Asymmetry properties of pure quantum states
Open accessAbstract
The asymmetry properties of a state relative to some symmetry group specify how and to what extent the given symmetry is broken by the state. Characterizing these is found to be surprisingly useful for addressing a very common problem: to determine what follows from a system's dynamics (possibly open) having that symmetry. We demonstrate and exploit the fact that the asymmetry properties of a state can be understood in terms of information-theoretic concepts. We show that for a pure state $\ensuremath{\psi}$ and a symmetry group $G$, they are completely specified by the characteristic function of the state, defined as ${\ensuremath{\chi}}_{\ensuremath{\psi}}(g)\ensuremath{\equiv}\ensuremath{\langle}\ensuremath{\psi}|U(g)|\ensuremath{\psi}\ensuremath{\rangle}$, where $g\ensuremath{\in}G$ and $U$ is the unitary representation of interest. Based on this observation, we study several important problems about the interconversion of pure states under symmetric dynamics, such as determining the conditions for reversible transformations, deterministic irreversible transformations, and asymptotic transformations.
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The relative entropy of coherence of Baumgratz et al. has been studied as a measure of asymmetry under the names G-asymmetry and relative entropy of asymmetry, and generalized to Holevo asymmetry measures.
“the function called relative entropy of coherence by Baumgratz et. al. [25] has been extensively studied as a measure of asymmetry under the names of G-asymmetry and relative entropy of asymmetry [29, 32, 39, 41], and it has been generalized to a family of measures of asymmetry, called Holevo asymmetry measures [21, 26]”
From Quantum speed limits, coherence, and asymmetry (2016) · cites this paper as [29]
In [25] it was shown that if F satisfies the 5 postulates then any such resource theory satisfies the EDP with f = E∞ being the regularized relative entropy of a resource.
“In [25] it was shown that if the set F satisfies the 5 postulates then any such resource theory satisfies the EDP with f = E ∞ being the regularized relative entropy of a resource.”
From Reversible Framework for Quantum Resource Theories (2015) · cites this paper as [25]
In [25] Proposition II.1 showed that in this case the relative entropy of a resource can be expressed as in Eq. (4).
“Furthermore, it was also shown in Proposition II.1 of [25] that in this case the relative entropy of a resource can be expressed as in Eq. (4).”
From Reversible Framework for Quantum Resource Theories (2015) · cites this paper as [25]
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Cites
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Self-citationThe resource theory of quantum reference frames: manipulations and monotones
Gour, G., & Spekkens, R. W. (2008) · New Journal of Physics · doi:10.1088/1367-2630/10/3/033023 · Cited by 423 · see citing works
Self-citationExtending Noether’s theorem by quantifying the asymmetry of quantum states
Marvian, I., & Spekkens, R. W. (2014) · Nature Communications · doi:10.1038/ncomms4821 · Cited by 327 · see citing works
Self-citationMarvian, I., & Spekkens, R. W. (2013) · New Journal of Physics · doi:10.1088/1367-2630/15/3/033001 · Cited by 228 · see citing works
Self-citationMeasuring the quality of a quantum reference frame: The relative entropy of frameness
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Self-citationOptimal cloning of pure states, testing single clones
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Research works printed but not linked: 6
- [1]I. Marvian and R. W. Spekkens, Nat. Commun. 5, 3821 (2014), quant-ph/1404.3236.
- [2]I. Marvian and R. W. Spekkens, New J. Phys. 15, 033001 (2013), quant-ph/1104.0018.
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Cited by
Sorted by citations
Reversible Framework for Quantum Resource Theories
Brandão, F. G. S. L., & Gour, G. (2015) · Physical Review Letters · doi:10.1103/physrevlett.115.070503 · Cited by 357 · see citing works
Quantum speed limits, coherence, and asymmetry
Marvian, I., Spekkens, R. W., & Zanardi, P. (2016) · Physical Review A · doi:10.1103/physreva.93.052331 · Cited by 260 · see citing works
Self-citationQuantum coherence sets the quantum speed limit for mixed states
Mondal, D., Datta, C., & Sazim, S. (2016) · Physics Letters A · doi:10.1016/j.physleta.2015.12.015 · Cited by 113 · see citing works
Error Correction of Quantum Reference Frame Information
Hayden, P., Nezami, S., Popescu, S., & Salton, G. (2021) · PRX Quantum · doi:10.1103/prxquantum.2.010326 · Cited by 41 · see citing works
- Authors
- Marvian, I., & Spekkens, R. W.
- Affiliations
- University of Southern California (US)
- Perimeter Institute (CA)
- Venue
- Physical Review A
- Publisher
- American Physical Society (APS)
- Published
- 2014-07-30
- Volume
- 90
- Issue
- 1
- ISSN
- 0556-2791 (ISSN-L)
- 1050-2947
- 1094-1622
- OpenAlex
- W2034341554
- Cited by
- 63
- References
- 9
- Citations by year
- 2026: 2 · 2025: 3 · 2024: 5 · 2023: 1 · 2022: 5 · 2021: 8 · 2020: 5 · 2019: 6 · 2018: 5 · 2017: 11 · 2016: 4 · 2015: 4 · 2014: 2 · 2013: 2
- FWCI
- 6.98
- Type
- journal article
- Language
- en
- Open access
- green
- arxiv.org
- Locations
- Physical Review A (publishedVersion)
- arXiv (Cornell University) (publishedVersion)
- arXiv (Cornell University)
- Bulletin of the American Physical Society
- Topics
- Physical Sciences › Computer Science › Artificial Intelligence › Quantum Information and Cryptography
- Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Quantum Mechanics and Applications
- Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Quantum many-body systems
- Keywords
- quantum asymmetry, pure states, symmetry groups, characteristic function, unitary representations, reversible transformation, irreversible transformation, open quantum systems, information measures
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