Searcharxiv⌕ Search

arXiv subjects

Z. Walczak

Publications and source records attributed to Z. Walczak.

9 recordsLinked to original sources
arXiv2006

An open quantum system approach to EPR correlations in K0-K0 system

We find the time evolution of the system of two non-interacting unstable particles, distinguishable as well as identical ones, in arbitrary reference frame having only the Kraus operators governing the evolution of its components in the rest frame. We than calculate in the rigorous way Einstein-Podolsky-Rosen quantum correlation functions for K0-K0 system in the singlet state taking into account CP-violation and decoherence and show that the results are exactly the same despite the fact we treat kaons as distinguishable or identical particles which means that the statistics of the particles plays no role, at least in considered cases.

quant-ph↗
arXiv2005

Unstable particles as open quantum systems

We present the probability preserving description of the decaying particle within the framework of quantum mechanics of open systems taking into account the superselection rule prohibiting the superposition of the particle and vacuum. In our approach the evolution of the system is given by a family of completely positive trace preserving maps forming one-parameter dynamical semigroup. We give the Kraus representation for the general evolution of such systems which allows one to write the evolution for systems with two or more particles. Moreover, we show that the decay of the particle can be regarded as a Markov process by finding explicitly the master equation in the Lindblad form. We also show that there are remarkable restrictions on the possible strength of decoherence.

quant-ph↗
arXiv2003

Kraus representation of destruction of states for one qudit

Quantum operations arise naturally in many fields of quantum information theory and quantum computing. One of the simplest example of quantum operation is the von Neumann-Lueders measurement. Destruction of states in quantum mechanics can be treated as a supplement to the von Neumann-Lueders measurement [P. Caban, J. Rembielinski, K. A. Smolinski and Z. Walczak, J. Phys. A 35, 3265 (2002)]. We show that destruction of states in one-qudit system is a quantum operation by finding its Kraus representation.

quant-ph↗
arXiv2003

Einstein-Podolsky-Rosen correlations and Galilean transformations

In this paper we calculate with full details Einstein-Podolsky-Rosen spin correlations in the framework of nonrelativistic quantum mechanics. We consider the following situation: two-particle state is prepared (we consider separately distinguishable and identical particles and take into account the space part of the wave function) and two observers in relative motion measure the spin component of the particle along given directions. The measurements are performed in bounded regions of space (detectors), not necessarily simultaneously. The resulting correlation function depends not only on the directions of spin measurements but also on the relative velocity of the observers.

quant-ph↗
arXiv2002

Destruction of states in quantum mechanics

A description of destruction of states on the grounds of quantum mechanics rather than quantum field theory is proposed. Several kinds of maps called supertraces are defined and used to describe the destruction procedure. The introduced algorithm can be treated as a supplement to the von Neumann-Lueders measurement. The discussed formalism may be helpful in a description of EPR type experiments and in quantum information theory.

quant-ph↗
arXiv1996

Bender-Dunne Orthogonal Polynomials and Quasi-Exact Solvability

The paper is devoted to the further study of the remarkable classes of orthogonal polynomials recently discovered by Bender and Dunne. We show that these polynomials can be generated by solutions of arbitrary quasi - exactly solvable problems of quantum mechanichs both one-dimensional and multi-dimensional. A general and model-independent method for building and studying Bender-Dunne polynomials is proposed. The method enables one to compute the weight functions for the polynomials and shows that they are the orthogonal polynomials in a discrete variable $E_k$ which takes its values in the set of exactly computable energy levels of the corresponding quasi-exactly solvable model. It is also demonstrated that in an important particular case, the Bender-Dunne polynomials exactly coincide with orthogonal polynomials appearing in Lanczos tridiagonalization procedure.

hep-th↗
arXiv1996

On the Duality of Quasi-Exactly Solvable Problems

It is demonstrated that quasi-exactly solvable models of quantum mechanics admit an interesting duality transformation which changes the form of their potentials and inverts the sign of all the exactly calculable energy levels. This transformation helps one to reveal some new features of quasi-exactly solvable models and associated orthogonal polynomials.

hep-th↗