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Can Entanglement Be Destroyed by Any Local Operation in Relativistic Quantum Field Theory?

Published online by Cambridge University Press:  01 January 2022

Giovanni Valente
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Abstract

This article investigates the nature of entangled correlations in algebraic quantum field theory (AQFT). We define a notion of local disentanglement, expressing the possibility of destroying entanglement by means of local operations. Contrary to the case of ordinary quantum mechanics, local disentanglement cannot be achieved in general in relativistic quantum field theory. However, we show that if the split property holds, there exists a local operation that can destroy entanglement between spacelike-separated quantum field systems.

Type
Research Article
Information
Philosophy of Science , Volume 77 , Issue 5 , December 2010 , pp. 1029 - 1041
Copyright
Copyright © The Philosophy of Science Association

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Footnotes

‡

The author is indebted to Miklos Redei for precious advice on the technical and conceptual development of this work. He also wishes to thank Hans Halvorson, David Malament, and Stephen Summers for helpful comments and discussions. Support for research leading to this article is acknowledged under National Science Foundation grant 0749856.

References

Bacciagaluppi, G. 1993. “Separation Theorems and Bell Inequalities in Algebraic Quantum Mechanics.” In Symposium on the Foundations of Modern Physics, 1993, ed. Busch, P. and Mittelstaedt, P., 29–37. Singapore: World Scientific.Google Scholar
Buchholz, D. 1974. “Product States for Local Algebras.” Communications in Mathematical Physics 36:287–304.10.1007/BF01646201CrossRefGoogle Scholar
Buchholz, D.. 2001. “Entanglement and Open Systems in Algebraic Quantum Field Theory.” Studies in History and Philosophy of Modern Physics 32:1–31.Google Scholar
Haag, R. 1996. Local Quantum Physics. 2nd ed. New York: Springer.CrossRefGoogle Scholar
Kraus, K. 1983. States, Effects and Operations. Vol. 190 of Lecture Notes in Physics. New York: Springer.Google Scholar
Redei, M., and Summers, S. J.. 2007. “Quantum Probability Theory.” Studies in History and Philosophy of Modern Physics 38:390–417.10.1016/j.shpsb.2006.05.006CrossRefGoogle Scholar
Redei, M., and Summers, S. J.. 2009. “When Are Quantum Systems Operationally Independent?” International Journal of Theoretical Physics. Published electronically May 23, doi: 10.1007/s10773-009-0010-5.CrossRefGoogle Scholar
Redei, M., and Valente, G.. 2011. “How Local Are Local Operations in Local Quantum Field Theory?” Studies in History and Philosophy of Modern Physics, forthcoming.10.1016/j.shpsb.2010.09.001CrossRefGoogle Scholar
Summers, S. 1990. “On the Independence of Local Algebras in Quantum Field Theory.” Reviews in Mathematical Physics 2:201–47.10.1142/S0129055X90000090CrossRefGoogle Scholar
Summers, S.. 2009. “Subsystems and Independence in Relativistic Microscopic Physics.” Studies in History and Philosophy of Modern Physics 40:133–41.10.1016/j.shpsb.2009.02.002CrossRefGoogle Scholar
Summers, S., and Werner, R.. 1985. Physics Letters A 110:257–59.Google Scholar
Summers, S., and Werner, R.. 1988. “Maximal Violation of Bell's Inequalities for Algebras of Observables in Tangent Spacetime Regions.” Annales de l’Institut Henri Poincaré (A) Physique Théorique 49:214–43.Google Scholar
Summers, S., and Werner, R.. 1995. “On Bell's Inequalities and Algebraic Invariants.” Letters in Mathematical Physics 33:321–34.CrossRefGoogle Scholar