Journal article
Duality of reduced density matrices and their eigenvalues
- Abstract:
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For states of quantum systems of N particles with harmonic interactions we prove that each reduced density matrix ρ obeys a duality condition. This condition implies duality relations for the eigenvalues λk of ρ and relates a harmonic model with length scales ${{\ell }_{1}},{{\ell }_{2}},\ldots ,{{\ell }_{N}}$ with another one with inverse lengths $1/{{\ell }_{1}},1/{{\ell }_{2}},\ldots ,1/{{\ell }_{N}}$. Entanglement entropies and correlation functions inherit duality from ρ. Self-duality can only occur for noninteracting particles in an isotropic harmonic trap.
- Publication status:
- Published
- Peer review status:
- Peer reviewed
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Access Document
- Files:
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(Preview, Accepted manuscript, pdf, 178.3KB, Terms of use)
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- Publisher copy:
- 10.1088/1751-8113/47/41/415305
Authors
- Publisher:
- IOP Publishing
- Journal:
- Journal of Physics A: Mathematical and Theoretical More from this journal
- Volume:
- 47
- Issue:
- 41
- Pages:
- 415305
- Publication date:
- 2014-09-29
- Acceptance date:
- 2014-09-03
- DOI:
- EISSN:
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1751-8121
- ISSN:
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1751-8113
- Keywords:
- Pubs id:
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pubs:538226
- UUID:
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uuid:a2a07426-6515-49c8-89e6-b17109f0eac0
- Local pid:
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pubs:538226
- Source identifiers:
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538226
- Deposit date:
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2017-04-01
Terms of use
- Copyright holder:
- IOP Publishing
- Copyright date:
- 2014
- Notes:
- © 2014 IOP Publishing Ltd. This is the accepted manuscript version of the article. The final version is available online from IOP Publishing at: https://doi.org/10.1088/1751-8113/47/41/415305
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