Nonnegative Discrete Symbols and Their Probabilistic Interpretation

P. Ádám, Vladimir A. Andreev, Margarita A. Man’ko, Vladimir I. Man’ko

Research output: Contribution to journalArticle

2 Citations (Scopus)

Abstract

We review the quantizer–dequantizer formalism of constructing symbols of the density operators and quantum observables, such as Wigner functions and tomographic-probability distributions. We present a tutorial consideration of the technique of obtaining minimal sets of dequantizers (quorum) related to the observable eigenvalues for one-qubit states. We discuss a generalization of the quantizer–dequantizer scheme on the example of spin-1/2 states. We consider the possibilities of extending the results to two-qubit systems using spin tomograms of the state density matrix.

Original languageEnglish
Pages (from-to)491-506
Number of pages16
JournalJournal of Russian Laser Research
Volume38
Issue number6
DOIs
Publication statusPublished - Nov 1 2017

Fingerprint

Probability distributions
Mathematical operators
eigenvalues
formalism
operators

Keywords

  • dequantizers
  • probability representation of the density operator
  • quantizers
  • quantum tomogram
  • qubit

ASJC Scopus subject areas

  • Atomic and Molecular Physics, and Optics
  • Engineering (miscellaneous)

Cite this

Nonnegative Discrete Symbols and Their Probabilistic Interpretation. / Ádám, P.; Andreev, Vladimir A.; Man’ko, Margarita A.; Man’ko, Vladimir I.

In: Journal of Russian Laser Research, Vol. 38, No. 6, 01.11.2017, p. 491-506.

Research output: Contribution to journalArticle

Ádám, P. ; Andreev, Vladimir A. ; Man’ko, Margarita A. ; Man’ko, Vladimir I. / Nonnegative Discrete Symbols and Their Probabilistic Interpretation. In: Journal of Russian Laser Research. 2017 ; Vol. 38, No. 6. pp. 491-506.
@article{7bb1e656f076480994d2263d1833b93e,
title = "Nonnegative Discrete Symbols and Their Probabilistic Interpretation",
abstract = "We review the quantizer–dequantizer formalism of constructing symbols of the density operators and quantum observables, such as Wigner functions and tomographic-probability distributions. We present a tutorial consideration of the technique of obtaining minimal sets of dequantizers (quorum) related to the observable eigenvalues for one-qubit states. We discuss a generalization of the quantizer–dequantizer scheme on the example of spin-1/2 states. We consider the possibilities of extending the results to two-qubit systems using spin tomograms of the state density matrix.",
keywords = "dequantizers, probability representation of the density operator, quantizers, quantum tomogram, qubit",
author = "P. {\'A}d{\'a}m and Andreev, {Vladimir A.} and Man’ko, {Margarita A.} and Man’ko, {Vladimir I.}",
year = "2017",
month = "11",
day = "1",
doi = "10.1007/s10946-017-9673-1",
language = "English",
volume = "38",
pages = "491--506",
journal = "Journal of Russian Laser Research",
issn = "1071-2836",
publisher = "Springer New York",
number = "6",

}

TY - JOUR

T1 - Nonnegative Discrete Symbols and Their Probabilistic Interpretation

AU - Ádám, P.

AU - Andreev, Vladimir A.

AU - Man’ko, Margarita A.

AU - Man’ko, Vladimir I.

PY - 2017/11/1

Y1 - 2017/11/1

N2 - We review the quantizer–dequantizer formalism of constructing symbols of the density operators and quantum observables, such as Wigner functions and tomographic-probability distributions. We present a tutorial consideration of the technique of obtaining minimal sets of dequantizers (quorum) related to the observable eigenvalues for one-qubit states. We discuss a generalization of the quantizer–dequantizer scheme on the example of spin-1/2 states. We consider the possibilities of extending the results to two-qubit systems using spin tomograms of the state density matrix.

AB - We review the quantizer–dequantizer formalism of constructing symbols of the density operators and quantum observables, such as Wigner functions and tomographic-probability distributions. We present a tutorial consideration of the technique of obtaining minimal sets of dequantizers (quorum) related to the observable eigenvalues for one-qubit states. We discuss a generalization of the quantizer–dequantizer scheme on the example of spin-1/2 states. We consider the possibilities of extending the results to two-qubit systems using spin tomograms of the state density matrix.

KW - dequantizers

KW - probability representation of the density operator

KW - quantizers

KW - quantum tomogram

KW - qubit

UR - http://www.scopus.com/inward/record.url?scp=85034257378&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85034257378&partnerID=8YFLogxK

U2 - 10.1007/s10946-017-9673-1

DO - 10.1007/s10946-017-9673-1

M3 - Article

VL - 38

SP - 491

EP - 506

JO - Journal of Russian Laser Research

JF - Journal of Russian Laser Research

SN - 1071-2836

IS - 6

ER -