Nonlocal Resources in the Presence of Superselection Rules
Open accessAbstract
Superselection rules severely alter the possible operations that can be implemented on a distributed quantum system. Whereas the restriction to local operations imposed by a bipartite setting gives rise to the notion of entanglement as a nonlocal resource, the superselection rule associated with particle number conservation leads to a new resource, the superselection induced variance of the local particle number. We show that, in the case of pure quantum states, one can quantify the nonlocal properties by only two additive measures, and that all states with the same measures can be asymptotically interconverted into each other by local operations and classical communication. Furthermore we discuss how superselection rules affect the concepts of majorization, teleportation, and mixed state entanglement.
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The results presented here cannot be applied directly to all QRTs because the paper considered only finite dimensional Hilbert spaces, and it is not applicable to the resource theory of Non-Gaussianity (also the set of Gaussian states is not convex [15]).
“The results presented here, however, can not be applied directly to all QRTs since for example we considered only finite dimensional Hilbert spaces, and especially it is not applicable for the resource theory of Non-Gaussianity (also the set of Gaussian states is not convex [15]).”
From Reversible Framework for Quantum Resource Theories (2015) · cites this paper as [15]
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Teleporting an unknown quantum state via dual classical and Einstein-Podolsky-Rosen channels
Bennett, C. H., Brassard, G., Crépeau, C., Jozsa, R., Peres, A., & Wootters, W. K. (1993) · Physical Review Letters · doi:10.1103/physrevlett.70.1895 · Cited by 13,703 · see citing works
Polynomial-time algorithms for prime factorization and discrete logarithms on a quantum computer
Shor, P. W. (1997) · SIAM Journal on Computing · doi:10.1137/s0097539795293172 · Cited by 8,472 · see citing works
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Entanglement in many-body systems
Amico, L., Fazio, R., Osterloh, A., & Vedral, V. (2008) · Reviews of Modern Physics · doi:10.1103/revmodphys.80.517 · Cited by 3,745 · see citing works
The classical-quantum boundary for correlations: Discord and related measures
Modi, K., Brodutch, A., Cable, H., Paterek, T., & Vedral, V. (2012) · Reviews of Modern Physics · doi:10.1103/revmodphys.84.1655 · Cited by 1,600 · see citing works
Reference frames, superselection rules, and quantum information
Bartlett, S. D., Rudolph, T., & Spekkens, R. W. (2007) · Reviews of Modern Physics · doi:10.1103/revmodphys.79.555 · Cited by 827 · see citing works
The 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
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
Marvian, I., & Spekkens, R. W. (2013) · New Journal of Physics · doi:10.1088/1367-2630/15/3/033001 · Cited by 228 · see citing works
- Authors
- Schuch, N., Verstraete, F., & Cirac, J. I.
- Affiliations
- Max Planck Institute of Quantum Optics (DE)
- Venue
- Physical Review Letters
- Publisher
- American Physical Society (APS)
- Published
- 2004-02-27
- Volume
- 92
- Issue
- 8
- Pages
- 087904-087904
- ISSN
- 0031-9007 (ISSN-L)
- 1079-7114
- OpenAlex
- W2085528506
- Cited by
- 102
- References
- 2
- Citations by year
- 2026: 3 · 2025: 5 · 2024: 3 · 2023: 6 · 2022: 8 · 2021: 12 · 2020: 13 · 2019: 2 · 2018: 5 · 2017: 1 · 2016: 6 · 2015: 4 · 2014: 1 · 2013: 4 · 2012: 1
- FWCI
- 5.41
- Type
- journal article
- Language
- en
- Open access
- bronze
- doi.org
- Locations
- Physical Review Letters (publishedVersion)
- PubMed (publishedVersion)
- arXiv (Cornell University) (submittedVersion)
- Ghent University Academic Bibliography (Ghent University) (submittedVersion, other-oa)
- CERN Document Server (European Organization for Nuclear Research) (submittedVersion)
- Max Planck Institute for Plasma Physics (submittedVersion)
- MPG.PuRe (Max Planck Society) (submittedVersion)
- arXiv (Cornell University)
- 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
- superselection rules, nonlocality, entanglement, particle number conservation, local operations and classical communication, majorization, quantum teleportation, mixed-state entanglement
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