Extending Noether’s theorem by quantifying the asymmetry of quantum states
Open accessAbstract
Noether's theorem is a fundamental result in physics stating that every symmetry of the dynamics implies a conservation law. It is, however, deficient in several respects: for one, it is not applicable to dynamics wherein the system interacts with an environment; furthermore, even in the case where the system is isolated, if the quantum state is mixed then the Noether conservation laws do not capture all of the consequences of the symmetries. Here we address these deficiencies by introducing measures of the extent to which a quantum state breaks a symmetry. Such measures yield novel constraints on state transitions: for nonisolated systems they cannot increase, whereas for isolated systems they are conserved. We demonstrate that the problem of finding non-trivial asymmetry measures can be solved using the tools of quantum information theory. Applications include deriving model-independent bounds on the quantum noise in amplifiers and assessing quantum schemes for achieving high-precision metrology.
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The Wigner-Yanase skew information is a measure of asymmetry relative to translations generated by H.
“It was shown that Wigner-Yanase skew information is a measure of asymmetry, and therefore quantifies symmetry-breaking relative to translations generated by H .”
From Quantum speed limits, coherence, and asymmetry (2016) · cites this paper as [21]
The function F_H is a faithful measure of asymmetry, vanishing if and only if the state is incoherent.
“is a faithful measure of asymmetry [21, 26], where faithfulness means that it vanishes if and only if the state is incoherent”
From Quantum speed limits, coherence, and asymmetry (2016) · cites this paper as [21]
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 [21]
F_H(ρ) has been previously studied as a measure of asymmetry.
“where F H ( ρ ) is given by Eq. (2.6) and has been previously studied as a measure of asymmetry [21, 26].”
From Quantum speed limits, coherence, and asymmetry (2016) · cites this paper as [21]
The Wigner-Yanase skew information has been shown to be a measure of asymmetry.
“The Wigner-Yanase skew information has been shown to be a measure of asymmetry [21] and has a simple interpretation in the context of quantum speed limits.”
From Quantum speed limits, coherence, and asymmetry (2016) · cites this paper as [21]
In [26] it was shown that the regularized relative entropy of a resource is the unique asymptotic rate of any reversible QRT.
“In [26] it was shown that the regularized relative entropy of a resource is the unique asymptotic rate of any reversible QRT.”
From Reversible Framework for Quantum Resource Theories (2015) · cites this paper as [26]
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- Authors
- Marvian, I., & Spekkens, R. W.
- Affiliations
- University of Southern California (US)
- Perimeter Institute (CA)
- Corresponding author
- Marvian, Iman
- Venue
- Nature Communications
- Published
- 2014-05-13
- Volume
- 5
- Issue
- 1
- Pages
- 3821-3821
- ISSN
- 2041-1723 (ISSN-L)
- OpenAlex
- W2083523039
- Cited by
- 327
- References
- 27
- Citations by year
- 2026: 16 · 2025: 25 · 2024: 29 · 2023: 24 · 2022: 31 · 2021: 34 · 2020: 32 · 2019: 28 · 2018: 23 · 2017: 33 · 2016: 30 · 2015: 18 · 2014: 4
- FWCI
- 28.24
- Type
- journal article
- Language
- en
- Open access
- bronze
- doi.org
- Licence
- Locations
- Nature Communications (publishedVersion)
- PubMed (publishedVersion)
- arXiv (Cornell University) (submittedVersion)
- RePEc: Research Papers in Economics (submittedVersion)
- arXiv (Cornell University)
- Funders
- Government of Canada
- Institut Périmètre de physique théorique
- Multidisciplinary University Research Initiative (W911NF-11-1-0268)
- Natural Sciences and Engineering Research Council of Canada
- Army Research Office (W911NF‐11‐1‐0268, MURI grant W911NF-11-1-0268, W911NF, W911NF-11)
- 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 › Statistical and Nonlinear Physics › Advanced Thermodynamics and Statistical Mechanics
- Keywords
- Noether's theorem, quantum asymmetry, symmetry breaking, conservation laws, open quantum systems, mixed quantum states, asymmetry measures, quantum metrology, quantum information
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