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We present a bouquet of continuity bounds for quantum entropies, falling broadly into two classes: First, a tight analysis of the Alicki-Fannes continuity bounds for the conditional von Neumann entropy, reaching almost the best possible form that depends only on the system dimension and the trace distance of the states.
E. Schrödinger, “Discussion of Probability Relations between Separated Systems”, Math. Proc. Cambridge Phil. Soc. 31
1936
Earlier work this paper cites.
H. Umegaki, “Conditional expectations in an operator alegebra IV (entropy and information)”, Kodai Math, Sem. Rep. 14
1962
Earlier work this paper cites.
H. Araki, E.H. Lieb, “Entropy inequalities”, Commun. Math. Phys. 18
1970
Earlier work this paper cites.
M. Fannes, “A continuity property of the entropy density for spin lattice systems”, Commun. Math. Phys. 31
1973
Earlier work this paper cites.
E.H. Lieb, M.-B. Ruskai, “Proof of the strong subadditivity of quantum-mechanical entropy”, J. Math. Phys. 14
1973
Earlier work this paper cites.
A. Wehrl, “General properties of entropy”, Rev. Mod. Phys. 50
1978
Earlier work this paper cites.
L.P. Hughston, R. Jozsa, W.K. Wootters, “A complete classification of quantum ensembles having a given density matrix”, Phys. Lett. A 183
1993
Earlier work this paper cites.
C.H. Bennett, D.P. DiVincenzo, J.A. Smolin, W.K. Wootters, “Mixed-state entanglement and quantum error correction”, Phys. Rev. A 54
1996
Earlier work this paper cites.
A.S. Holevo, “On Quantum Communication Channels with Constrained Inputs”, arXiv:quant-ph/9705054 (1997)
1997
Earlier work this paper cites.
V. Vedral, M.B. Plenio, M.A. Rippin, P.L. Knight, “Quantifying Entanglement”, Phys. Rev. Lett. 78
1997
Earlier work this paper cites.
M.J. Donald, M. Horodecki, “Continuity of relative entropy of entanglement”, Phys. Lett. A 264
1999
Earlier work this paper cites.
C.A. Fuchs, J. van de Graaf, “Cryptographic Distinguishability Measures for Quantum-Mechanical States”, IEEE Trans. Inf. Theory 45
1999
Earlier work this paper cites.
M.A. Nielsen, “Continuity bounds for entanglement”, Phys. Rev. A 61
2000
Earlier work this paper cites.
P.M. Hayden, M. Horodecki, B.M. Terhal, “The asymptotic entanglement cost of preparing a quantum state”, J. Phys. A: Math. Gen. 34
2001
Earlier work this paper cites.
K.G.H. Vollbrecht, R.F. Werner, “Entanglement measures under symmetry”, Phys. Rev. A 64
2001
Earlier work this paper cites.
J. Eisert, C. Simon, M.B. Plenio, “On the quantification of entanglement in infinite-dimensional quantum systems”, J. Phys. A: Math. Gen. 35
2002
Earlier work this paper cites.
M. Christandl, A. Winter, “ ‘Squashed entanglement’ – An additive entanglement measure”, J. Math. Phys. 45
2003
Earlier work this paper cites.
R. Alicki, M. Fannes, “Continuity of quantum conditional information”, J. Phys. A: Math. Gen. 37
2004
Earlier work this paper cites.
M. Ohya, D. Petz, Quantum Entropy and Its Use , 2nd edition, Springer Verlag, Berlin Heidelberg, 2004
2004
Cited alongside, same era.
A. Winter, “ ‘Extrinsic’ and ‘Intrinsic’ Data in Quantum Measurements: Asymptotic Convex Decomposition of Positive Operator Valued Measures”, Commun. Math. Phys. 244
2004
Cited alongside, same era.
I. Devetak, P.W. Shor, “The capacity of a quantum channel for simultaneous transmission of classical and quantum information”, Commun. Math. Phys. 256
2005
Cited alongside, same era.
K. Horodecki, M. Horodecki, P. Horodecki, J. Oppenheim, “Locking Entanglement with a Single Qubit”, Phys. Rev. Lett. 94
2005
Cited alongside, same era.
