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Cited by 13Quantum many-body systemsQuantum Mechanics and ApplicationsQuantum Information and Cryptography

Simulating symmetric time evolution with local operations

Open access
Toloui, Borzu, Gour, Gilad·2012·New Journal of Physics
DOI 10.1088/1367-2630/14/12/123026
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Abstract

In closed systems, dynamical symmetries lead to conservation laws. However, conservation laws are not applicable to open systems that undergo irreversible transformations. More general selection rules are needed to determine whether, given two states, the transition from one state to the other is possible. The usual approach to the problem of finding such rules relies heavily on group theory and involves a detailed study of the structure of the respective symmetry group. We approach the problem in a completely new way by using entanglement to investigate the asymmetry properties of quantum states. To this end, we embed the space state of the system in a tensor product Hilbert space, whereby symmetric transformations between two states are replaced with local operations on their bipartite images.The embedding enables us to use the well-studied theory of entanglement to investigate the consequences of dynamic symmetries. Moreover, under reversible transformations, the entanglement of the bipartite image states becomes a conserved quantity. These entanglement-based conserved quantities are new and different from the conserved quantities based on expectation values of the Hamiltonian symmetry generators. Our method is not group-specific and applies to general symmetries associated with any semi-simple Lie group.

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Crossref · 10.1088/1367-2630/14/12/123026

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  • Any translationally invariant operation can be implemented by applying an energy-conserving unitary on the system and an environment initially in an incoherent state.

    “any TI operation can be implemented by applying an energy-conserving unitary on the system and an environment , which is initially in an incoherent state (See also [35]).”

    From Quantum speed limits, coherence, and asymmetry (2016) · cites this paper as [35]

  • The robustness measure in entanglement theory measures the amount of noise that can be added to an entangled state before it becomes unentangled (separable).

    “The measure of robustness [23, 33, 34] in entanglement theory measures the amount of noise that can be added to an entangled state before it becomes unentangled (separable).”

    From Reversible Framework for Quantum Resource Theories (2015) · cites this paper as [23]

  • General QRTs may have many inequivalent maximal resource states, unlike entanglement theory which has a unique golden unit such as the Bell/Singlet state.

    “Unlike entanglement theory, that have a unique 'golden' unit such as the Bell/Singlet state, general QRTs may have many such units, and more precisely, can have many inequivalent maximal resource states.”

    From Reversible Framework for Quantum Resource Theories (2015) · cites this paper as [23]

  • The proof of the main theorem cannot follow directly from its analog in entanglement theory [23].

    “Note however that the proof of the theorem above can not follow directly from its analog in entanglement theory [23].”

    From Reversible Framework for Quantum Resource Theories (2015) · cites this paper as [23]

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1 of the 30 references couldn’t be matched to a known paper.

Research works printed but not linked: 1

  1. [32]M. Horodecki, and J. Oppenheim, arXiv:1111.3834v1 [quant-ph] (2011). · arXiv

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Authors
Toloui, B., & Gour, G.
Affiliations
University of Calgary (CA)
Corresponding author
  • Toloui, Borzu
  • Gour, Gilad
ORCID
Gour, Gilad
Venue
New Journal of Physics
Publisher
IOP Publishing
Published
2012-12-14
Volume
14
Issue
12
Pages
123026
ISSN
1367-2630 (ISSN-L)
DOI
10.1088/1367-2630/14/12/123026
OpenAlex
W2145422772
Cited by
13
References
30
Citations by year
2024: 1 · 2021: 1 · 2018: 2 · 2017: 2 · 2016: 2 · 2015: 2 · 2014: 2 · 2013: 1
FWCI
0.83
Type
journal article
Language
en
Open access
Licence
cc-by
Locations
  • New Journal of Physics (publishedVersion, cc-by)
  • arXiv (Cornell University) (submittedVersion)
  • DOAJ (DOAJ: Directory of Open Access Journals) (submittedVersion)
  • arXiv (Cornell University)
Funders
  • Mitacs
  • Alberta Innovates
  • Natural Sciences and Engineering Research Council of Canada
Topics
  • Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Quantum many-body systems
  • Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Quantum Mechanics and Applications
  • Physical Sciences › Computer Science › Artificial Intelligence › Quantum Information and Cryptography
Keywords
dynamical symmetry, open quantum systems, selection rules, entanglement, local operations, irreversible transformation, compact semisimple Lie groups, conservation laws, quantum transitions

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