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Relative Entropy of States of von Neumann Algebras
Open accessAbstract
Relative entropy of two states of a von Neumann algebra is defined in terms of the relative modular operator. The strict positivity, lower semicontinuity, convexity and monotonicity of relative entropy are proved. The Wigner-Yanase-Dyson-Lieb concavity is also proved for general von Neumann algebra.
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Cited by
Relative entropy equals bulk relative entropy
Jafferis, D. L., Lewkowycz, A., Maldacena, J., & Suh, S. J. (2016) · Journal of High Energy Physics · doi:10.1007/jhep06(2016)004 · Cited by 539
Relative entropy equals bulk relative entropy
Jafferis, D. L., Lewkowycz, A., Maldacena, J., & Suh, S. J. (2015) · arXiv · doi:10.48550/arxiv.1512.06431 · Cited by 534
The proper formula for relative entropy and its asymptotics in quantum probability
Hiai, F., & Petz, D. (1991) · Communications in Mathematical Physics · doi:10.1007/bf02100287 · Cited by 522
Sufficient subalgebras and the relative entropy of states of a von Neumann algebra
Petz, D. (1986) · Communications in Mathematical Physics · doi:10.1007/bf01212345 · Cited by 333
Modular Hamiltonians for deformed half-spaces and the averaged null energy condition
Faulkner, T., Leigh, R. G., Parrikar, O., & Wang, H. (2016) · Journal of High Energy Physics · doi:10.1007/jhep09(2016)038 · Cited by 230
Metadata
- Authors
- Araki, H.
- Venue
- Publications of the Research Institute for Mathematical Sciences
- Published
- 1975-12-31
- Volume
- 11
- Issue
- 3
- Pages
- 809-833
- ISSN
- 0034-5318 (ISSN-L)
- 1663-4926
- OpenAlex
- W4239588355
- Cited by
- 383
- References
- 0
- FWCI
- 1.83
- Type
- journal article
- Language
- en
- Open access
- bronze
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- Araki, H. (1975). Relative Entropy of States of von Neumann Algebras. Publications of the Research Institute for Mathematical Sciences. https://doi.org/10.2977/prims/1195191148
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