INFORMATION-THEORY OF QUANTUM ENTANGLEMENT AND MEASUREMENT

We present a quantum information theory that allows for a consistent d escription of entanglement. It parallels classical (Shannon) informati on theory but is based entirely on density matrices rather than probab ility distributions for the description of quantum ensembles. We find that quantum (von Neumann) conditional entropies can be negative for e ntangled systems, which leads to a violation of entropic Bell inequali ties. Quantum inseparability can be related, in this theory, to the ap pearance of ''unclassical'' eigenvalues in the spectrum of a condition al ''amplitude'' matrix that underlies the quantum conditional entropy . Such a unified information-theoretic description of classical correl ation and quantum entanglement clarifies the link between them: the la tter can be viewed as ''super-correlation'' which can induce classical correlation when considering a tripartite or larger system. Furthermo re, the characterization of entanglement with negative conditional ent ropies paves the way to a natural information-theoretic description of the measurement process. This model, while unitary and causal, implie s the well-known probabilistic results of conventional quantum mechani cs. It also results in a simple interpretation of the Levitin-Kholevo theorem limiting the accessible information in a quantum measurement. (C) 1998 Published by Elsevier Science B.V. All rights reserved.