.cosrev.2018.11.002 · Cited by 646 · see citing works
Quantum Open System Theory: Bipartite Aspects
Yu, T., & Eberly, J. H. (2006) · Physical Review Letters · doi:10.1103/physrevlett.97.140403 · Cited by 632 · see citing works
Measurement-Induced Phase Transitions in the Dynamics of Entanglement
Skinner, B. J., Ruhman, J., & Nahum, A. (2019) · DSpace@MIT (Massachusetts Institute of Technology) · Cited by 619 · see citing works
Quantum control theory and applications: a survey
Dong, D., & Petersen, I. R. (2010) · IET Control Theory and Applications · doi:10.1049/iet-cta.2009.0508 · Cited by 603 · see citing works
Liu, B.-H., Li, L., Huang, Y.-F., Li, C.-F., Guo, G.-C., Laine, E.-M., Breuer, H.-P., & Piilo, J. (2011) · Nature Physics · doi:10.1038/nphys2085 · Cited by 574 · see citing works
Self-citationVibrations, quanta and biology
Huelga, S. F., & Plenio, M. B. (2013) · Contemporary Physics · doi:10.1080/00405000.2013.829687 · Cited by 568 · see citing works
Quantum Fisher information flow and non-Markovian processes of open systems
Lu, X.-M., Wang, X., & Sun, C. P. (2010) · Physical Review A · doi:10.1103/physreva.82.042103 · Cited by 534 · see citing works
Sudden Transition between Classical and Quantum Decoherence
Mazzola, L., Piilo, J., & Maniscalco, S. (2010) · Physical Review Letters · doi:10.1103/physrevlett.104.200401 · Cited by 519 · see citing works
Quantum machine learning: a classical perspective
Ciliberto, C., Herbster, M., Ialongo, A. D., Pontil, M., Rocchetto, A., Severini, S., & Wossnig, L. (2018) · Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences · doi:10.1098/rspa.2017.0551 · Cited by 518 · see citing works
Environment-Assisted Quantum Transport
Rebentrost, P., Mohseni, M., Kassal, I., Lloyd, S., & Aspuru‐Guzik, A. (2008) · Digital Access to Scholarship at Harvard (DASH) (Harvard University) · Cited by 512 · see citing works
Quantum Speed Limit for Non-Markovian Dynamics
Deffner, S., & Lutz, E. (2013) · Physical Review Letters · doi:10.1103/physrevlett.111.010402 · Cited by 511 · see citing works
Third quantization: a general method to solve master equations for quadratic open Fermi systems
Prosen, T. (2008) · New Journal of Physics · doi:10.1088/1367-2630/10/4/043026 · Cited by 528 · see citing works
Control of quantum phenomena: past, present and futurePreprint
Brif, C., Chakrabarti, R., & RABITZ, H. A. (2010) · Cited by 548 · see citing works
Measure for the non-Markovianity of quantum processes
Laine, E.-M., Piilo, J., & Breuer, H.-P. (2010) · Physical Review A · doi:10.1103/physreva.81.062115 · Cited by 484 · see citing works
Self-citationRameshti, B. Z., Kusminskiy, S. V., Haigh, J. A., Usami, K., Lachance-Quirion, D., Nakamura, Y., Hu, C. ‐., Tang, H. X., Bauer, G. E. W., & Blanter, Y. M. (2022) · Physics Reports · doi:10.1016/j.physrep.2022.06.001 · Cited by 474 · see citing works
Keldysh field theory for driven open quantum systems
Sieberer, L. M., Buchhold, M., & Diehl, S. (2016) · Kölner Universitäts PublikationsServer (Universität zu Köln) · Cited by 468 · see citing works
Non-Markovian dynamics of quantum discord
Fanchini, F. F., Werlang, T., Brasil, C. A., Arruda, L. G. E., & Caldeira, A. O. (2010) · Physical Review A · doi:10.1103/physreva.81.052107 · Cited by 464 · see citing works
How Small Can Thermal Machines Be? The Smallest Possible Refrigerator
Linden, N., Popescu, S., & Skrzypczyk, P. (2010) · Physical Review Letters · doi:10.1103/physrevlett.105.130401 · Cited by 453 · see citing works
Quantum Coherence, Time-Translation Symmetry, and Thermodynamics
