arXiv subjects

Igor Bjelakovic

Publications and source records attributed to Igor Bjelakovic.

23 records · Page 2Linked to original sources

arXiv2006

Structure of Optimal Input Covariance Matrices for MIMO Systems with Covariance Feedback under General Correlated Fading

We describe the structure of optimal Input covariance matrices for single user multiple-input/multiple-output (MIMO) communication system with covariance feedback and for general correlated fading. Our approach is based on the novel concept of right commutant and recovers previously derived results for the Kronecker product models. Conditions are derived which allow a significant simplification of the optimization problem.

cs.IT↗

arXiv2003

An Ergodic Theorem for the Quantum Relative Entropy

We prove the ergodic version of the quantum Stein's lemma which was conjectured by Hiai and Petz. The result provides an operational and statistical interpretation of the quantum relative entropy as a statistical measure of distinguishability, and contains as a special case the quantum version of the Shannon-McMillan theorem for ergodic states. A version of the quantum relative Asymptotic Equipartition Property (AEP) is given.

quant-ph↗

arXiv2003

Chained Typical Subspaces - a Quantum Version of Breiman's Theorem

We give an equivalent finitary reformulation of the classical Shannon-McMillan-Breiman theorem which has an immediate translation to the case of ergodic quantum lattice systems. This version of a quantum Breiman theorem can be derived from the proof of the quantum Shannon-McMillan theorem presented in our previous work (math.DS/0207121).

quant-ph↗

arXiv2003

The Data Compression Theorem for Ergodic Quantum Information Sources

We extend the data compression theorem to the case of ergodic quantum information sources. Moreover, we provide an asymptotically optimal compression scheme which is based on the concept of high probability subspaces. The rate of this compression scheme is equal to the von Neumann entropy rate.

quant-ph↗

arXiv2002

The Shannon-McMillan Theorem for Ergodic Quantum Lattice Systems

We formulate and prove a quantum Shannon-McMillan theorem. The theorem demonstrates the significance of the von Neumann entropy for translation invariant ergodic quantum spin systems on n-dimensional lattices: the entropy gives the logarithm of the essential number of eigenvectors of the system on large boxes. The one-dimensional case covers quantum information sources and is basic for coding theorems.

math.DS↗