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We introduce quantum versions of the $\chi^2$-divergence, provide a detailed analysis of their properties, and apply them in the investigation of mixing times of quantum Markov processes.
E.H. Lieb: Convex trace functions and the Wigner-Yanase-Dyson Conjecture, Adv. Math. 11 267–288 (1973)
1973
Earlier work this paper cites.
E. Lieb “Convex trace functions and the Wigner-Yanase-Dyson conjecture”, Adv. Math
1973
Earlier work this paper cites.
G. Lindbald, Commun. Math. Phys. 48, 119 (1976)
1976
Earlier work this paper cites.
H. Araki, ÔÔRelative entropy of state of von Neumann algebras,ÕÕ Publ. RIMS Kyoto Univ. 9, 809 – 833 (1976)
1976
Earlier work this paper cites.
R. Alicki Rep.Math.Phys: 10, 249-258 (1976)
1976
Earlier work this paper cites.
A Kossakowski, A Frigerio, V Gorini, M Verri: Commun. Math. Phys. 57, 97-110 (1977)
1977
Earlier work this paper cites.
W.A. Majewski, The detailed balance condition in quantum statistical mechanics J. Math. Phys. 25 614 (1984)
1984
Earlier work this paper cites.
D. Petz, “Quasi-Entropies for Finite quantum Systems” Reports on Math. Phys. 23, 57 Ð 65 (1986)
1986
Earlier work this paper cites.
D. Petz, Quasi-entropies for finite quantum systems, Rep. Math. Phys., 23(1986), 57 – 65
1986
Earlier work this paper cites.
H. Araki, ÔÔRecent progress in entropy and relative entropy,ÕÕ Proceedings of the VIIIth International Congress on Mathematical Physics, edited by R. Seneor and M. Mebkhout (World ScientiÞc, Singapore, 1987), pp. 354 – 365
1987
Earlier work this paper cites.
H. Araki, On an inequality of Lieb and Thirring, Lett. Math. Phys. 19, 167â 170 (1990)
1990
Earlier work this paper cites.
Ruskai, M. B. and Stillinger, F. H., Convexity inequalities for estimating free energy and relative entropy, J. Phys. A 23, 2421â 2437 (1990)
1990
Earlier work this paper cites.
A. Frigerio, Simulated annealing and quantum detailed balance, J. Stat. Phys. , Vol. 58, Nos. 1/2, (1990)
1990
Cited alongside, same era.
E.A. Morozova and N.N. Chentsov, Markov invariant geometry on the state manifolds (Russian), Itogi Nauki i Tekhniki 36:69-102 (1990)
1990
Cited alongside, same era.
P. Diaconis and D. Stroock, Geometric bounds or eigenvalues of Markov chains, The Annals of Applied Probability, Vol. 1, No .1(Feb., 1991),pp 36-61
1991
Cited alongside, same era.
J. A. Fill, Eigenvalue bounds on convergence to stationarity for nonreversible Markov chains with an application to the exclusion process, The Annals of Applied Probability, Vol. 1, No. 1(Feb. 1991), pp. 62-87
1991
Cited alongside, same era.
M. Fannes, B. Nachtergaele, and R. F. Werner, Finitely Correlated States On Quantum Spin Chains, Commun. Math. Phys. 144, 443 (1992)
1992
A. Lesniewski, M.B. Ruskai, Monotone Riemannian metrics and relative entropy on noncommutative probability spaces, J. Math. Phys. 40 (1999), 5702â 5724
1999
Later among the works it cites.
B. M. Terhal and D. P. DiVincenzo, Phys. Rev. A 61, 2301 (2000)
2000
Later among the works it cites.
A. Amari and H. Nagaoka, Methods of Information Geometry
2000
Later among the works it cites.
A. S. Holevo, S tatistical Structure of Quantum Theory, Springer Lecture Notes in Physics (2001)
2001
Later among the works it cites.
R. A. Horn and C. R. Johnson T opics in Matrix Analysis Cambridge University Press (2006)
2006
Later among the works it cites.
D. Perez-Garcia, M.M. Wolf, D. Petz, M.B. Ruskai: J. Math. Phys. 47, 083506 (2006)
2006
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Cited alongside, same era.
H. Hasegawa, α \alpha -divergence of the non-commutative information geometry, Reports Math. Phys., 33, 87-93 (1993)
1993
Cited alongside, same era.
M. B. Ruskai, âBeyond Strong Subadditivity? Improved Bounds on the Contraction of Generalized Relative Entropy, Rev. Math. Phys. 6 1147â 1161 (1994)
1994
Cited alongside, same era.
D. Petz, ÔÔMonotone metrics on matrix spaces,ÕÕ Linear Algebr. Appl. 244, 81 Ð 96 (1996)
1996
Cited alongside, same era.
D. Petz and Cs. Sudar, ÔÔGeometries of quantum states,ÕÕ J. Math. Phys. 37, 2662 Ð 2673 (1996)
1996
Cited alongside, same era.
R. Bhatia, M atrix Analysis, Springer-Verlag, New York, 1997
1997
Cited alongside, same era.
D. Petz, Quasi-entropies for states of a von Neumann algebra, Publ. RIMS. Kyoto Univ. 21(1985), 781–800 InÞnite Dimensional Anal. 1, 83 Ð 89 (1998)
1998
Cited alongside, same era.
A. Majewski, R.F. Streater, Detailed balance and quantum dynamical maps, J. Phys. A 31 (1998) 7981-7995
1998
Cited alongside, same era.
Later among the works it cites.
R. A. Horn and C. R. Johnson M atrix Analysis Cambridge University Press (2007)
2007
Later among the works it cites.
M.B. Hastings, Random untaries give quantum expanders, Phys. Rev. A 76, 032315 (2007)
2007
Later among the works it cites.
D. A. Levin, Y. Peres and E. L. Wilmer M arkov Chains and Mixing Times, Amer. Math. Soc., Providence, RI (2008)
2008
Later among the works it cites.
2008
Later among the works it cites.
F. Verstraete, M. M. Wolf and J. I. Cirac, Quantum computation and quantum-state engineering driven by dissipation, Nature Physics 5, 633 - 636 (2009)
2009
Later among the works it cites.