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The Ergodic Theorem in Quantum Statistical Mechanics

Elsevier eBooksJan 1, 19631 citation

An improved version of an ergodic theorem in quantum mechanics

Giovanni Maria Prosperi, Alexandria Scotti

Il Nuovo CimentoJul 1, 19605 citations

Limit Theorems for Quantum Entropies and Applications

Igor Bjelaković

We present our recent results on limit theorems for quantum entropies and their applications in quantum information theory. They include the full extensions of the fundamental asymptotic equipartition property (AEP) to ergodic quantum informations sources and the ergodic version of Stein's Lemma on quantum hypothesis testing. These limit theorems are then used to obtain a data compression theorem for ergodic quantum sources and a quantum version of Sanov's theorem on large deviations for uncorrelated quantum sources. Moreover, Stein's lemma clearifies the operational interpretation of the quantum Kullback-Leibler distance (relative entropy), and this operational understanding of this quantity can be employed to give a new intuitive proof of the monotonicity of this statistical distance measure relying on information-theoretic methods.We present our recent results on limit theorems for quantum entropies and their applications in quantum information theory. They include the full extensions of the fundamental asymptotic equipartition property (AEP) to ergodic quantum informations sources and the ergodic version of Stein's Lemma on quantum hypothesis testing. These limit theorems are then used to obtain a data compression theorem for ergodic quantum sources and a quantum version of Sanov's theorem on large deviations for uncorrelated quantum sources. Moreover, Stein's lemma clearifies the operational interpretation of the quantum Kullback-Leibler distance (relative entropy), and this operational understanding of this quantity can be employed to give a new intuitive proof of the monotonicity of this statistical distance measure relying on information-theoretic methods.

Apr 3, 20060 citations

Quantum Relative Entropy

Айрат Мидхатович Бикчентаев, Fuad Kıttaneh, Mohammad Sal Moslehian +1 more

Forum for interdisciplinary mathematicsJan 1, 20240 citations

Pauli, an ergodic theorem and related matters

Peter T. Landsberg

Time averages are important in physics and in statistical mechanics. An ergodic theorem is a way of justifying the replacement of time averages by averages in phase space. A derivation of this theorem from quantum mechanics was given by von Neumann in 1929. Pauli and Fierz found a shorter argument in 1937. They agreed that for ergodicity to hold there should be no energy degeneracy in the Hamiltonian. I trace the circumstances and consequences of a disproof of these arguments.

American Journal of PhysicsJan 13, 20055 citations

A Note on Quantum Entropy

Frank Hansen

arXiv:1511.09189Mathematical Physics Analysis and GeometryMay 12, 20161 citation

An Ergodic Theorem for the Quantum Relative Entropy

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