Lostaglio, M., Korzekwa, K., Jennings, D., & Rudolph, T. (2015) · Physical Review X · doi:10.1103/physrevx.5.021001 · Cited by 451 · see citing works
Bengtsson, I., & Życzkowski, K. (2006) · doi:10.2277/0521814510 · Cited by 502 · see citing works
Symmetries and conserved quantities in Lindblad master equations
Albert, V. V., & Jiang, L. (2014) · Physical Review A · doi:10.1103/physreva.89.022118 · Cited by 448 · see citing works
Entropy production as correlation between system and reservoir
Esposito, M., Lindenberg, K., & den Broeck, C. V. (2010) · New Journal of Physics · doi:10.1088/1367-2630/12/1/013013 · Cited by 447 · see citing works
Quantum-enhanced measurements without entanglement
Braun, D., Adesso, G., Benatti, F., Floreanini, R., Marzolino, U., Mitchell, M. W., & Pirandola, S. (2018) · Reviews of Modern Physics · doi:10.1103/revmodphys.90.035006 · Cited by 434 · see citing works
Ishizaki, A., & Fleming, G. R. (2009) · The Journal of Chemical Physics · doi:10.1063/1.3155214 · Cited by 430 · see citing works
Open Quantum Systems. An Introduction
Rivas, Á., & Huelga, S. F. (2011) · arXiv · doi:10.48550/arxiv.1104.5242 · Cited by 424 · see citing works
Minganti, F., Miranowicz, A., Chhajlany, R. W., & Nori, F. (2019) · Physical Review A · doi:10.1103/physreva.100.062131 · Cited by 418 · see citing works
Spectral theory of Liouvillians for dissipative phase transitions
Minganti, F., Biella, A., Bartolo, N., & Ciuti, C. (2018) · Physical Review A · doi:10.1103/physreva.98.042118 · Cited by 413 · see citing works
Environment Induced Entanglement in Markovian Dissipative Dynamics
Benatti, F., Roberto Floreanini, B., & Piani, M. (2003) · Physical Review Letters · doi:10.1103/physrevlett.91.070402 · Cited by 402 · see citing works
Finite-temperature transport in one-dimensional quantum lattice models
Bertini, B., Heidrich‐Meisner, F., Karrasch, C., Prosen, T., Steinigeweg, R., & Žnidarič, M. (2021) · Reviews of Modern Physics · doi:10.1103/revmodphys.93.025003 · Cited by 415 · see citing works
Stochastic thermodynamics under coarse graining
Esposito, M. (2012) · Physical Review E · doi:10.1103/physreve.85.041125 · Cited by 397 · see citing works
Observation of a Dissipative Phase Transition in a One-Dimensional Circuit QED Lattice
Fitzpatrick, M., Sundaresan, N. M., Li, A. C. Y., Koch, J., & Houck, A. A. (2017) · Physical Review X · doi:10.1103/physrevx.7.011016 · Cited by 397 · see citing works
Squeezed Optomechanics with Phase-Matched Amplification and Dissipation
Lü, X., Wu, Y., Johansson, J. R., Jing, H., Zhang, J., & Nori, F. (2015) · Physical Review Letters · doi:10.1103/physrevlett.114.093602 · Cited by 392 · see citing works
Irreversible entropy production: From classical to quantum
Landi, G. T., & Paternostro, M. (2021) · Reviews of Modern Physics · doi:10.1103/revmodphys.93.035008 · Cited by 388 · see citing works
An introduction to quantum machine learningPreprint
Schuld, M., Sinayskiy, I., & Petruccione, F. (2014) · Cited by 435 · see citing works
Self-citationCanonical form of master equations and characterization of non-Markovianity
Hall, M. J. W., Cresser, J. D., Li, L., & Andersson, E. (2014) · Physical Review A · doi:10.1103/physreva.89.042120 · Cited by 378 · see citing works
Quasilocal charges in integrable lattice systems
Ilievski, E., Medenjak, M., Prosen, T., & Zadnik, L. (2016) · Journal of Statistical Mechanics Theory and Experiment · doi:10.1088/1742-5468/2016/06/064008 · Cited by 375 · see citing works
A note on symmetry reductions of the Lindblad equation: transport in constrained open spin chains
