Limit relation for quantum entropy and channel capacity per unit cost

I. Csiszár, Fumio Hiai, D. Petz

Research output: Contribution to journalArticle

4 Citations (Scopus)

Abstract

In a thermodynamic model, Diósi [Int. J. Quantum Inf. 4, 99-104 (2006)] arrived at a conjecture stating that certain differences of von Neumann entropies converge to relative entropy as system size goes to infinity. The conjecture is proven in this paper for density matrices. The analytic proof uses the quantum law of large numbers and the inequality between the Belavkin-Staszewski and Umegaki relative entropies. Moreover, the concept of channel capacity per unit cost is introduced for classical-quantum channels. For channels with binary input alphabet, this capacity is shown to equal the relative entropy. The result provides a second proof of the conjecture and a new interpretation. Both approaches lead to generalizations of the conjecture.

Original languageEnglish
Article number092102
JournalJournal of Mathematical Physics
Volume48
Issue number9
DOIs
Publication statusPublished - 2007

Fingerprint

Quantum Entropy
channel capacity
Quantum Channel
Channel Capacity
Relative Entropy
entropy
costs
Unit
Costs
alphabets
Law of large numbers
Density Matrix
infinity
Thermodynamics
Entropy
Infinity
Binary
Converge
thermodynamics

ASJC Scopus subject areas

  • Physics and Astronomy(all)
  • Statistical and Nonlinear Physics
  • Mathematical Physics

Cite this

Limit relation for quantum entropy and channel capacity per unit cost. / Csiszár, I.; Hiai, Fumio; Petz, D.

In: Journal of Mathematical Physics, Vol. 48, No. 9, 092102, 2007.

Research output: Contribution to journalArticle

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