CoChat
Sign Up
Cited by 1,649Advanced Operator Algebra ResearchQuantum Mechanics and ApplicationsAdvanced Banach Space Theory

The ‘transition probability’ in the state space of a—algebra

Uhlmann, A.·1976·Reports on Mathematical Physics
DOI 10.1016/0034-4877(76)90060-4
Open this paper in CoChat — free account

Integrity signals

Registry

Crossref · 10.1016/0034-4877(76)90060-4

Cites

4 of 4 references verified0 citation errors · 0 not checkable

Statistics

Recomputing p-values needs the paper’s full text.

Claims the paper makes

We couldn’t retrieve this paper’s full text, so its claims and self-check weren’t run. The registry and citation checks still apply.

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?

  • Uhlmann identified quantum fidelity as the proper generalization of wavefunction overlap to mixed states.

    “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]

  • The quantum statistical distance, also called the Bures angle, is given by the arccosine of the square root of the quantum fidelity.

    “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]

  • For ε = 0, the condition F(̺,̺(t)) = 0 is equivalent to Tr[̺(t)̺] = 0.

    “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 TIM, when disorder strength is comparable with the interactions, the critical point disappears and is replaced by a Griffiths phase extending across a region of size proportional to the disorder strength.

    “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]

Cites

Flagged first, then by citations

Cited by

Sorted by citations

Related

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)
DOI
10.1016/0034-4877(76)90060-4
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
Licence
www.elsevier.com/tdm/userlicense/1.0/ (tdm)
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

About these checks

Registry, retraction, Cites and statistics results are computed, not judged, with one exception: a printed reference that no index lists is read once by a model before it counts as a citation error. Claims are extracted by a model and kept only when their quote appears verbatim in the text; each cited source is then checked, with a model’s help, for whether it says what the claim relies on. Those verdicts can be wrong — read the claim’s quote and the cited source before relying on one.

Statistics and arithmetic are recomputed, not judged.

Confidence bands are shown only for fields calibrated on our annotated test set. None is calibrated yet, so no band is shown.

What counts as a claim ›How we measure confidence ›How we check this ›

Are you an author, or do you see a problem with this page? Request a review