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
Overview
Integrity signals
Registry
Cites
Statistics
Verification
Claims the paper makes
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
Items 301–400 of 1,000
Datta, N., Mosonyi, M., Hsieh, M.-H., & Brandão, F. G. S. L. (2013) · IEEE Transactions on Information Theory · doi:10.1109/tit.2013.2282160 · Cited by 52
One-Shot Coherence Distillation: Towards Completing the Picture
Zhao, Q., Liu, Y., Yuan, X., Chitambar, E., & Winter, A. (2019) · IEEE Transactions on Information Theory · doi:10.1109/tit.2019.2911102 · Cited by 55
Gour, G., & Wilde, M. M. (2021) · Physical Review Research · doi:10.1103/physrevresearch.3.023096 · Cited by 114
Operational distance and fidelity for quantum channels
Belavkin, V. P., D’Ariano, G. M., & Raginsky, M. (2005) · Journal of Mathematical Physics · doi:10.1063/1.1904510 · Cited by 47
Environment-invariant measure of distance between evolutions of an open quantum system
Grace, M. D., Dominy, J., Kosut, R. L., Brif, C., & RABITZ, H. A. (2010) · New Journal of Physics · doi:10.1088/1367-2630/12/1/015001 · Cited by 53
Quantum microwave-optical interface with nitrogen-vacancy centers in diamond
Li, B., Li, F., Zhou, Y., Ma, S.-L., & Li, F. (2017) · Physical Review A · doi:10.1103/physreva.96.032342 · Cited by 51
Quantifying the resource content of quantum channels: An operational approach
Li, L., Bu, K., & Liu, Z.-W. (2020) · Physical Review A · doi:10.1103/physreva.101.022335 · Cited by 51
Sharma, K., Wilde, M. M., Adhikari, S., & Takeoka, M. (2018) · Civil War Book Review · Cited by 50
Quantum Private Queries: Security Analysis
Giovannetti, V., Lloyd, S., & Maccone, L. (2009) · DSpace@MIT (Massachusetts Institute of Technology) · Cited by 51
Quantum natural gradient generalized to noisy and nonunitary circuits
Koczor, B., & Benjamin, S. C. (2022) · Physical Review A · doi:10.1103/physreva.106.062416 · Cited by 108
Energy–time and frequency–time uncertainty relations: exact inequalities
Dodonov, V. V., & Dodonov, A. V. (2015) · Physica Scripta · doi:10.1088/0031-8949/90/7/074049 · Cited by 53
Min- and Max-Entropy in Infinite Dimensions
Furrer, F., Åberg, J., & Renner, R. (2011) · Communications in Mathematical Physics · doi:10.1007/s00220-011-1282-1 · Cited by 50
Applications of position-based coding to classical communication over quantum channels
Qi, H., Wang, Q., & Wilde, M. M. (2018) · Journal of Physics A Mathematical and Theoretical · doi:10.1088/1751-8121/aae290 · Cited by 53
Minimum-error discrimination of quantum states: Bounds and comparisons
Qiu, D., & Li, L. (2010) · Physical Review A · doi:10.1103/physreva.81.042329 · Cited by 48
Adiabatic approximation for weakly open systems
Thunström, P., Åberg, J., & Sjöqvist, E. (2005) · Physical Review A · doi:10.1103/physreva.72.022328 · Cited by 49
Generation of cluster states in optomechanical quantum systems
Houhou, O., Aissaoui, H., & Ferraro, A. (2015) · Physical Review A · doi:10.1103/physreva.92.063843 · Cited by 50
A Tight Lower Bound on the Classical Communication Cost of Entanglement Dilution
Harrow, A. W., & Lo, H. (2004) · IEEE Transactions on Information Theory · doi:10.1109/tit.2003.822597 · Cited by 49
Energy-sensitive and “Classical-like” Distances between Quantum States
Dodonov, V. V., Man’ko, O. V., Man’ko, V. I., & Wünsche, A. (1999) · Physica Scripta · doi:10.1238/physica.regular.059a00081 · Cited by 47
Towards a formal definition of security for quantum protocols
Crépeau, C., & van de Graaf, J. (1998) · Cited by 52
