The resource theory of quantum reference frames: manipulations and monotones
Open accessAbstract
Every restriction on quantum operations defines a resource theory, determining how quantum states that cannot be prepared under the restriction may be manipulated and used to circumvent the restriction. A superselection rule (SSR) is a restriction that arises through the lack of a classical reference frame and the states that circumvent it (the resource) are quantum reference frames. We consider the resource theories that arise from three types of SSRs, associated respectively with lacking: (i) a phase reference, (ii) a frame for chirality, and (iii) a frame for spatial orientation. Focusing on pure unipartite quantum states (and in some cases restricting our attention even further to subsets of these), we explore single-copy and asymptotic manipulations. In particular, we identify the necessary and sufficient conditions for a deterministic transformation between two resource states to be possible and, when these conditions are not met, the maximum probability with which the transformation can be achieved. We also determine when a particular transformation can be achieved reversibly in the limit of arbitrarily many copies and find the maximum rate of conversion. A comparison of the three resource theories demonstrates that the extent to which resources can be interconverted decreases as the strength of the restriction increases. Along the way, we introduce several measures of frameness and prove that these are monotonically non-increasing under various classes of operations that are permitted by the SSR.
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The variance of energy ∆E^2 is nonincreasing for pure-to-pure state transformations achieved by TI quantum operations.
“Note that all the properties (i), (ii) and (iii) of A min/max are also satisfied by the variance of the energy, ∆ 2 E , and consequently, using essentially the same argument, one can show that the variance is also nonincreasing for pure to pure state transformations that are achieved by TI quantum opertations [28, 30].”
From Quantum speed limits, coherence, and asymmetry (2016) · cites this paper as [28]
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Self-citation
- Authors
- Gour, G., & Spekkens, R. W.
- Affiliations
- University of Calgary (CA)
- University of Cambridge (GB)
- Venue
- New Journal of Physics
- Publisher
- IOP Publishing
- Published
- 2008-03-17
- Volume
- 10
- Issue
- 3
- Pages
- 033023
- ISSN
- 1367-2630 (ISSN-L)
- OpenAlex
- W2084575582
- Cited by
- 423
- References
- 46
- Citations by year
- 2026: 23 · 2025: 36 · 2024: 34 · 2023: 34 · 2022: 26 · 2021: 36 · 2020: 42 · 2019: 34 · 2018: 38 · 2017: 29 · 2016: 31 · 2015: 17 · 2014: 15 · 2013: 11 · 2012: 7
- FWCI
- 5.28
- Type
- journal article
- Language
- en
- Open access
- gold
- doi.org
- Licence
- cc-by
- Locations
- New Journal of Physics (publishedVersion, cc-by)
- arXiv (Cornell University) (publishedVersion)
- arXiv (Cornell University)
- Funders
- Natural Sciences and Engineering Research Council of Canada
- 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 › Computer Science › Artificial Intelligence › Quantum Computing Algorithms and Architecture
- Keywords
- quantum reference frames, resource theory, superselection rules, phase reference, chirality, spatial orientation, monotones, quantum state transformation, reversible transformation
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