Weak measurement

In quantum mechanics (and computation & information), weak measurements are a type of quantum measurement that results in an observer obtaining very little information about the system on average, but also disturbs the state very little.^[1] From Busch's theorem^[2] the system is necessarily disturbed by the measurement. In the literature weak measurements are also known as unsharp,^[3] fuzzy,^[3]^[4] dull, noisy,^[5] approximate, and gentle^[6] measurements. Additionally weak measurements are often confused with the distinct but related concept of the weak value.^[7]

^ Todd A Brun (2002). "A simple model of quantum trajectories". Am. J. Phys. 70 (7): 719–737. arXiv:quant-ph/0108132. Bibcode:2002AmJPh..70..719B. doi:10.1119/1.1475328. S2CID 40746086.
^ Paul Busch (2009). J. Christian; W.Myrvold (eds.). "No Information Without Disturbance": Quantum Limitations of Measurement. Invited contribution, "Quantum Reality, Relativistic Causality, and Closing the Epistemic Circle: An International Conference in Honour of Abner Shimony", Perimeter Institute, Waterloo, Ontario, Canada, July 18–21, 2006. Vol. 73. Springer-Verlag, 2008. pp. 229–256. arXiv:0706.3526. doi:10.1007/978-1-4020-9107-0. ISBN 978-1-4020-9106-3. ISSN 1566-659X. {{cite book}}: |journal= ignored (help)
^ ^a ^b Gudder, Stan (2005). "Non-disturbance for fuzzy quantum measurements". Fuzzy Sets and Systems. 155 (1): 18–25. doi:10.1016/j.fss.2005.05.009.
^ Asher Peres (1993). Quantum Theory, Concepts and Methods. Kluwer. p. 387. ISBN 978-0-7923-2549-9.
^ A. N. Korotkov (2003). "Noisy Quantum Measurement of Solid-State Qubits: Bayesian Approach". In Y. v. Nazarov (ed.). Quantum Noise in Mesoscopic Physics. Springer Netherlands. pp. 205–228. arXiv:cond-mat/0209629. doi:10.1007/978-94-010-0089-5_10. ISBN 978-1-4020-1240-2. S2CID 9025386.
^ Cite error: The named reference Winter1999 was invoked but never defined (see the help page).
^ Yakir Aharonov; David Z. Albert & Lev Vaidman (1988). "How the result of a measurement of a component of the spin of a spin-1/2 particle can turn out to be 100". Physical Review Letters. 60 (14): 1351–1354. Bibcode:1988PhRvL..60.1351A. doi:10.1103/PhysRevLett.60.1351. PMID 10038016. S2CID 46042317.

[Brun2002-1] Todd A Brun (2002). "A simple model of quantum trajectories". Am. J. Phys. 70 (7): 719–737. arXiv:quant-ph/0108132. Bibcode:2002AmJPh..70..719B. doi:10.1119/1.1475328. S2CID 40746086.

[Busch2009-2] Paul Busch (2009). J. Christian; W.Myrvold (eds.). "No Information Without Disturbance": Quantum Limitations of Measurement. Invited contribution, "Quantum Reality, Relativistic Causality, and Closing the Epistemic Circle: An International Conference in Honour of Abner Shimony", Perimeter Institute, Waterloo, Ontario, Canada, July 18–21, 2006. Vol. 73. Springer-Verlag, 2008. pp. 229–256. arXiv:0706.3526. doi:10.1007/978-1-4020-9107-0. ISBN 978-1-4020-9106-3. ISSN 1566-659X. {{cite book}}: |journal= ignored (help)

[Gudder2005-3] Gudder, Stan (2005). "Non-disturbance for fuzzy quantum measurements". Fuzzy Sets and Systems. 155 (1): 18–25. doi:10.1016/j.fss.2005.05.009.

[PeresBook-4] Asher Peres (1993). Quantum Theory, Concepts and Methods. Kluwer. p. 387. ISBN 978-0-7923-2549-9.

[Korotkov2003-5] A. N. Korotkov (2003). "Noisy Quantum Measurement of Solid-State Qubits: Bayesian Approach". In Y. v. Nazarov (ed.). Quantum Noise in Mesoscopic Physics. Springer Netherlands. pp. 205–228. arXiv:cond-mat/0209629. doi:10.1007/978-94-010-0089-5_10. ISBN 978-1-4020-1240-2. S2CID 9025386.

[Winter1999-6] Cite error: The named reference Winter1999 was invoked but never defined (see the help page).

[Aharonov1988-7] Yakir Aharonov; David Z. Albert & Lev Vaidman (1988). "How the result of a measurement of a component of the spin of a spin-1/2 particle can turn out to be 100". Physical Review Letters. 60 (14): 1351–1354. Bibcode:1988PhRvL..60.1351A. doi:10.1103/PhysRevLett.60.1351. PMID 10038016. S2CID 46042317.

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