Conjugate degradability and the quantum capacity of cloning channels
Brádler, K., Dutil, N., Hayden, P. M., & Muhammad, A. (2010) · Journal of Mathematical Physics · doi:10.1063/1.3449555 · Cited by 51
Quantum Zeno Dynamics Through Stochastic Protocols
Müller, M. M., Gherardini, S., & Caruso, F. (2017) · Annalen der Physik · doi:10.1002/andp.201600206 · Cited by 47
Kubica, A., & Demkowicz-Dobrzański, R. (2021) · Physical Review Letters · doi:10.1103/physrevlett.126.150503 · Cited by 50
Restricted numerical range: A versatile tool in the theory of quantum information
Gawron, P., Puchała, Z., Miszczak, J. A., Skowronek, Ł., & Życzkowski, K. (2010) · Journal of Mathematical Physics · doi:10.1063/1.3496901 · Cited by 49
Classicality and anticlassicality measures of pure and mixed quantum states
Dodonov, V. V., & Renó, M. B. (2003) · Physics Letters A · doi:10.1016/s0375-9601(03)00066-5 · Cited by 45
Quantum and classical correlations inside the entanglement wedge
Umemoto, K. (2019) · Physical review. D/Physical review. D. · doi:10.1103/physrevd.100.126021 · Cited by 48
Drawbacks of the use of fidelity to assess quantum resources
Bina, M., Mandarino, A., Olivares, S., & Paris, M. G. A. (2014) · Physical Review A · doi:10.1103/physreva.89.012305 · Cited by 46
Position-based coding and convex splitting for private communication over quantum channels
Wilde, M. M. (2017) · Quantum Information Processing · doi:10.1007/s11128-017-1718-4 · Cited by 46
A family of norms with applications in quantum information theory
Johnston, N., & Kribs, D. W. (2010) · Journal of Mathematical Physics · doi:10.1063/1.3459068 · Cited by 46
Quantum probing beyond pure dephasing
Tamascelli, D., Benedetti, C., Breuer, H.-P., & Paris, M. G. A. (2020) · New Journal of Physics · doi:10.1088/1367-2630/aba0e5 · Cited by 48
Deterministic Microwave-Optical Transduction Based on Quantum Teleportation
Wu, J., Cui, C., Fan, L., & Zhuang, Q. (2021) · Physical Review Applied · doi:10.1103/physrevapplied.16.064044 · Cited by 49
Cloning of Gaussian states by linear optics
Olivares, S., Paris, M. G. A., & Andersen, U. L. (2006) · Physical Review A · doi:10.1103/physreva.73.062330 · Cited by 42
Quantum Benchmark for Teleportation and Storage of Squeezed States
Adesso, G., & Chiribella, G. (2008) · Physical Review Letters · doi:10.1103/physrevlett.100.170503 · Cited by 46
Identifying the Information Gain of a Quantum Measurement
Berta, M., Renes, J. M., & Wilde, M. M. (2014) · IEEE Transactions on Information Theory · doi:10.1109/tit.2014.2365207 · Cited by 60
Uhlmann, A. (2008) · Springer eBooks · doi:10.1007/3-540-53941-7_4 · Cited by 45
Self-citationVersatile Gaussian probes for squeezing estimation
Rigovacca, L., Farace, A., Souza, L. A. M., Pasquale, A. D., Giovannetti, V., & Adesso, G. (2017) · Physical Review A · doi:10.1103/physreva.95.052331 · Cited by 47
Gour, G., & Wilde, M. M. (2021) · Civil War Book Review · Cited by 45
Multiparameter quantum critical metrology
Fresco, G. D., Spagnolo, B., Valenti, D., & Carollo, A. C. M. (2022) · SciPost Physics · doi:10.21468/scipostphys.13.4.077 · Cited by 47
Catalysis of entanglement and other quantum resources
Datta, C., Kondra, T. V., Miller, M., & Streltsov, A. (2023) · Reports on Progress in Physics · doi:10.1088/1361-6633/acfbec · Cited by 49
Converting multilevel nonclassicality into genuine multipartite entanglement
Regula, B., Piani, M., Cianciaruso, M., Bromley, T. R., Streltsov, A., & Adesso, G. (2018) · New Journal of Physics · doi:10.1088/1367-2630/aaae9d · Cited by 44
