Optimizing Quantum Models of Classical Channels: The Reverse Holevo Problem

Given a classical channel—a stochastic map from inputs to outputs—the input can often be transformed into an intermediate variable that is informationally smaller than the input. The new channel accurately simulates the original but at a smaller transmission rate. Here, we examine this procedure when the intermediate variable is a quantum state. We determine when and how well quantum simulations of classical channels may improve upon the minimal rates of classical simulation. This inverts Holevo’s original question of quantifying the capacity of quantum channels with classical resources: We determine the lowest-capacity quantum channel required to simulate a classical channel. We also show that this problem is equivalent to another, involving the local generation of a distribution from common entanglement

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http://www.archive.org/details/interpretationof00crutU.S. Navy (U.S.N.) author

Regeneration limit of classical Shannon capacity

Since Shannon derived the seminal formula for the capacity of the additive linear white Gaussian noise channel, it has commonly been interpreted as the ultimate limit of error-free information transmission rate. However, the capacity above the corresponding linear channel limit can be achieved when noise is suppressed using nonlinear elements; that is, the regenerative function not available in linear systems. Regeneration is a fundamental concept that extends from biology to optical communications. All-optical regeneration of coherent signal has attracted particular attention. Surprisingly, the quantitative impact of regeneration on the Shannon capacity has remained unstudied. Here we propose a new method of designing regenerative transmission systems with capacity that is higher than the corresponding linear channel, and illustrate it by proposing application of the Fourier transform for efficient regeneration of multilevel multidimensional signals. The regenerative Shannon limit -the upper bound of regeneration efficiency -is derived

Competitive Interactions between Invasive Nile Tilapia and Native Fish: The Potential for Altered Trophic Exchange and Modification of Food Webs

Recent studies have highlighted both the positive and negative impacts of species invasions. Most of these studies have been conducted on either immobile invasive plants or sessile fauna found at the base of food webs. Fewer studies have examined the impacts of vagile invasive consumers on native competitors. This is an issue of some importance given the controlling influence that consumers have on lower order plants and animals. Here, we present results of laboratory experiments designed to assess the impacts of unintended aquaculture releases of the Nile tilapia (Oreochromis niloticus), in estuaries of the Gulf of Mexico, on the functionally similar redspotted sunfish (Lepomis miniatus). Laboratory choice tests showed that tilapia prefer the same structured habitat that native sunfish prefer. In subsequent interspecific competition experiments, agonistic tilapia displaced sunfish from their preferred structured habitats. When a piscivore (largemouth bass) was present in the tank with both species, the survival of sunfish decreased. Based on these findings, if left unchecked, we predict that the proliferation of tilapia (and perhaps other aggressive aquaculture fishes) will have important detrimental effects on the structure of native food webs in shallow, structured coastal habitats. While it is likely that the impacts of higher trophic level invasive competitors will vary among species, these results show that consequences of unintended releases of invasive higher order consumers can be important

Neutrality and Robustness in Evo-Devo: Emergence of Lateral Inhibition

Embryonic development is defined by the hierarchical dynamical process that translates genetic information (genotype) into a spatial gene expression pattern (phenotype) providing the positional information for the correct unfolding of the organism. The nature and evolutionary implications of genotype–phenotype mapping still remain key topics in evolutionary developmental biology (evo-devo). We have explored here issues of neutrality, robustness, and diversity in evo-devo by means of a simple model of gene regulatory networks. The small size of the system allowed an exhaustive analysis of the entire fitness landscape and the extent of its neutrality. This analysis shows that evolution leads to a class of robust genetic networks with an expression pattern characteristic of lateral inhibition. This class is a repertoire of distinct implementations of this key developmental process, the diversity of which provides valuable clues about its underlying causal principles

Highly symmetric POVMs and their informational power

We discuss the dependence of the Shannon entropy of normalized finite rank-1 POVMs on the choice of the input state, looking for the states that minimize this quantity. To distinguish the class of measurements where the problem can be solved analytically, we introduce the notion of highly symmetric POVMs and classify them in dimension two (for qubits). In this case we prove that the entropy is minimal, and hence the relative entropy (informational power) is maximal, if and only if the input state is orthogonal to one of the states constituting a POVM. The method used in the proof, employing the Michel theory of critical points for group action, the Hermite interpolation and the structure of invariant polynomials for unitary-antiunitary groups, can also be applied in higher dimensions and for other entropy-like functions. The links between entropy minimization and entropic uncertainty relations, the Wehrl entropy and the quantum dynamical entropy are described.Comment: 40 pages, 3 figure