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On the Debate Concerning the Proper Characterization of Quantum Dynamical Evolution

Published online by Cambridge University Press:  01 January 2022

Michael E. Cuffaro  and
Wayne C. Myrvold
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Abstract

There has been a long-standing and sometimes passionate debate between physicists over whether a dynamical framework for quantum systems should incorporate not completely positive (NCP) maps in addition to completely positive (CP) maps. Despite the reasonableness of the arguments for complete positivity, we argue that NCP maps should be allowed, with a qualification: these should be understood, not as reflecting ‘not completely positive’ evolution, but as linear extensions, to a system’s entire state space, of CP maps that are only partially defined. Beyond the domain of definition of a partial-CP map, we argue, much may be permitted.

Information

Type
General Philosophy of Science
Information
Philosophy of Science , Volume 80 , Issue 5 , December 2013 , pp. 1125 - 1136
Copyright
Copyright © The Philosophy of Science Association

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Footnotes

†

This work was sponsored in part by a grant from the Foundational Questions Institute (FQXi).

References

Alicki, Robert. 1995. “Comment on ‘Reduced Dynamics Need Not Be Completely Positive.’” Physical Review Letters 75:3020.CrossRefGoogle ScholarPubMed
Choi, Man-Duen. 1972. “Positive Linear Maps on C∗-Algebras.” Canadian Journal of Mathematics 24:520–29.CrossRefGoogle Scholar
Devi, A. Usha, R., Rajagopal, A. K., and Sudha, . 2011. “Quantumness of Correlations and Entanglement.” International Journal of Quantum Information 9:1757–71.Google Scholar
Jordan, Thomas F., Shaji, Anil, and Sudarshan, E. C. G.. 2004. “Dynamics of Initially Entangled Open Quantum Systems.” Physical Review A 70:052110.CrossRefGoogle Scholar
Jordan, Thomas F., and Sudarshan, E. C. G.. 1961. “Dynamical Mappings of Density Operators in Quantum Mechanics.” Journal of Mathematical Physics 2:772–75.CrossRefGoogle Scholar
Kraus, Karl. 1983. States, Effects, and Operators. Berlin: Springer.Google Scholar
Nielsen, Michael A., and Chuang, Isaac L.. 2000. Quantum Computation and Quantum Information. Cambridge: Cambridge University Press.Google Scholar
Pechukas, Philip. 1994. “Reduced Dynamics Need Not Be Completely Positive.” Physical Review Letters 73:1060–62.CrossRefGoogle Scholar
Pechukas, Philip 1995. “Pechukas Replies.” Physical Review Letters 75:3021.CrossRefGoogle ScholarPubMed
Raggio, G. A., and Primas, H.. 1982. “Remarks on ‘On Completely Positive Maps in Generalized Quantum Dynamics.’” Foundations of Physics 12:433–35.CrossRefGoogle Scholar
Rodríguez-Rosario, César A., Modi, Kavan, and Aspuru-Guzik, Alán. 2010. “Linear Assignment Maps for Correlated System-Environment States.” Physical Review A 81:012313.CrossRefGoogle Scholar
Shaji, Anal, and Sudarshan, E. C. G.. 2005. “Who’s Afraid of Not Completely Positive Maps?” Physics Letters A 341:48–54.CrossRefGoogle Scholar
Simmons, Ralph F. Jr., and Park, James L.. 1981. “On Completely Positive Maps in Generalized Quantum Dynamics.” Foundations of Physics 11:47–55.CrossRefGoogle Scholar
Simmons, Ralph F. Jr., and Park, James L. 1982. “Another Look at Complete Positivity in Generalized Quantum Dynamics: Reply to Raggio and Primas.” Foundations of Physics 12:437–39.CrossRefGoogle Scholar
Sudarshan, E. C. G., Mathews, P. M., and Rau, Jayaseetha. 1961. “Stochastic Dynamics of Quantum-Mechanical Systems.” Physical Review 121:920–24.CrossRefGoogle Scholar