Fetching the paper…
Reading the bibliography…
We study quantum statistical inference tasks of hypothesis testing and their canonical variations, in order to review relations between their corresponding figures of merit---measures of statistical distance---and demonstrate the crucial differences which arise in the quantum regime in contrast to the classical setting.
L. Mandelstam and I. Tamm, “The uncertainty relation between energy and time in non-relativistic quantum mechanics,” J. Phys. USSR 9
1945
Earlier work this paper cites.
H. Jeffreys, “An invariant form for the prior probability in estimation problems,” Proc. R. Soc. A. 186
1946
Earlier work this paper cites.
S. Kullback and R. A. Leibler, “On information and sufficiency,” The Annals of Mathematical Statistics 22
1951
Earlier work this paper cites.
R. R. Bahadur and R. R. Rao, “On deviations of the sample mean,” Ann. Math. Statist. 31
1960
Earlier work this paper cites.
A. Rényi et al. , “On measures of entropy and information,” in Proceedings of the Fourth Berkeley Symposium on Mathematical Statistics and Probability, Volume 1: Contributions to the Theory of Statistics (The Regents of the University of California, 1961)
1961
Earlier work this paper cites.
H. Umegaki, “Conditional expectation in an operator algebra, IV (Entropy and information),” Kodai Mathematical Seminar Reports , 14
1962
Earlier work this paper cites.
E. P. Wigner and M. M. Yanase, “Information content of distributions,” Proc. Natl. Acad. Sci. U.S.A 49
1963
Earlier work this paper cites.
J. S. Bell, “On the Einstein-Podolsky-Rosen paradox,” Physics 1
1964
Earlier work this paper cites.
M. S. Ali and S. D. Silvey, “A general class of coefficients of divergence of one distribution from another,” J. Roy. Statist. Soc. B 28
1966
Earlier work this paper cites.
I. Csiszár, “Information-type measures of difference of probability distributions and indirect observations,” Studia Sci. Math. Hungar. 2
1967
Earlier work this paper cites.
M. L. Cohen, “The fisher information and convexity,” IEEE Trans. Inf. Theor. 14
1968
Earlier work this paper cites.
D. Bures, “An extension of Kakutani’s theorem on infinite product measures to the tensor product of semifinite w*-algebras,” Trans. Am. Math. Soc 135
1969
Earlier work this paper cites.
E. H. Lieb, “Convex trace functions and the Wigner-Yanase-Dyson conjecture,” Adv. Math. 11
1973
Earlier work this paper cites.
M. Zakai and J. Ziv, “A generalization of the rate-distortion theory and applications,” in Information Theory New Trends and Open Problems (Springer, 1975) pp. 87–123
1975
Earlier work this paper cites.
C. W. Helstrom, Quantum Detection and Estimation Theory (Academic Press, 1976)
1976
Earlier work this paper cites.
A. Uhlmann, “The ‘transition probability” in the state space of a *-algebra,” Rep. Math. Phys. 9
1976
Earlier work this paper cites.
N. N. Chentsov, “Algebraic foundation of mathematical statistics,” Math. Operationsforsch. statist. Serie Statistics. 9
1978
Earlier work this paper cites.
F. Kubo and T. Ando, “Means of positive linear operators,” Math. Ann. 246
1980
Earlier work this paper cites.
F. Hiai, M. Ohya, and M. Tsukada, “Sufficiency, KMS condition and relative entropy in von Neumann algebras.” Pacific J. Math. 96
1981
Earlier work this paper cites.
S. Amari, Differential-geometrical Methods in Statistics , edited by J. Berger, S. Feinberg, J. Gani, K. Krickeberg, I. Olkin, and B. Singer, Lecture Notes in Statistics, Vol. 28 (Springer-Verlag, 1985)
1985
Earlier work this paper cites.
D. Petz, “Quasi-entropies for states of a von neumann algebra,” Publ. RIMS. Kyouto Univ. 21
1985
Earlier work this paper cites.
L. L. Campbell, “An extended Čencov characterization of the information metric,” Proc. Amer. Math. Soc. 98
1986
Earlier work this paper cites.
D. Petz, “Quasi-entropies for finite quantum systems,” Rep. Math. Phys. 23
1986
Earlier work this paper cites.
T. M. Cover and J. A. Thomas, Elements of Information Theory , edited by D. L. Schilling (Wiley-VCH, 1991)
1991
Earlier work this paper cites.
