Monotonicity of a relative Rényi entropy - INSPIRE

DataBETA

Monotonicity of a relative Rényi entropy

Dec 1, 2013

Published in:

J.Math.Phys. 54 (2013) 12, 122201

Published: Dec 1, 2013

DOI:

10.1063/1.4838835

reference search111 citations

Citations per year

Abstract: (AIP)

We show that a recent definition of relative Rényi entropy is monotone under completely positive, trace preserving maps. This proves a recent conjecture of Müller-Lennert et al [“On quantum Rényi entropies: A new definition, some properties,” J. Math. Phys. 54, 122203 (2013); e-print arXiv:1306.3142v1; see also e-print arXiv:1306.3142].

References(18)

Figures(0)

[1]

Convexity of certain maps on positive definite matrices and applications to Hadamard products

T. Ando

- Linear Algebra Appl. 26 (1979) 203-241
•
DOI:
- 10.1016/0024-3795(79)90179-4

[2]

On joint convexity of trace functions

T. Bekjan

- Linear Algebra Appl. 390 (2004) 321-327
•
DOI:
- 10.1016/j.laa.2004.05.002

[3]

Sandwiched Rényi divergence satisfies data processing inequality

Salman Beigi

- J.Math.Phys. 54 (2013) 12, 122202
•
DOI:
- 10.1063/1.4838855

[3]

Sandwiched Rényi divergence satisfies data processing inequality

Salman Beigi

- J.Math.Phys. 54 (2013) 12, 122202
•
DOI:
- 10.1063/1.4838855

[4]

Trace inequalities and quantum entropy. An introductory course

E.A. Carlen

[5]

A Minkowski type trace inequality and strong subadditivity of quantum entropy II: convexity and concavity

E.A. Carlen
,
E.H. Lieb

- Lett.Math.Phys. 83 (2008) 107-126
•
DOI:
- 10.1007/s11005-008-0223-1

[6]

Remarks on two theorems of E. Lieb

H. Epstein

- Commun.Math.Phys. 31 (1973) 317-325
•
DOI:
- 10.1007/BF01646492

[7]

Entropic fluctuations in quantum statistical mechanics. An introduction

V. Jaksic
,
Y. Ogata
,
Y. Pautrat
,
C.-A. Pillet

[8]

Convex trace functions and the Wigner-Yanase-Dyson conjecture

E.H. Lieb

- Adv.Math. 11 (1973) 267-288
•
DOI:
- 10.1016/0001-8708(73)90011-X

[9]

Inequalities for the moments of the eigenvalues of the Schrödinger Hamiltonian and their relation to Sobolev inequalities

E.H. Lieb
,
W. Thirring

[10]

Expectations and entropy inequalities for finite quantum systems

G. Lindblad

- Commun.Math.Phys. 39 (1974) 111-119
•
DOI:
- 10.1007/BF01608390

[11]

On the quantum Renyi relative entropies and related capacity formulas

M. Mosonyi
,
F. Hiai

- IEEE Trans.Info.Theor. 57 2474
•
e-Print:
- 0912.1286
•
DOI:
- 10.1109/TIT.2011.2110050

[12]

On quantum Rényi entropies: A new generalization and some properties

- J.Math.Phys. 54 (2013) 12, 122203,
- J.Math.Phys. 54 (2013) 122203
•
e-Print:
- 1306.3142
•
DOI:
- 10.1063/1.4838856

[12]

On quantum Rényi entropies: A new generalization and some properties

- J.Math.Phys. 54 (2013) 12, 122203,
- J.Math.Phys. 54 (2013) 122203
•
e-Print:
- 1306.3142
•
DOI:
- 10.1063/1.4838856

[12]

On quantum Rényi entropies: A new generalization and some properties

- J.Math.Phys. 54 (2013) 12, 122203,
- J.Math.Phys. 54 (2013) 122203
•
e-Print:
- 1306.3142
•
DOI:
- 10.1063/1.4838856

[13]

Positive functions on C*-algebras

W.F. Stinespring

- Proc.Am.Math.Soc. 6 (1955) 211-216
•
DOI:
- 10.1090/S0002-9939-1955-0069403-4

[14]

Endlich-dimensionale Dichtematrizen II

A. Uhlmann

[15]

Strong Converse for the Classical Capacity of Entanglement-Breaking and Hadamard Channels via a Sandwiched Renyi Relative Entropy

- Commun.Math.Phys. 331 (2014) 2, 593-622
•
e-Print:
- 1306.1586
•
DOI:
- 10.1007/s00220-014-2122-x