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Publications Influence

Proof of the strong subadditivity of quantum‐mechanical entropy

- E. Lieb, M. B. Ruskai
- Mathematics, Physics
- 1 December 1973

We prove several theorems about quantum‐mechanical entropy, in particular, that it is strongly subadditive.

502 27

Inequalities for quantum entropy: A review with conditions for equality

- M. B. Ruskai
- Mathematics, Physics
- 13 May 2002

This article presents self-contained proofs of the strong subadditivity inequality for von Neumann’s quantum entropy, S(ρ), and some related inequalities for the quantum relative entropy, most… Expand

178 17- PDF

Minimal entropy of states emerging from noisy quantum channels

- Christopher King, M. B. Ruskai
- Mathematics, Computer Science
- IEEE Trans. Inf. Theory
- 17 November 1999

TLDR

301 15- PDF

Monotone Riemannian metrics and relative entropy on noncommutative probability spaces

- Andrew S. Lesniewski, M. B. Ruskai
- Mathematics, Physics
- 30 August 1998

We use the relative modular operator to define a generalized relative entropy for any convex operator function g on (0,∞) satisfying g(1)=0. We show that these convex operator functions can be… Expand

121 11- PDF

The χ2-divergence and mixing times of quantum Markov processes

- K. Temme, M. Kastoryano, M. B. Ruskai, M. M. Wolf, F. Verstraete
- Mathematics, Physics
- 13 May 2010

We introduce quantum versions of the χ2-divergence, provide a detailed analysis of their properties, and apply them in the investigation of mixing times of quantum Markov processes. An approach… Expand

80 10- PDF

Multiplicativity of Completely Bounded p-Norms Implies a New Additivity Result

- I. Devetak, M. Junge, C. King, M. B. Ruskai
- Mathematics, Physics
- 23 June 2005

AbstractWe prove additivity of the minimal conditional entropy associated with a quantum channel Φ, represented by a completely positive (CP), trace-preserving map, when the infimum of S(γ12) − S(γ1)… Expand

95 8- PDF

Contractivity of positive and trace-preserving maps under Lp norms

- D. Pérez-García, M. Wolf, D. Petz, M. B. Ruskai
- Mathematics, Physics
- 30 January 2006

We provide a complete picture of contractivity of trace preserving positive maps with respect to p-norms. We show that for p>1 contractivity holds in general if and only if the map is unital. When… Expand

88 6- PDF

A UNIFIED TREATMENT OF CONVEXITY OF RELATIVE ENTROPY AND RELATED TRACE FUNCTIONS, WITH CONDITIONS FOR EQUALITY

- A. Jencová, M. B. Ruskai
- Physics, Mathematics
- 17 March 2009

We consider a generalization of relative entropy derived from the Wigner–Yanase–Dyson entropy and give a simple, self-contained proof that it is convex. Moreover, special cases yield the joint… Expand

54 5- PDF

A Fundamental Property of Quantum-Mechanical Entropy

- E. Lieb, M. B. Ruskai
- Physics
- 5 March 1973

There are some properties of entropy, such as concavity and subadditivity, that are known to hold (in classical and in quantum mechanics) irrespective of any assumptions on the detailed dynamics of a… Expand

143 4

BEYOND STRONG SUBADDITIVITY? IMPROVED BOUNDS ON THE CONTRACTION OF GENERALIZED RELATIVE ENTROPY

- M. B. Ruskai
- Mathematics
- 1994

New bounds are given on the contraction of certain generalized forms of the relative entropy of two positive semi-definite operators under completely positive mappings. In addition, several… Expand

114 4