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Data Compression Limit for an Information Source of Interacting Qubits

Nilanjana Datta, Yuri Suhov

arXiv:quant-ph/0207069Quantum Information ProcessingAug 1, 20028 citations

Quantum Source Coding and Data Compression

Dėnes Petz

Springer eBooksApr 3, 20073 citations

Quantum Information Compression

François Chapeau‐Blondeau

Springer eBooksJan 1, 20260 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

The Ergodic Theorem in Quantum Statistical Mechanics

Elsevier eBooksJan 1, 19631 citation

Weak measurements and universal compression of quantum information sources

Alexei Kaltchenko

We present a new quantum data compression scheme, which optimally compresses any completely ergodic quantum information source with a Markovian property. The scheme does not assume any apriory knowledge of the source (other than complete ergodicity and the Markovian property) and uses so-called "weak" (non-demolition) measurements to estimate the eigenbasis and entropy rate of the source. The scheme is fully universal in the sense of being source independent.

Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIEAug 24, 20040 citations

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