Chapter 33 Further Reading: Open Quantum Systems and Decoherence

Textbooks

Schlosshauer, M. Decoherence and the Quantum-to-Classical Transition (Springer, 2007). The definitive textbook on decoherence. Accessible to advanced undergraduates, comprehensive, and beautifully written. Chapters 1--4 are essential reading for this chapter's material.
Breuer, H.-P. & Petruccione, F. The Theory of Open Quantum Systems (Oxford University Press, 2002). The standard graduate-level reference. Rigorous derivations of the Lindblad equation, non-Markovian dynamics, and applications. Chapters 3 and 4 cover the Born-Markov derivation in full detail.
Nielsen, M. A. & Chuang, I. L. Quantum Computation and Quantum Information (Cambridge University Press, 10th Anniversary Edition, 2010). Chapter 8 (Quantum Noise and Quantum Operations) provides an excellent treatment of quantum channels, Kraus operators, and the operator-sum representation from the quantum information perspective.

Wiseman, H. M. & Milburn, G. J. Quantum Measurement and Control (Cambridge University Press, 2009). Advanced treatment of open quantum systems from the perspective of quantum measurement theory. Excellent coverage of quantum trajectories, feedback control, and continuous measurement.
Gardiner, C. W. & Zoller, P. Quantum Noise: A Handbook of Markovian and Non-Markovian Quantum Stochastic Methods with Applications to Quantum Optics (Springer, 3rd edition, 2004). The authoritative reference on quantum noise, master equations, and stochastic methods. Essential for anyone working in quantum optics.
Rivas, A. & Huelga, S. F. Open Quantum Systems: An Introduction (Springer, 2012). A concise modern introduction with excellent coverage of non-Markovian dynamics and measures of non-Markovianity.

Zeh, H. D. "On the interpretation of measurement in quantum theory." Foundations of Physics 1, 69--76 (1970). The paper that started it all. Zeh's original insight that the environment plays a crucial role in the quantum measurement process.
Zurek, W. H. "Pointer basis of quantum apparatus: Into what mixture does the wave packet collapse?" Physical Review D 24, 1516 (1981). Introduced the concept of the pointer basis and einselection.
Zurek, W. H. "Decoherence, einselection, and the quantum origins of the classical." Reviews of Modern Physics 75, 715--775 (2003). A comprehensive review of the decoherence program, including quantum Darwinism. Accessible and authoritative.
Joos, E. & Zeh, H. D. "The emergence of classical properties through interaction with the environment." Zeitschrift fur Physik B 59, 223--243 (1985). The first quantitative calculations of decoherence timescales for macroscopic objects.

Lindblad, G. "On the generators of quantum dynamical semigroups." Communications in Mathematical Physics 48, 119--130 (1976). The original derivation of the most general Markovian master equation.
Gorini, V., Kossakowski, A. & Sudarshan, E. C. G. "Completely positive dynamical semigroups of N-level systems." Journal of Mathematical Physics 17, 821 (1976). Independent derivation of the same result, published simultaneously with Lindblad's paper.

Shor, P. W. "Scheme for reducing decoherence in quantum computer memory." Physical Review A 52, R2493 (1995). The first quantum error-correcting code (nine qubits).
Steane, A. M. "Error correcting codes in quantum theory." Physical Review Letters 77, 793 (1996). The seven-qubit Steane code and the connection to classical coding theory.
Knill, E. & Laflamme, R. "Theory of quantum error-correcting codes." Physical Review A 55, 900 (1997). The general conditions (Knill-Laflamme conditions) for quantum error correction.
Aharonov, D. & Ben-Or, M. "Fault-tolerant quantum computation with constant error rate." SIAM Journal on Computing 38, 1207--1282 (2008). The threshold theorem (originally circulated as a preprint in 1997).
Dennis, E., Kitaev, A., Landahl, A. & Preskill, J. "Topological quantum memory." Journal of Mathematical Physics 43, 4452--4505 (2002). The surface code as a topological quantum memory, including the threshold calculation.

Brune, M. et al. "Observing the progressive decoherence of the 'meter' in a quantum measurement." Physical Review Letters 77, 4887 (1996). Direct observation of the decoherence of a Schrodinger cat state in cavity QED.
Hornberger, K. et al. "Collisional decoherence observed in matter wave interferometry." Physical Review Letters 90, 160401 (2003). Controlled observation of decoherence in C$_{70}$ fullerene interferometry.
Fein, Y. Y. et al. "Quantum superposition of molecules beyond 25 kDa." Nature Physics 15, 1242--1245 (2019). Quantum interference of the largest molecules to date.
Google Quantum AI. "Exponential suppression of bit or phase errors with cyclic error correction." Nature 595, 383--387 (2021). First demonstration of the exponential scaling of error suppression with code distance.
Google Quantum AI. "Quantum error correction below the surface code threshold." Preprint, arXiv:2408.13687 (2024). Demonstration of a distance-7 surface code on the Willow processor.

Schlosshauer, M. "Decoherence, the measurement problem, and interpretations of quantum mechanics." Reviews of Modern Physics 76, 1267--1305 (2005). Excellent review connecting decoherence to the foundations of quantum mechanics.
Terhal, B. M. "Quantum error correction for quantum memories." Reviews of Modern Physics 87, 307 (2015). Comprehensive review of quantum error correction with emphasis on the surface code.
de Vega, I. & Alonso, D. "Dynamics of non-Markovian open quantum systems." Reviews of Modern Physics 89, 015001 (2017). Modern review of non-Markovian dynamics, including measures of non-Markovianity and simulation methods.
Lidar, D. A. "Review of decoherence-free subspaces, noiseless subsystems, and dynamical decoupling." Advances in Chemical Physics 154, 295--354 (2014). Comprehensive review of passive and active methods for fighting decoherence.

Preskill, J. Lecture Notes on Quantum Computation (Caltech, continually updated). Available at http://theory.caltech.edu/~preskill/ph219/. Chapter 3 covers quantum noise and Chapter 7 covers fault-tolerant quantum computation. Exceptionally clear and pedagogical.
Wilde, M. M. From Classical to Quantum Shannon Theory (Cambridge University Press, 2017; also available on arXiv). Chapters 4 and 9 provide a rigorous information-theoretic treatment of quantum channels.
QuTiP (Quantum Toolbox in Python). Open-source software for simulating open quantum systems, including Lindblad master equations and quantum trajectories. Documentation at https://qutip.org/. The code examples in this chapter use QuTiP.