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arXiv:quant-ph/0205031 · Physical Review A

Quantum information in basendefined by state partitions

Karl Svozil

Published Oct 24, 2002• 18 citations
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Abstract

We define a ``nit'' as a radix n measure of quantum information which is based on state partitions associated with the outcomes of n-ary observables and which, for $n>2,$ is fundamentally irreducible to a binary coding. Properties of this measure for entangled many-particle states are discussed. k particles specify k nits in such a way that k mutually commuting measurements of observables with n possible outcomes are sufficient to determine the information.

DOI
10.1103/physreva.66.044306

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We define a ``nit'' as a radix n measure of quantum information which is based on state partitions associated with the outcomes of n-ary observables and which, for n>2,n>2,n>2, is fundamentally irreducible to a binary coding. Properties of this measure for entangled many-particle states are discussed. k particles specify k nits in such a way that k mutually commuting measurements of observables with n possible outcomes are sufficient to determine the information.
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A context translation principle is introduced relating the origin of quantum randomness to the uncontrollable degrees of freedom of the quasi-classical measurement interface, thereby translating a mismatch between the state prepared and the state measured. For many-particle systems, quantum information in arbitrary base nnn is defined by partitioning the set of states according to the outcomes of nnn-ary joined multi-particle observables.
We propose a new measure of quantum entanglement. Our measure is defined in terms of conditional information transmission for a Quantum Bayesian Net. We show that our measure is identically equal to the Entanglement of Formation in the case of a bipartite (two listener) system occupying a pure state. In the case of mixed states, the relationship between these two measures is not known yet. We discuss some properties of our measure. Our measure can be easily and naturally generalized to handle n-partite (n-listener) systems. It is non-negative for any n. It vanishes for conditionally separable states with n listeners. It is symmetric under permutations of the n listeners. It decreases if listeners are merged, pruned or removed. Most promising of all, it is intimately connected with the Data Processing Inequalities. We also find a new upper bound for classical mutual information which is of interest in its own right.