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arXiv:hep-th/9404137

The Advantage of a Multi-User Mode

Denis V. Juriev

Published Apr 22, 1994• 3 citations
arXivHTMLPDF

Abstract

The purpose of this very short note, which maybe considered as a comment on "hep-th/9401067", is to prove the following proposition. PROPOSITION. There exist certain models of Mobilevision, in which interpretational figures are observable only in a multi--user mode in contrast to single--user ones. This result maybe interesting as for applications as for the understanding of theoretical foundations of quantum interactive processes (hep-th/9403015).

DOI
10.48550/arxiv.hep-th/9404137

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The purpose of this very short note, which maybe considered as a comment on "hep-th/9401067", is to prove the following proposition. PROPOSITION. There exist certain models of Mobilevision, in which interpretational figures are observable only in a multi--user mode in contrast to single--user ones. This result maybe interesting as for applications as for the understanding of theoretical foundations of quantum interactive processes (hep-th/9403015).
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We explain why the main conclusion of Bender et al, hep-th/0511229 [J. Phys. A 39 (2006) 1657] regarding the practical superiority of the non-Hermitian description of PT-symmetric quantum systems over their Hermitian description is not valid. Recalling the essential role played by the Hermitian description in the characterization and interpretation of the physical observables, we maintain that as far as the physical aspects of the theory are concerned the Hermitian description is not only unavoidable but also indispensable.
We give a simple proof of a Chernoff bound for the spectrum of a kkk-local Hamiltonian based on Weyl's inequalities. The complexity of estimating the spectrum's ε(n)ε(n)ε(n)-th quantile up to constant relative error thus exhibits the following dichotomy: For ε(n)=d−nε(n)=d^{-n}ε(n)=d−n the problem is NP-hard and maybe even QMA-hard, yet there exists constant a>1a>1a>1 such that the problem is trivial for ε(n)=a−nε(n)=a^{-n}ε(n)=a−n. We note that a related Chernoff bound due to Kuwahara and Saito (Ann. Phys. '20) for a generalized problem is also sufficient to establish such a dichotomy, its proof relying on a careful analysis of the \emph{cluster expansion}.