Buča, B., & Prosen, T. (2012) · New Journal of Physics · doi:10.1088/1367-2630/14/7/073007 · Cited by 361 · see citing works
Colloquium: Protecting quantum information against environmental noise
Suter, D., & Álvarez, G. A. (2016) · Reviews of Modern Physics · doi:10.1103/revmodphys.88.041001 · Cited by 350 · see citing works
Role of Quantum Coherence and Environmental Fluctuations in Chromophoric Energy Transport
Rebentrost, P., Mohseni, M., & Aspuru‐Guzik, A. (2009) · The Journal of Physical Chemistry B · doi:10.1021/jp901724d · Cited by 357 · see citing works
Photon Blockade in the Ultrastrong Coupling Regime
Ridolfo, A., Leib, M., Savasta, S., & Hartmann, M. J. (2012) · Physical Review Letters · doi:10.1103/physrevlett.109.193602 · Cited by 347 · see citing works
Degree of Non-Markovianity of Quantum Evolution
Chruściński, D., & Maniscalco, S. (2014) · Physical Review Letters · doi:10.1103/physrevlett.112.120404 · Cited by 349 · see citing works
General Non-Markovian Dynamics of Open Quantum Systems
Zhang, W.-M., Lo, P.-Y., Xiong, H.-N., Tu, M. W.-Y., & Nori, F. (2012) · Physical Review Letters · doi:10.1103/physrevlett.109.170402 · Cited by 349 · see citing works
Subwavelength vacuum lattices and atom–atom interactions in two-dimensional photonic crystals
Gonz'alez-Tudela, A., Hung, C.-L., Chang, D., Cirac, J., & Kimble, H. J. (2014) · Nature Photonics · doi:10.1038/nphoton.2015.54 · Cited by 285 · see citing works
Non-Markovianity and reservoir memory of quantum channels: a quantum information theory perspective
Bylicka, B., Chruściński, D., & Maniscalco, S. (2014) · Scientific Reports · doi:10.1038/srep05720 · Cited by 348 · see citing works
Quantum channels and memory effects
Caruso, F., Giovannetti, V., Lupo, C., & Mancini, S. (2014) · Reviews of Modern Physics · doi:10.1103/revmodphys.86.1203 · Cited by 329 · see citing works
Fisher information under decoherence in Bloch representation
Zhong, W., Sun, Z., Ma, J., Wang, X., & Nori, F. (2013) · Physical Review A · doi:10.1103/physreva.87.022337 · Cited by 320 · see citing works
IBM Q Experience as a versatile experimental testbed for simulating open quantum systems
García-Pérez, G., Rossi, M. A. C., & Maniscalco, S. (2020) · npj Quantum Information · doi:10.1038/s41534-019-0235-y · Cited by 318 · see citing works
Entanglement in a fermion chain under continuous monitoring
Cao, X., Tilloy, A., & Luca, A. D. (2019) · SciPost Physics · doi:10.21468/scipostphys.7.2.024 · Cited by 372 · see citing works
The Quantum Coherent Mechanism for Singlet Fission: Experiment and Theory
Chan, W. L., Berkelbach, T. C., Provorse, M. R., Monahan, N. R., Tritsch, J. R., Hybertsen, M. S., Reichman, D. R., Gao, J., & Zhu, X.-Y. (2013) · Accounts of Chemical Research · doi:10.1021/ar300286s · Cited by 320 · see citing works
Piilo, J., Maniscalco, S., Härkönen, K., & Suominen, K. (2008) · Physical Review Letters · doi:10.1103/physrevlett.100.180402 · Cited by 317 · see citing works
Vanishing Quantum Discord is Necessary and Sufficient for Completely Positive Maps
Shabani, A., & Lidar, D. A. (2009) · Physical Review Letters · doi:10.1103/physrevlett.102.100402 · Cited by 309 · see citing works
From a quantum-electrodynamical light–matter description to novel spectroscopies
Ruggenthaler, M., Tancogne-Dejean, N., Flick, J., Appel, H., & Rubio, Á. (2018) · Nature Reviews Chemistry · doi:10.1038/s41570-018-0118 · Cited by 299 · see citing works
Probabilistic error cancellation with sparse Pauli–Lindblad models on noisy quantum processors
