The DOI matches its Crossref record; 3 of the 3 references it cites were found in a registry or an index.
Geometries of quantum states
Abstract
The quantum analog of the Fisher information metric of a probability simplex is searched and several Riemannian metrics on the set of positive definite density matrices are studied. Some of them appeared in the literature in connection with Cramér–Rao-type inequalities or the generalization of the Berry phase to mixed states. They are shown to be stochastically monotone here. All stochastically monotone Riemannian metrics are characterized by means of operator monotone functions and it is proven that there exist a maximal and a minimal among them. A class of metrics can be extended to pure states and a constant multiple of the Fubini–Study metric appears in the extension.
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Citations
Cites
Statistical distance and the geometry of quantum states
Braunstein, S. L., & Caves, C. M. (1994) · Physical Review Letters · doi:10.1103/physrevlett.72.3439 · Cited by 3,176
Probabilistic and Statistical Aspects of Quantum Theory
Holevo, A. (2011) · doi:10.1007/978-88-7642-378-9 · Cited by 2,582
Differential-Geometrical Methods in Statistics
Amari, S.-I. (1985) · Lecture Notes in Statistics · doi:10.1007/978-1-4612-5056-2 · Cited by 1,673
Cited by
Observable Measure of Quantum Coherence in Finite Dimensional Systems
Girolami, D. (2014) · Physical Review Letters · doi:10.1103/physrevlett.113.170401 · Cited by 537
A Survey on Quantum Channel Capacities
Gyongyosi, L., Imre, S., & Nguyen, H. V. (2018) · IEEE Communications Surveys & Tutorials · doi:10.1109/comst.2017.2786748 · Cited by 337
Multi-parameter quantum metrology
Szczykulska, M., Baumgratz, T., & Datta, A. (2016) · Advances in Physics: X · doi:10.1080/23746149.2016.1230476 · Cited by 267
Bures volume of the set of mixed quantum states
Sommers, H.-J. R., & Zyczkowski, K. (2003) · Journal of Physics A Mathematical and General · doi:10.1088/0305-4470/36/39/308 · Cited by 163
Average fidelity between random quantum states
Życzkowski, K., & Sommers, H.-J. (2005) · Physical Review A · doi:10.1103/physreva.71.032313 · Cited by 135
Covariance and Fisher information in quantum mechanics
Petz, D. (2002) · Journal of Physics A: Mathematical and General · doi:10.1088/0305-4470/35/4/305 · Cited by 132
Self-citationWigner–Yanase information on quantum state space: The geometric approach
Gibilisco, P., & Isola, T. (2003) · Journal of Mathematical Physics · doi:10.1063/1.1598279 · Cited by 105
Riemannian metrics on positive definite matrices related to means
Hiai, F., & Petz, D. (2009) · Linear Algebra and its Applications · doi:10.1016/j.laa.2009.01.025 · Cited by 92
Self-citationFleming, C. H., & Hu, B. L. (2012) · Annals of Physics · doi:10.1016/j.aop.2011.12.006 · Cited by 59
Information geometry of density matrices and state estimation
Brody, D. C. (2011) · Journal of Physics A: Mathematical and Theoretical · doi:10.1088/1751-8113/44/25/252002 · Cited by 32
Metadata
- Authors
- Petz, D., & Sudár, C.
- Venue
- Journal of Mathematical Physics
- Publisher
- AIP Publishing
- Published
- 1996-06-01
- Volume
- 37
- Issue
- 6
- Pages
- 2662-2673
- ISSN
- 0022-2488 (ISSN-L)
- 1089-7658
- OpenAlex
- W2016823915
- Cited by
- 233
- References
- 3
- FWCI
- 3.36
- Type
- journal article
- Language
- en
- Open access
- closed
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