Geometric distinguishability measures limit quantum channel estimation and discrimination
Katariya, V., & Wilde, M. M. (2021) · Quantum Information Processing · doi:10.1007/s11128-021-02992-7 · Cited by 68
Security of EPR-based quantum cryptography against incoherent symmetric attacks
Inamori, H., Rallan, L., & Vedral, V. (2001) · Journal of Physics A Mathematical and General · doi:10.1088/0305-4470/34/35/317 · Cited by 45
Discrimination with error margin between two states: Case of general occurrence probabilities
Sugimoto, H., Hashimoto, T., Horibe, M., & Hayashi, A. (2009) · Physical Review A · doi:10.1103/physreva.80.052322 · Cited by 44
Effect of phase noise on quantum correlations in Bose-Josephson junctions
Ferrini, G., Spehner, D., Minguzzi, A., & Hekking, F. W. J. (2011) · Physical Review A · doi:10.1103/physreva.84.043628 · Cited by 45
Rényi Divergences as Weighted Non-commutative Vector-Valued $$L_p$$ L p -Spaces
Berta, M., Scholz, V. B., & Tomamichel, M. (2018) · Annales Henri Poincaré · doi:10.1007/s00023-018-0670-x · Cited by 51
Reconstructing entanglement Hamiltonian via entanglement eigenstates
Zhu, W., Huang, Z., & He, Y.-C. (2019) · Physical review. B./Physical review. B · doi:10.1103/physrevb.99.235109 · Cited by 46
Constraining quantum fields using modular theory
Lashkari, N. (2019) · Journal of High Energy Physics · doi:10.1007/jhep01(2019)059 · Cited by 49
Ma, J., Xu, L., Xiong, H.-N., & Wang, X. (2008) · Physical Review E · doi:10.1103/physreve.78.051126 · Cited by 45
A property of quantum relative entropy with an application to privacy in quantum communication
Jain, R., Radhakrishnan, J., & Sen, P. (2009) · Journal of the ACM · doi:10.1145/1568318.1568323 · Cited by 55
Interaction in Quantum Communication
Klauck, H., Nayak, A., Ta‐Shma, A., & Zuckerman, D. (2007) · IEEE Transactions on Information Theory · doi:10.1109/tit.2007.896888 · Cited by 41
Multiple phase estimation for arbitrary pure states under white noise
Yao, Y., Ge, L., Xiao, X., Wang, X., & Sun, C. P. (2014) · Physical Review A · doi:10.1103/physreva.90.062113 · Cited by 42
Complex quantum networks: a topical review
Nokkala, J., Piilo, J., & Bianconi, G. (2024) · Journal of Physics A Mathematical and Theoretical · doi:10.1088/1751-8121/ad41a6 · Cited by 55
“Pretty Strong” Converse for the Quantum Capacity of Degradable Channels
Morgan, C., & Winter, A. (2013) · IEEE Transactions on Information Theory · doi:10.1109/tit.2013.2288971 · Cited by 43
Heinosaari, T., Jivulescu, M. A., Reeb, D., & Wolf, M. M. (2012) · Journal of Mathematical Physics · doi:10.1063/1.4755845 · Cited by 42
Catalysis of Entanglement Manipulation for Mixed States
Eisert, J., & Wilkens, M. (2000) · Physical Review Letters · doi:10.1103/physrevlett.85.437 · Cited by 48
Sudden death of distillability in qutrit-qutrit systems
Song, W., Chen, L., & Zhu, S.-L. (2009) · Physical Review A · doi:10.1103/physreva.80.012331 · Cited by 43
Quantum Communication in Rindler Spacetime
Brádler, K., Hayden, P. M., & Panangaden, P. (2012) · Communications in Mathematical Physics · doi:10.1007/s00220-012-1476-1 · Cited by 48
Reduced fidelity in topological quantum phase transitions
Eriksson, E., & Johannesson, H. (2009) · Physical Review A · doi:10.1103/physreva.79.060301 · Cited by 41
Objectivity in the non-Markovian spin-boson model
Lampo, A., Tuziemski, J., Lewenstein, M., & Korbicz, J. K. (2017) · Physical Review A · doi:10.1103/physreva.96.012120 · Cited by 44
Channel Simulation in Quantum Metrology