F. Hiai and D. Petz, “The proper formula for relative entropy and its asymptotics in quantum probability,” Commun. Math. Phys. 143
1991
Earlier work this paper cites.
E. A. Morozova and N. Chentsov, N., “Markov invariant geometry on state manifolds,” J. Soviet Math. 3656
1991
Earlier work this paper cites.
R. Jozsa, “Fidelity for mixed quantum states,” J Mod Opt 41
1994
Earlier work this paper cites.
S. L. Braunstein and C. M. Caves, “Statistical distance and the geometry of quantum states,” Phys. Rev. Lett. 72
1994
Earlier work this paper cites.
S. Massar and S. Popescu, “Optimal extraction of information from finite quantum ensembles,” Phys. Rev. Lett. 74
1995
Earlier work this paper cites.
D. Petz, “Monotone metrics on matrix spaces,” Linear Algebr. Appl. 244
1996
Earlier work this paper cites.
J. M. Corcuera and F. Giummolè, “A characterization of monotone and regular divergences,” Ann. Inst. Stat. Math 50
1998
Earlier work this paper cites.
E. L. Lehmann and G. Casella, Theory of Point Estimation , Vol. 31 (Springer, 1998)
1998
Cited alongside, same era.
N. Margolus and L. B. Levitin, “The maximum speed of dynamical evolution,” Physica D 120
1998
Cited alongside, same era.
C. H. Bennett, D. P. DiVincenzo, C. A. Fuchs, T. Mor, E. Rains, P. W. Shor, J. A. Smolin, and W. K. Wootters, “Quantum nonlocality without entanglement,” Phys. Rev. A 59
1999
Cited alongside, same era.
C. J. Isham, Modern Differential Geometry for Physicists , Vol. 61 (World Scientific, 1999)
1999
Cited alongside, same era.
A. Leśniewski and M. B. Ruskai, “Monotone riemannian metrics and relative entropy on non-commutative probability spaces,” J. Math. Phys. 40
1999
Cited alongside, same era.
M. Nussbaum and A. Szkoła, “The Chernoff lower bound for symmetric quantum hypothesis testing,” Ann. Stat. 37
2009
Later among the works it cites.
C. Villani, Optimal Transport: Old and New , Vol. 338 (Springer-Verlag Berlin Heidelberg, 2009)
2009
Later among the works it cites.
M. Tomamichel, R. Colbeck, and R. Renner, “A fully quantum asymptotic equipartition property,” 55
2009
Later among the works it cites.
S. Amari and A. Cichocki, “Information geometry of divergence functions,” Bull. Polish Acad. Sci. Tech. Sci. 58
2010
Later among the works it cites.
S. Deffner and E. Lutz, “Generalized clausius inequality for nonequilibrium quantum processes,” Phys. Rev. Lett. 105
2010
Later among the works it cites.
alphaXiv searches the wider corpus for related work and actual follow-ups.
alphaXiv is searching for related work…
C. A. Fuchs and J. van de Graaf, “Cryptographic distinguishability measures for quantum-mechanical states,” 45
1999
Cited alongside, same era.
T. Ogawa and H. Nagaoka, “Strong converse and Stein’s lemma in the quantum hypothesis testing,” IEEE Trans. Inf. Theor. 46
2000
Cited alongside, same era.
S. Amari and H. Nagaoka, Methods of Information Geometry , edited by S. Kobayashi and M. Takesaki, Translations of Mathematical Monographs, Vol. 191 (Oxford University Press, 2000)
2000
Cited alongside, same era.
M. A. Nielsen and I. L. Chuang, Quantum Computing and Quantum Information (Cambridge University Press, 2000)
2000
Cited alongside, same era.
O. E. Barndorff-Nielsen and R. D. Gill, “Fisher information in quantum statistics,” J. Phys. A 33
2000
Cited alongside, same era.
A. S. Holevo, Statistical Structure of Quantum Theory , Lecture Notes in Physics Monographs, Vol. 67 (Springer-Verlag, 2001)
2001
Cited alongside, same era.
H. Lee, P. Kok, and J. P. Dowling, “A quantum rosetta stone for interferometry,” J. Mod. Opt. 49
2002
Cited alongside, same era.
2011
Later among the works it cites.
