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Annals of the New York Academy of Sciences

Bounds for Accessible Information in Quantum Mechanicsa

Christopher A. Fuchs, Carlton M. Caves

Published Apr 1, 1995• 4 citations
Publisher
DOI
10.1111/j.1749-6632.1995.tb39012.x

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We consider fundamental limits on accessible information from molecular-scale volumes in electronic systems. Our approach is based on a quantitative measure—the volume accessible information—which we define as the Shannon mutual information associated with the best possible quantum measurement that can access a system through a specified readout volume. Specifically, we obtain a general expression for an upper bound on the volume accessible information that depends only on the manner in which information is encoded in electron states and specification of the readout volume. This bound is obtained within a tight-binding framework for simplicity and compatibility with atomistic descriptions of molecular-scale electronic systems. As an illustration, we study the volume accessible information bound for measurements accessing finite segments of long polyparaphenylene (PPP) molecules with binary information encoded in the states of electrons in the lowest unoccupied molecular orbital band. Evaluation of this bound reveals severe limits on the amount of information accessible from measurements on short PPP chain segments, where the state distinguishability required for reliable information extraction is diminished.

Journal of Applied Physics•Feb 15, 2006•5 citations
The accessible information and the informational power quantify the maximum amount of information that can be extracted from a quantum ensemble and by a quantum measurement, respectively. Here, we investigate the tradeoff between the accessible information (informational power, respectively) and the purity of the states of the ensemble (the elements of the measurement, respectively). Under any given lower bound on the purity, 1) we compute the minimum informational power and show that it is attained by the depolarized uniformly-distributed measurement; and 2) we give a lower bound on the accessible information. Under any given upper bound on the purity, 1) we compute the maximum accessible information and show that it is attained by an ensemble of pairwise commuting states with at most two distinct non-null eigenvalues; and 2) we give a lower bound on the maximum informational power. The present results provide, as a corollary, novel sufficient conditions for the tightness of the Jozsa-Robb-Wootters lower bound to the accessible information.
We find a universal lower bound on locally accessible information for arbitrary bipartite quantum ensembles, when one of the parties is two dimensional. In higher dimensions and in a higher number of parties, the bound is on accessible information by separable operations. We show that for any given density matrix (of an arbitrary number of parties and dimensions), there exists an ensemble, which averages to the given density matrix and whose locally accessible information saturates the lower bound. Moreover, we give a general method to obtain bounds on the yield of singlets in distillation protocols that involves local distinguishing, by using lower and upper bounds on locally accessible information. We then illustrate it by using our lower bound, along with a previously obtained upper bound, on locally accessible information.
We consider fundamental limits on accessible information from molecular-scale volumes in electronic systems. Our approach is based on a quantitative measure—the volume accessible information—which we define as the Shannon mutual information associated with the best possible quantum measurement that can access a system through a specified readout volume. Specifically, we obtain a general expression for an upper bound on the volume accessible information that depends only on the manner in which information is encoded in electron states and specification of the readout volume. This bound is obtained within a tight-binding framework for simplicity and compatibility with atomistic descriptions of molecular-scale electronic systems. As an illustration, we study the volume accessible information bound for measurements accessing finite segments of long polyparaphenylene (PPP) molecules with binary information encoded in the states of electrons in the lowest unoccupied molecular orbital band. Evaluation of this bound reveals severe limits on the amount of information accessible from measurements on short PPP chain segments, where the state distinguishability required for reliable information extraction is diminished.