Laurenza, R., Lupo, C., Spedalieri, G., Braunstein, S. L., & Pirandola, S. (2018) · Quantum Measurements and Quantum Metrology · doi:10.1515/qmetro-2018-0001 · Cited by 39
The Transition Probability for States of *‐Algebras
Uhlmann, A. (1985) · Annalen der Physik · doi:10.1002/andp.19854970419 · Cited by 43
Self-citationDistributed compression and multiparty squashed entanglement
Avis, D., Hayden, P. M., & Savov, I. (2008) · Journal of Physics A Mathematical and Theoretical · doi:10.1088/1751-8113/41/11/115301 · Cited by 46
Distinguishability and nonclassicality of one-mode Gaussian states
Marian, P., Marian, T. A., & Scutaru, H. (2004) · Physical Review A · doi:10.1103/physreva.69.022104 · Cited by 41
Distance between density operators: Applications to the Jaynes-Cummings model
Knöll, L., & Orłowski, A. (1995) · Physical Review A · doi:10.1103/physreva.51.1622 · Cited by 43
Kobayashi, H., Nonaka, K., & Shikano, Y. (2014) · Physical Review A · doi:10.1103/physreva.89.053816 · Cited by 42
Nonasymptotic assisted distillation of quantum coherence
Regula, B., Lami, L., & Streltsov, A. (2018) · Physical Review A · doi:10.1103/physreva.98.052329 · Cited by 42
Quantum speedup in the identification of cause–effect relations
Chiribella, G., & Ebler, D. (2019) · Nature Communications · doi:10.1038/s41467-019-09383-8 · Cited by 46
Geometric distinguishability measures limit quantum channel estimation and discrimination
Katariya, V., & Wilde, M. M. (2021) · Civil War Book Review · Cited by 42
Spheres and hemispheres as quantum state spaces
Uhlmann, A. (1996) · Journal of Geometry and Physics · doi:10.1016/0393-0440(95)00004-6 · Cited by 42
Self-citationWarren, C., Fernández-Pendás, J., Ahmed, S., Abad, T., Bengtsson, A., Biznárová, J., Debnath, K., Gu, X. Q., Križan, C., Osman, A., et al. (2023) · npj Quantum Information · doi:10.1038/s41534-023-00711-x · Cited by 42
Souquet, J.-R., & Clerk, A. A. (2016) · Physical Review A · doi:10.1103/physreva.93.060301 · Cited by 38
Probabilistic quantum teleportation in the presence of noise
Fortes, R., & Rigolin, G. (2016) · Physical Review A · doi:10.1103/physreva.93.062330 · Cited by 41
Unconditional preparation of nonclassical states via linear-and-quadratic optomechanics
Brunelli, M., Houhou, O., Moore, D. W., Nunnenkamp, A., Paternostro, M., & Ferraro, A. (2018) · Physical Review A · doi:10.1103/physreva.98.063801 · Cited by 45
Fidelity susceptibility in Gaussian random ensembles
Sierant, P., Maksymov, A., Kuś, M., & Zakrzewski, J. (2019) · Physical review. E · doi:10.1103/physreve.99.050102 · Cited by 41
Probabilistic nonunitary gate in imaginary time evolution
Liu, T., Liu, J.-G., & Fan, H. (2021) · Quantum Information Processing · doi:10.1007/s11128-021-03145-6 · Cited by 44
Fundamental Energy Requirement of Reversible Quantum Operations
Chiribella, G., Yang, Y., & Renner, R. (2021) · Physical Review X · doi:10.1103/physrevx.11.021014 · Cited by 46
The smooth entropy formalism for von Neumann algebras
Berta, M., Furrer, F., & Scholz, V. B. (2015) · Journal of Mathematical Physics · doi:10.1063/1.4936405 · Cited by 41
Bures distance as a measure of entanglement for symmetric two-mode Gaussian states
Marian, P., & Marian, T. A. (2008) · Physical Review A · doi:10.1103/physreva.77.062319 · Cited by 45
2 AN INTUITIVE PROOF OF THE DATA PROCESSING INEQUALITYPreprint
Beaudry, N. J., & Renner, R. (2016) · Cited by 41
On quantum coding for ensembles of mixed statesPreprint
Barnum, H., Caves, C. M., Fuchs, C. A., Jozsa, R., & Schumacher, B. (2000) · Cited by 42
Entanglement Swapping and Swapped Entanglement