F. Hiai, M. Mosonyi, D. Petz, and C. Beny, “Quantum f-divergence and error correction,” Rev. Math. Phys. 23
2011
Later among the works it cites.
S. Luo, S. Fu, and C. H. Oh, “Quantifying correlations via the Wigner-Yanase skew information,” Phys. Rev. A 85
2012
Later among the works it cites.
R. König and G. Smith, “Limits on classical communication from quantum entropy power inequalities,” Nature Photon. 7
2013
Later among the works it cites.
A. del Campo, I. L. Egusquiza, M. B. Plenio, and S. F. Huelga, “Quantum speed limits in open system dynamics,” Phys. Rev. Lett. 110
2013
Later among the works it cites.
M. M. Taddei, B. M. Escher, L. Davidovich, and R. L. de Matos Filho, “Quantum speed limit for physical processes,” Phys. Rev. Lett. 110
2013
Later among the works it cites.
P. Busch, P. Lahti, and R. F. Werner, “Colloquium: Quantum root-mean-square error and measurement uncertainty relations,” Rev. Mod. Phys. 86
2014
Later among the works it cites.
K. M. R. Audenaert, “Comparisons between quantum state distinguishability measures,” Quant. Inf. Comp. 14
2014
Later among the works it cites.
I. Marvian and R. Spekkens, “Extending noethers theorem by quantifying the asymmetry of quantum states,” Nat. Comm. 5
2014
Later among the works it cites.
D. Girolami, “Observable measure of quantum coherence in finite dimensional systems,” Phys. Rev. Lett. 113
2014
Later among the works it cites.
C. Beny and T. J. Osborne, “The renormalization group via statistical inference,” New J. Phys. 17
2015
Later among the works it cites.
I. Sason and S. Verdú, “ f f -divergence inequalities,” IEEE Transactions on Information Theory 62
2016
Later among the works it cites.
D. Virosztek, “Quantum f-divergence preserving maps on positive semidefinite operators acting on finite dimensional Hilbert spaces,” Linear Algebra Appl 501
2016
Later among the works it cites.
J. M. DeBrota, “A quantum information geometric approach to renormalization,” ArXiv e-prints , 1609:09440 (2016)
2016
Later among the works it cites.
M. Oszmaniec, R. Augusiak, C. Gogolin, J. Kołodyński, A. Acín, and M. Lewenstein, “Random bosonic states for robust quantum metrology,” Phys. Rev. X 6
2016
Later among the works it cites.
D. P. Pires, M. Cianciaruso, L. C. Céleri, G. Adesso, and D. O. Soares-Pinto, “Generalized geometric quantum speed limits,” Phys. Rev. X 6
2016
Later among the works it cites.
C. L. Degen, F. Reinhard, and P. Cappellaro, “Quantum sensing,” Rev. Mod. Phys. 89
2017
Later among the works it cites.
M. M. Wilde, M. Tomamichel, and M. Berta, “Converse bounds for private communication over quantum channels,” IEEE Trans. Inf. Theor. 63
2017
Later among the works it cites.
P. A. Gagniuc, Markov Chains: From Theory to Implementation and Experimentation (John Wiley & Sons, 2017)
2017
Later among the works it cites.
F. Hiai and M. Mosonyi, “Different quantum f-divergences and the reversibility of quantum operations,” Rev. Math. Phys. 29
2017
Later among the works it cites.
D. Šafránek, “Discontinuities of the quantum Fisher information and the Bures metric,” Phys. Rev. A 95
2017
Later among the works it cites.
V. I. Man’ko, G. Marmo, F. Ventriglia, and P. Vitale, “Metric on the space of quantum states from relative entropy. tomographic reconstruction,” J. Phys. A: Math. Theor. 50
2017
Later among the works it cites.
J. Czajkowski, M. Jarzyna, and R. Demkowicz-Dobrzański, “Super-additivity in communication of classical information through quantum channels from a quantum parameter estimation perspective,” New J. Phys. 19
2017
Later among the works it cites.
L. Seveso, F. Albarelli, M. G. Genoni, and M. G. A. Paris, “On the discontinuity of the quantum Fisher information for quantum statistical models with parameter dependent rank,” J. Phys. A: Math. Theor. 53
2019
Later among the works it cites.
S. Deffner and S. Campbell, Quantum Thermodynamics , 2053-2571 (Morgan & Claypool Publishers, 2019)
2019
Later among the works it cites.