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1

Entropic upper bound for Bayes risk in the quantum case

Wieczorek R., Podsędkowska H.

Probability and Mathematical Statistics

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2018

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Vol. 38, Fasc. 2

429--440

EN

The entropic upper bound for Bayes risk in a general quantum case is presented. We obtained generalization of the entropic Lower bound for probability of detection. Our result indicates upper bound for Bayes risk (in a particular case of loss function – for probability of detection) in a pretty general setting of an arbitrary finite von Neumann algebra. It is also shown under which condition the indicated upper bound is achieved.

2

Algebraic Characterization of the Class of Languages Recognized by Measure Only Quantum Automata

Comin C.

Fundamenta Informaticae

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2014

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Vol. 134, nr 3/4

335--353

EN

We study a model of one-way quantum automaton where only measurement operations are allowed (MON-1QFA). We give an algebraic characterization of LMO(Σ), showing that the syntactic monoids of the languages in LMO(Σ) are exactly the J-trivial literally idempotent syntactic monoids, where J is the Green’s relation determined by two-sided ideals. We also prove that LMO(Σ) coincides with the literal variety of literally idempotent piecewise testable languages. This allows us to prove the existence of a polynomial-time algorithm for deciding whether a regular language belongs to LMO(Σ).

3

On Indistinguishability of Quantum States

Adamczyk M.

Probability and Mathematical Statistics

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2012

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Vol. 32, Fasc. 1

1--10

EN

In this paper we shall study quantum ancillary statistics. For a given quantum measurement M we will define the indistinguishability relation of states in the following way: Two states are indistinguishable by M if they generate with M the same probability measure. For such a relation the equivalence classes will be described. At the end we will give some elementary examples of informationally complete measurements that arise from the theorems characterizing the indistinguishability relation.

4

Analysis of wave packet interference pattern in Young experiment

Cieślak K., Olchowik J. M.

Materials Science Poland

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2006

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Vol. 24, No. 4

1037--1042

EN

Since its beginning the quantum mechanics has been so controversial theory, that not all physicist ware able to agree with its assumptions. Nowadays it seems that the problem does not exist any more, although the quantum theory is still incomplete. The main point of the discussion, which has been risen all the time, is the problem of the measurement understood as the influence of the observer or the detector presence on the wave pocket describing the state of the observed system. In this paper the problem of the detector influence on the state of the system is reported on the basis of two-slit experiment described in new formalism called projection evolution. This new approach connects two ways of state evolution: unitary evolution and evolution visible during the measurement.

5

Flows of quantum noise

Hudson R. L., Lindsay J. M., Parthasarathy K. R.

Journal of Applied Analysis

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1998

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Vol. 4, nr 2

143-160

EN

The dynamics of classical and quantum systems in the presence of noise is usually described in the language of stochastic differential equations. When the system observables comprise a C*-algebra, stochastic evolutions are obtained by solving such equations driven by creation, preservation and annihilation processes on Fock space, with linear maps on the algebra as coefficients.*-Homomorphic evolutions are obtained precisely when the collection of maps has a certain structure; this structure admits a cohomological description. Here we consider equations governing the joint evolution of the system and noise (from input to output) by supposing that the characteristics of the (input) noise processes are given by a group representation. The structure required for *-homomorphic evolution is determined.