The DOI matches its Crossref record; 4 of the 4 references it cites were found in a registry or an index.
The ‘transition probability’ in the state space of a—algebra
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Claims other papers make about this one
Each is checked against this paper’s own text: does it say what the citing paper says it does?
In the citing paper
“It was Uhlmann [62] who realised that the proper generalisation of the overlap of wavefunctions is given by the quantum fidelity,”
From Quantum speed limits: from Heisenberg’s uncertainty principle to optimal quantum control (2017) · cites this paper as [62]
In the citing paper
“the quantum statistical distance, aka the Bures angle is given by L(ρ 1 , ρ 2 ) = arccos F(ρ 1 , ρ 2 ) ,(70)”
From Quantum speed limits: from Heisenberg’s uncertainty principle to optimal quantum control (2017) · cites this paper as [62]
In the citing paper
“Notice, finally, that for ǫ = 0 we reobtain all the results that were given in [6], since in this case the condition (7) is equivalent to the condition Tr[ ̺ ( t ) ̺ ] = 0 that was employed there [8].”
From Quantum limits to dynamical evolution (2003) · cites this paper as [8]
In the citing paper
“Indeed, in the TIM when the disorder strength is comparable with the interactions, the critical point disappears and is replaced by a so called Griffiths phase [180], extending across a region of size proportional to the disorder strength.”
From Can one trust quantum simulators? (2012) · cites this paper as [180]
Citations
Cites
C[*]-algebras and W[*]-algebras
Sakai, S. (1971) · Springer eBooks · Cited by 1,336
On equivalence of infinite product measures
Kakutani, S. (1948) · The Annals of Mathematics · doi:10.2307/1969123 · Cited by 424
Bures, D. (1969) · Transactions of the American Mathematical Society · doi:10.1090/s0002-9947-1969-0236719-2 · Cited by 363
Functional calculus for sesquilinear forms and the purification map
Pusz, W., & Woronowicz, S. L. (1975) · Reports on Mathematical Physics · doi:10.1016/0034-4877(75)90061-0 · Cited by 348
Research works printed but not linked: 3
- Araki, 1973, RIMS-151
- Bures, 1969, Trans. Amer. Math. Soc., 135, 199
- Uhlmann, 1974, E2-9149
Cited by
Sorted by citations
Horodecki, R., Horodecki, P., Horodecki, M., & Horodecki, K. (2009) · Reviews of Modern Physics · doi:10.1103/revmodphys.81.865 · Cited by 10,118
Weedbrook, C., Pirandola, S., García−Patrón, R., Cerf, N. J., Ralph, T. C., Shapiro, J. H., & Lloyd, S. (2012) · Reviews of Modern Physics · doi:10.1103/revmodphys.84.621 · Cited by 3,843
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
Entanglement of a pair of quantum bits
Hill, S., & Wootters, W. K. (1997) · Physical Review Letters · doi:10.1103/physrevlett.78.5022 · Cited by 2,823
Baumgratz, T., Cramer, M., & Plenio, M. B. (2014) · Physical Review Letters · doi:10.1103/physrevlett.113.140401 · Cited by 2,721
Metadata
- Authors
- Uhlmann, A.
- Affiliations
- Joint Institute for Nuclear Research (RU)
- Corresponding author
- Uhlmann, A.
- Venue
- Reports on Mathematical Physics
- Publisher
- Elsevier BV
- Published
- 1976-04
- Volume
- 9
- Issue
- 2
- Pages
- 273-279
- ISSN
- 0034-4877 (ISSN-L)
- OpenAlex
- W1621050367
- Cited by
- 1,649
- References
- 4
- Citations by year
- 2026: 73 · 2025: 95 · 2024: 77 · 2023: 120 · 2022: 87 · 2021: 83 · 2020: 85 · 2019: 86 · 2018: 106 · 2017: 54 · 2016: 74 · 2015: 60 · 2014: 69 · 2013: 61 · 2012: 41
- FWCI
- 1.78
- Type
- journal article
- Language
- en
- Open access
- closed
- Locations
- Reports on Mathematical Physics (publishedVersion)
- Topics
- Physical Sciences › Mathematics › Mathematical Physics › Advanced Operator Algebra Research
- Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Quantum Mechanics and Applications
- Physical Sciences › Mathematics › Mathematical Physics › Advanced Banach Space Theory
- Keywords
- transition probabilities, vector states, representation theory of algebras, quantum mechanics, state space
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