Quantum information theory of entanglement and measurement
Abstract
We present a quantum information theory that allows for a consistent description of entanglement. It parallels classical (Shannon) information theory but is based entirely on density matrices rather than probability distributions for the description of quantum ensembles. We find that quantum (von Neumann) conditional entropies can be negative for entangled systems, which leads to a violation of entropic Bell inequalities. Quantum inseparability can be related, in this theory, to the appearance of “unclassical” eigenvalues in the spectrum of a conditional “amplitude” matrix that underlies the quantum conditional entropy. Such a unified informationtheoretic description of classical correlation and quantum entanglement clarifies the link between them: the latter can be viewed as “supercorrelation” which can induce classical correlation when considering a tripartite or larger system. Furthermore, the characterization of entanglment with negative conditional entropies paves the way to a natural informationtheoretic description of the measurement process. This model, while unitary and causal, implies the wellknown probabilistic results of conventional quantum mechanics. It also results in a simple interpretation of the LevitinKholevo theorem limiting the accessible information in a quantum measurement.
 Publication:

Physica D Nonlinear Phenomena
 Pub Date:
 September 1998
 DOI:
 10.1016/S01672789(98)000451
 arXiv:
 arXiv:quantph/9605039
 Bibcode:
 1998PhyD..120...62C
 Keywords:

 QUANTUM INFORMATION THEORY;
 ENTANGLEMENT;
 QUANTUM MEASUREMENT;
 QUANTUM NONLOCALITY;
 Quantum Physics
 EPrint:
 26 pages with 6 figures. Expanded version of PhysComp'96 contribution