van den Berg, E., Minev, Z. K., Kandala, A., & Temme, K. (2023) · Nature Physics · doi:10.1038/s41567-023-02042-2 · Cited by 305 · see citing works
Individual Quantum Probes for Optimal Thermometry
Correa, L. A., Mehboudi, M., Adesso, G., & Sanpera, A. (2015) · Physical Review Letters · doi:10.1103/physrevlett.114.220405 · Cited by 299 · see citing works
Damping of Exciton Rabi Rotations by Acoustic Phonons in Optically Excited InGaAs/GaAs Quantum Dots
Ramsay, A. J., Achanta, V. G., Gauger, E. M., Nazir, A., Lovett, B. W., Fox, A. M., & Skolnick, M. S. (2010) · Physical Review Letters · doi:10.1103/physrevlett.104.017402 · Cited by 303 · see citing works
Photosynthetic light harvesting: excitons and coherence
Fassioli, F., Dinshaw, R., Arpin, P. C., & Scholes, G. D. (2013) · Journal of The Royal Society Interface · doi:10.1098/rsif.2013.0901 · Cited by 297 · see citing works
Witnessing Quantum Coherence: from solid-state to biological systems
Li, C., Lambert, N., Chen, Y.-N., Chen, G.-Y., & Nori, F. (2012) · Scientific Reports · doi:10.1038/srep00885 · Cited by 297 · see citing works
Quantum trajectory approach to circuit QED: Quantum jumps and the Zeno effect
Gambetta, J., Blais, A., Boissonneault, M., Houck, A., Schuster, D., & Girvin, S. M. (2008) · Physical Review A · doi:10.1103/physreva.77.012112 · Cited by 296 · see citing works
Non-Markovian effect on the quantum discord
Wang, B., Xu, Z., Chen, Z., & Feng, M. (2010) · Physical Review A · doi:10.1103/physreva.81.014101 · Cited by 290 · see citing works
Exact Nonequilibrium Steady State of a Strongly Driven Open XXZ Chain
Prosen, T. (2011) · Physical Review Letters · doi:10.1103/physrevlett.107.137201 · Cited by 290 · see citing works
Entanglement dynamics of two independent qubits in environments with and without memory
Bellomo, B., Franco, R. L., & Compagno, G. (2008) · Physical Review A · doi:10.1103/physreva.77.032342 · Cited by 286 · see citing works
Quantum Coherence in Photosynthetic Light Harvesting
Ishizaki, A., & Fleming, G. R. (2011) · Annual Review of Condensed Matter Physics · doi:10.1146/annurev-conmatphys-020911-125126 · Cited by 282 · see citing works
Entanglement in a free fermion chain under continuous monitoring
Cao, X., Tilloy, A., & Luca, A. D. (2019) · MPG.PuRe (Max Planck Society) · Cited by 281 · see citing works
Universal decoherence due to gravitational time dilation
Pikovski, I., Zych, M., Costa, F., & Brukner, Č. (2015) · Nature Physics · doi:10.1038/nphys3366 · Cited by 279 · see citing works
Vanner, M. R., Pikovski, I., Cole, G. D., Kim, M. S., Brukner, Č., Hammerer, K., Milburn, G. J., & Aspelmeyer, M. (2011) · Proceedings of the National Academy of Sciences · doi:10.1073/pnas.1105098108 · Cited by 279 · see citing works
Quantum-enhanced absorption refrigerators
Correa, L. A., Palao, J. P., Alonso, D., & Adesso, G. (2014) · Scientific Reports · doi:10.1038/srep03949 · Cited by 265 · see citing works
Charger-mediated energy transfer for quantum batteries: An open-system approach
Farina, D., Andolina, G. M., Mari, A., Polini, M., & Giovannetti, V. (2019) · Physical review. B./Physical review. B · doi:10.1103/physrevb.99.035421 · Cited by 273 · see citing works
Controlling open quantum systems: tools, achievements, and limitations
Koch, C. P. (2016) · Journal of Physics Condensed Matter · doi:10.1088/0953-8984/28/21/213001 · Cited by 270 · see citing works
Measures of non-Markovianity: Divisibility versus backflow of information
Chruściński, D., Kossakowski, A., & Rivas, Á. (2011) · Physical Review A · doi:10.1103/physreva.83.052128 · Cited by 270 · see citing works
