Quantum Indistinguishability through Exchangeable Desirable Gambles

Alessio Benavoli, Alessandro Facchini, Marco Zaffalon
Proceedings of the Twelveth International Symposium on Imprecise Probability: Theories and Applications, PMLR 147:22-31, 2021.

Abstract

Two particles are identical if all their intrinsic properties, such as spin and charge, are the same, meaning that no quantum experiment can distinguish them. In addition to the well known principles of quantum mechanics, understanding systems of identical particles requires a new postulate, the so called symmetrization postulate. In this work, we show that the postulate corresponds to exchangeability assessments for sets of observables (gambles) in a quantum experiment, when quantum mechanics is seen as a normative and algorithmic theory guiding an agent to assess her subjective beliefs represented as (coherent) sets of gambles. Finally, we show how sets of exchangeable observables (gambles) may be updated after a measurement and discuss the issue of defining entanglement for indistinguishable particle systems.

Cite this Paper

BibTeX
@InProceedings{pmlr-v147-benavoli21a, title = {Quantum Indistinguishability through Exchangeable Desirable Gambles}, author = {Benavoli, Alessio and Facchini, Alessandro and Zaffalon, Marco}, booktitle = {Proceedings of the Twelveth International Symposium on Imprecise Probability: Theories and Applications}, pages = {22--31}, year = {2021}, editor = {Cano, Andrés and De Bock, Jasper and Miranda, Enrique and Moral, Serafı́n}, volume = {147}, series = {Proceedings of Machine Learning Research}, month = {06--09 Jul}, publisher = {PMLR}, pdf = {http://proceedings.mlr.press/v147/benavoli21a/benavoli21a.pdf}, url = {https://proceedings.mlr.press/v147/benavoli21a.html}, abstract = {Two particles are identical if all their intrinsic properties, such as spin and charge, are the same, meaning that no quantum experiment can distinguish them. In addition to the well known principles of quantum mechanics, understanding systems of identical particles requires a new postulate, the so called symmetrization postulate. In this work, we show that the postulate corresponds to exchangeability assessments for sets of observables (gambles) in a quantum experiment, when quantum mechanics is seen as a normative and algorithmic theory guiding an agent to assess her subjective beliefs represented as (coherent) sets of gambles. Finally, we show how sets of exchangeable observables (gambles) may be updated after a measurement and discuss the issue of defining entanglement for indistinguishable particle systems.} }
Endnote
%0 Conference Paper %T Quantum Indistinguishability through Exchangeable Desirable Gambles %A Alessio Benavoli %A Alessandro Facchini %A Marco Zaffalon %B Proceedings of the Twelveth International Symposium on Imprecise Probability: Theories and Applications %C Proceedings of Machine Learning Research %D 2021 %E Andrés Cano %E Jasper De Bock %E Enrique Miranda %E Serafı́n Moral %F pmlr-v147-benavoli21a %I PMLR %P 22--31 %U https://proceedings.mlr.press/v147/benavoli21a.html %V 147 %X Two particles are identical if all their intrinsic properties, such as spin and charge, are the same, meaning that no quantum experiment can distinguish them. In addition to the well known principles of quantum mechanics, understanding systems of identical particles requires a new postulate, the so called symmetrization postulate. In this work, we show that the postulate corresponds to exchangeability assessments for sets of observables (gambles) in a quantum experiment, when quantum mechanics is seen as a normative and algorithmic theory guiding an agent to assess her subjective beliefs represented as (coherent) sets of gambles. Finally, we show how sets of exchangeable observables (gambles) may be updated after a measurement and discuss the issue of defining entanglement for indistinguishable particle systems.
APA
Benavoli, A., Facchini, A. & Zaffalon, M.. (2021). Quantum Indistinguishability through Exchangeable Desirable Gambles. Proceedings of the Twelveth International Symposium on Imprecise Probability: Theories and Applications, in Proceedings of Machine Learning Research 147:22-31 Available from https://proceedings.mlr.press/v147/benavoli21a.html.

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