B. Synak-Radtke, M. Horodecki, “On asymptotic continuity of functions of quantum states”, arXiv:quant-ph/0507126 (2005)
2005
Cited alongside, same era.
G. Kimura, T. Miyadera, H. Imai, “Optimal state discrimination in general probabilistic theories”, Phys. Rev. A 79
2009
Later among the works it cites.
D. Leung, G. Smith, “Continuity of quantum channel capacities”, Commun. Math. Phys. 292
2009
Later among the works it cites.
P. Kok, B.W. Lovett, Introduction to Optical Quantum Information Processing , Cambridge University Press, 2010
2010
Later among the works it cites.
M.E. Shirkov, “Continuity of the von Neumann entropy”, Commun. Math. Phys. 296
2010
Later among the works it cites.
M. Mosonyi, F. Hiai, “On the Quantum Rényi Relative Entropies and Related Capacity Formulas”, IEEE Trans. Inf. Theory 57
2011
Later among the works it cites.
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M. Christandl, The Structure of Bipartite Quantum States — Insights from Group Theory and Cryptography , PhD Thesis, Department of Applied Mathematics and Theoretical Physics, Cambridge University, 2006; arXiv:quant-ph/0604183
2006
Cited alongside, same era.
T.M. Cover, J.A. Thomas, Elements of Information Theory , 2nd ed., John Wiley & Sons, 2006
2006
Cited alongside, same era.
A.S. Holevo, “Entanglement-Assisted Capacities of Constrained Quantum Channels”, Theory Probab. Appl. 48
2006
Cited alongside, same era.
A.S. Holevo, M.E. Shirokov, “Continuous Ensembles and the Capacity of Infinite-Dimensional Quantum Channels”, Theory Probab. Appl. 50
2006
Cited alongside, same era.
M.E. Shirokov, “Entropy characteristics of subsets of states. I”, Izvestiya: Mathematics 70
2006
Cited alongside, same era.
K.M.R. Audenaert, “A sharp continuity estimate for the von Neumann entropy”, J. Math. Phys. A: Math. Theor. 40
2007
Cited alongside, same era.
Z. Zhang, “Estimating Mutual Information Via Kolmogorov Distance”, IEEE Trans. Inf. Theory 53
2007
Cited alongside, same era.
2012
Later among the works it cites.
M. Christandl, N. Schuch, A. Winter, “Entanglement of the Antisymmetric State”, Commun. Math. Phys. 311
2012
Later among the works it cites.
C. Weedbrook, S. Pirandola, R. García-Patrón, N.J. Cerf, T.C. Ralph, J.H. Shapiro, S. Lloyd, “Gaussian quantum information”, Rev. Mod. Phys. 84
2012
Later among the works it cites.
S. Weis, A. Knauf, “Entropy distance: new quantum phenomena”, J. Math. Phys. 53
2012
Later among the works it cites.
R. Horn, Ch. Johnson, Matrix analysis , Cambridge University Press, 2nd edition, 2013
2013
Later among the works it cites.
I. Sason, “Entropy Bounds for Discrete Random Variables via Maximal Coupling”, IEEE Trans. Inf. Theory 59
2013
Later among the works it cites.
M.M. Wilde, Quantum Information Theory , Cambridge University Press, 2013
2013
Later among the works it cites.
I. Kim, M.-B. Ruskai, “Bounds on the concavity of entropy”, J. Math. Phys. 55
2014
Later among the works it cites.
Y. Ouyang, “Channel covariance, twirling, contraction, and some upper bounds on the quantum capacity”, Quantum Inf. Comput. 14
2014
Later among the works it cites.
M.E. Shirokov, “Measures of quantum correlations in infinite-dimensional systems”, arXiv[quant-ph]:1506.06377 (2015)
2015
Closest in time.
M.E. Shirokov, “Squashed entanglement in infinite dimensions”, arXiv[quant-ph]:1507.08964v3 (2015)
2015
Closest in time.
D. Sutter, V.B. Scholz, R. Renner, A. Winter, “Approximate Degradable Quantum Channels”, arXiv[quant-ph]:1412.0980v2 (2015)
2015
Closest in time.