Neural-Network Approach to Dissipative Quantum Many-Body Dynamics
Hartmann, M. J., & Carleo, G. (2019) · Physical Review Letters · doi:10.1103/physrevlett.122.250502 · Cited by 263 · see citing works
Non-Markovian Quantum Dynamics: Local versus Nonlocal
Chruściński, D., & Kossakowski, A. (2010) · Physical Review Letters · doi:10.1103/physrevlett.104.070406 · Cited by 261 · see citing works
Sudden death and sudden birth of entanglement in common structured reservoirs
Mazzola, L., Maniscalco, S., Piilo, J., Suominen, K., & Garraway, B. M. (2009) · Physical Review A · doi:10.1103/physreva.79.042302 · Cited by 261 · see citing works
Nonequilibrium physics in biology
Fang, X., Kruse, K., Lu, T., & Wang, J. (2019) · Reviews of Modern Physics · doi:10.1103/revmodphys.91.045004 · Cited by 255 · see citing works
Open-system dynamics of entanglement:a key issues review
Aolita, L., de Melo, F., & Davidovich, L. (2015) · Refubium (Universitätsbibliothek der Freien Universität Berlin) · doi:10.17169/refubium-20820 · Cited by 258 · see citing works
Quantum Absorption Refrigerator
Levy, A., & Kosloff, R. (2012) · Physical Review Letters · doi:10.1103/physrevlett.108.070604 · Cited by 257 · see citing works
Schröter, M., Ivanov, S. D., Schulze, J., Polyutov, S. P., Yan, Y., Pullerits, T., & Kühn, O. (2014) · Physics Reports · doi:10.1016/j.physrep.2014.12.001 · Cited by 254 · see citing works
- Authors
- Breuer, H.-P., & Petruccione, F.
- Affiliations
- University of Freiburg (DE)
- University of KwaZulu-Natal (ZA)
- Publisher
- Oxford University PressOxford
- Published
- 2007-01-25
- OpenAlex
- W1578322733
- Cited by
- 5,938
- References
- 0
- Citations by year
- 2026: 240 · 2025: 369 · 2024: 303 · 2023: 260 · 2022: 286 · 2021: 386 · 2020: 332 · 2019: 368 · 2018: 289 · 2017: 296 · 2016: 354 · 2015: 303 · 2014: 312 · 2013: 316 · 2012: 281
- FWCI
- 64.38
- Type
- book
- Language
- en
- Open access
- closed
- Locations
- CERN Document Server (European Organization for Nuclear Research) (submittedVersion)
- Topics
- Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Quantum Mechanics and Applications
- Physical Sciences › Computer Science › Artificial Intelligence › Quantum Information and Cryptography
- Physical Sciences › Physics and Astronomy › Statistical and Nonlinear Physics › Advanced Thermodynamics and Statistical Mechanics
- Keywords
- open quantum systems, quantum measurement theory, quantum operations, quantum effects, density matrix theory, quantum Markov processes, master equation, environmental decoherence, non-Markovian dynamics, Monte Carlo methods, influence functional, relativistic quantum electrodynamics, statistical interpretation of quantum mechanics
About these checks
Registry, retraction, Cites and statistics results are computed, not judged, with one exception: a printed reference that no index lists is read once by a model before it counts as a citation error. Claims are extracted by a model and kept only when their quote appears verbatim in the text; each cited source is then checked, with a model’s help, for whether it says what the claim relies on. Those verdicts can be wrong — read the claim’s quote and the cited source before relying on one.
Statistics and arithmetic are recomputed, not judged.
Confidence bands are shown only for fields calibrated on our annotated test set. None is calibrated yet, so no band is shown.
What counts as a claim ›How we measure confidence ›How we check this ›
Are you an author, or do you see a problem with this page? Request a review
