117,536 research outputs found
Quantum Information and Entropy
Thermodynamic entropy is not an entirely satisfactory measure of information
of a quantum state. This entropy for an unknown pure state is zero, although
repeated measurements on copies of such a pure state do communicate
information. In view of this, we propose a new measure for the informational
entropy of a quantum state that includes information in the pure states and the
thermodynamic entropy. The origin of information is explained in terms of an
interplay between unitary and non-unitary evolution. Such complementarity is
also at the basis of the so-called interaction-free measurement.Comment: 21 pages, 3 figure
Logical Entropy: Introduction to Classical and Quantum Logical Information theory
Logical information theory is the quantitative version of the logic of partitions just as logical probability theory is the quantitative version of the dual Boolean logic of subsets. The resulting notion of information is about distinctions, differences and distinguishability and is formalized using the distinctions of a partition. All the definitions of simple, joint, conditional and mutual entropy of Shannon information theory are derived by a uniform transformation from the corresponding definitions at the logical level. The purpose of this paper is to give the direct generalization to quantum logical information theory that similarly focuses on the pairs of eigenstates distinguished by an observable, i.e., qudits of an observable. The fundamental theorem for quantum logical entropy and measurement establishes a direct quantitative connection between the increase in quantum logical entropy due to a projective measurement and the eigenstates that are distinguished by the measurement. Both the classical and quantum versions of logical entropy have simple interpretations as “two-draw” probabilities for distinctions. The conclusion is that quantum logical entropy is the simple and natural notion of information for quantum information theory focusing on the distinguishing of quantum states
Intrinsic Quantum Computation
We introduce ways to measure information storage in quantum systems, using a
recently introduced computation-theoretic model that accounts for measurement
effects. The first, the quantum excess entropy, quantifies the shared
information between a quantum process's past and its future. The second, the
quantum transient information, determines the difficulty with which an observer
comes to know the internal state of a quantum process through measurements. We
contrast these with von Neumann entropy and quantum entropy rate and provide a
closed-form expression for the latter for the class of deterministic quantum
processes.Comment: 5 pages, 1 figure, 1 table; updated with corrections;
http://cse.ucdavis.edu/~cmg/compmech/pubs/iqc.ht
The information entropy of quantum mechanical states
It is well known that a Shannon based definition of information entropy leads
in the classical case to the Boltzmann entropy. It is tempting to regard the
Von Neumann entropy as the corresponding quantum mechanical definition. But the
latter is problematic from quantum information point of view. Consequently we
introduce a new definition of entropy that reflects the inherent uncertainty of
quantum mechanical states. We derive for it an explicit expression, and discuss
some of its general properties. We distinguish between the minimum uncertainty
entropy of pure states, and the excess statistical entropy of mixtures.Comment: 7 pages, 1 figur
- …