Zangi, S. M., Shukla, C., Rahman, A. U., & Zheng, B. (2023) · Entropy · doi:10.3390/e25030415 · Cited by 40
Coherence in a cold-atom photon switch
Li, W., & Lesanovsky, I. (2015) · Physical Review A · doi:10.1103/physreva.92.043828 · Cited by 42
Quantum Rate-Distortion Coding With Auxiliary Resources
Wilde, M. M., Datta, N., Hsieh, M.-H., & Winter, A. (2013) · IEEE Transactions on Information Theory · doi:10.1109/tit.2013.2271772 · Cited by 39
Approximate Quantum Error Correction Revisited: Introducing the Alpha-Bit
Hayden, P., & Penington, G. (2020) · Communications in Mathematical Physics · doi:10.1007/s00220-020-03689-1 · Cited by 40
Amortized entanglement of a quantum channel and approximately teleportation-simulable channels
Kaur, E., & Wilde, M. M. (2017) · Journal of Physics A Mathematical and Theoretical · doi:10.1088/1751-8121/aa9da7 · Cited by 48
Ground-state fidelity at first-order quantum transitions
Rossini, D., & Vicari, E. (2018) · Physical review. E · doi:10.1103/physreve.98.062137 · Cited by 41
One-Shot Lossy Quantum Data Compression
Datta, N., Renes, J. M., Renner, R., & Wilde, M. M. (2013) · IEEE Transactions on Information Theory · doi:10.1109/tit.2013.2283723 · Cited by 42
Nha, H., & Carmichael, H. J. (2005) · Physical Review A · doi:10.1103/physreva.71.032336 · Cited by 38
Geometric phases in open tripod systems
Møller, D., Madsen, L. B., & Mølmer, K. (2008) · Physical Review A · doi:10.1103/physreva.77.022306 · Cited by 40
Implementation of quantum maps by programmable quantum processors
Hillery, M. S., Ziman, M., & Bužek, V. (2002) · Physical Review A · doi:10.1103/physreva.66.042302 · Cited by 40
Security of EPR-based Quantum Cryptography against Incoherent Symmetric Attacks
Inamori, H., Rallan, L., & Vedral, V. (2001) · CERN Document Server (European Organization for Nuclear Research) · Cited by 40
Binder, M., & Barthel, T. (2015) · Physical Review B · doi:10.1103/physrevb.92.125119 · Cited by 38
Generalized fidelity susceptibility at phase transitions
You, W., & He, L. (2015) · Journal of Physics Condensed Matter · doi:10.1088/0953-8984/27/20/205601 · Cited by 37
Discriminating strength: a bona fide measure of non-classical correlations
Farace, A., Pasquale, A. D., Rigovacca, L., & Giovannetti, V. (2014) · New Journal of Physics · doi:10.1088/1367-2630/16/7/073010 · Cited by 39
Approximate quantum error correction, random codes, and quantum channel capacity
Klesse, R. (2007) · Physical Review A · doi:10.1103/physreva.75.062315 · Cited by 44
Ektesabi, A., Behzadi, N., & Faizi, E. (2017) · Physical Review A · doi:10.1103/physreva.95.022115 · Cited by 39
Das, S., Bäuml, S., & Wilde, M. M. (2020) · Physical Review A · doi:10.1103/physreva.101.012344 · Cited by 42
Fundamental Limits on the Capacities of Bipartite Quantum Interactions
Bäuml, S., Das, S., & Wilde, M. M. (2018) · Physical Review Letters · doi:10.1103/physrevlett.121.250504 · Cited by 39
A short impossibility proof of quantum bit commitment
Chiribella, G., D’Ariano, G. M., Perinotti, P., Schlingemann, D., & Werner, R. F. (2013) · Physics Letters A · doi:10.1016/j.physleta.2013.02.045 · Cited by 39
Universal recovery from a decrease of quantum relative entropyPreprint
Junge, M., Renner, R., Sutter, D., Wilde, M. M., & Winter, A. (2015) · arXiv (Cornell University) · Cited by 39
Probabilistic quantum teleportation via thermal entanglement
Fortes, R., & Rigolin, G. (2017) · Physical Review A · doi:10.1103/physreva.96.022315 · Cited by 38
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
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
