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Article: Symmetries of quantum evolutions
Title | Symmetries of quantum evolutions |
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Authors | |
Issue Date | 2021 |
Publisher | American Physical Society. The Journal's web site is located at https://journals.aps.org/prresearch/ |
Citation | Physical Review Research, 2021, v. 3 n. 3, p. article no. 033028 How to Cite? |
Abstract | A cornerstone of quantum mechanics is the characterization of symmetries provided by Wigner's theorem. Wigner's theorem establishes that every symmetry of the quantum state space must be either a unitary transformation or an antiunitary transformation. Here we extend Wigner's theorem from quantum states to quantum evolutions, including both the deterministic evolution associated with the dynamics of closed systems and the stochastic evolutions associated with the outcomes of quantum measurements. We prove that every symmetry of the space of quantum evolutions can be decomposed into two state space symmetries that are either both unitary or both antiunitary. Building on this result, we show that it is impossible to extend the time-reversal symmetry of unitary quantum dynamics to a symmetry of the full set of quantum evolutions. Our no-go theorem implies that any time-symmetric formulation of quantum theory must either restrict the set of the allowed evolutions or modify the operational interpretation of quantum states and processes. Here we propose a time-symmetric formulation of quantum theory where the allowed quantum evolutions are restricted to a suitable set, which includes both unitary evolution and projective measurements but excludes the deterministic preparation of pure states. The standard operational formulation of quantum theory can be retrieved from this time-symmetric version by introducing an operation of conditioning on the outcomes of past experiments. |
Persistent Identifier | http://hdl.handle.net/10722/309050 |
ISSN | 2023 Impact Factor: 3.5 2023 SCImago Journal Rankings: 1.689 |
ISI Accession Number ID |
DC Field | Value | Language |
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dc.contributor.author | Chiribella, G | - |
dc.contributor.author | Aurell, E | - |
dc.contributor.author | Zyczkowski, K | - |
dc.date.accessioned | 2021-12-14T01:39:55Z | - |
dc.date.available | 2021-12-14T01:39:55Z | - |
dc.date.issued | 2021 | - |
dc.identifier.citation | Physical Review Research, 2021, v. 3 n. 3, p. article no. 033028 | - |
dc.identifier.issn | 2643-1564 | - |
dc.identifier.uri | http://hdl.handle.net/10722/309050 | - |
dc.description.abstract | A cornerstone of quantum mechanics is the characterization of symmetries provided by Wigner's theorem. Wigner's theorem establishes that every symmetry of the quantum state space must be either a unitary transformation or an antiunitary transformation. Here we extend Wigner's theorem from quantum states to quantum evolutions, including both the deterministic evolution associated with the dynamics of closed systems and the stochastic evolutions associated with the outcomes of quantum measurements. We prove that every symmetry of the space of quantum evolutions can be decomposed into two state space symmetries that are either both unitary or both antiunitary. Building on this result, we show that it is impossible to extend the time-reversal symmetry of unitary quantum dynamics to a symmetry of the full set of quantum evolutions. Our no-go theorem implies that any time-symmetric formulation of quantum theory must either restrict the set of the allowed evolutions or modify the operational interpretation of quantum states and processes. Here we propose a time-symmetric formulation of quantum theory where the allowed quantum evolutions are restricted to a suitable set, which includes both unitary evolution and projective measurements but excludes the deterministic preparation of pure states. The standard operational formulation of quantum theory can be retrieved from this time-symmetric version by introducing an operation of conditioning on the outcomes of past experiments. | - |
dc.language | eng | - |
dc.publisher | American Physical Society. The Journal's web site is located at https://journals.aps.org/prresearch/ | - |
dc.relation.ispartof | Physical Review Research | - |
dc.rights | Copyright [2021] by The American Physical Society. This article is available online at [http://hub.hku.hk/handle/10722/309050]. | - |
dc.rights | This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License. | - |
dc.title | Symmetries of quantum evolutions | - |
dc.type | Article | - |
dc.identifier.email | Chiribella, G: giulio@cs.hku.hk | - |
dc.identifier.authority | Chiribella, G=rp02035 | - |
dc.description.nature | published_or_final_version | - |
dc.identifier.doi | 10.1103/PhysRevResearch.3.033028 | - |
dc.identifier.scopus | eid_2-s2.0-85112115356 | - |
dc.identifier.hkuros | 330853 | - |
dc.identifier.volume | 3 | - |
dc.identifier.issue | 3 | - |
dc.identifier.spage | article no. 033028 | - |
dc.identifier.epage | article no. 033028 | - |
dc.identifier.isi | WOS:000671591600011 | - |
dc.publisher.place | United States | - |