Efficient quantum tomography needs complementary and symmetric measurements

D. Petz, László Ruppert

Research output: Contribution to journalArticle

13 Citations (Scopus)

Abstract

In this study the determinant of the average quadratic error matrix is used as the measure of state estimation efficiency. Minimizing this quantity gives us the optimal measurements in different scenarios. We present applications when von Neumann measurements or a single positive operator-valued measure are used, when there is no known information or a part of the parameters of the state is given. Under some restrictions the optimality is found for n-level systems. The optimal measurements have some complementary relation to each other and to the available data, moreover, symmetric informationally complete systems appear, containing a new, conditional version.

Original languageEnglish
Pages (from-to)161-177
Number of pages17
JournalReports on Mathematical Physics
Volume69
Issue number2
DOIs
Publication statusPublished - Apr 2012

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Tomography
tomography
state estimation
Positive Operator
State Estimation
determinants
Optimality
constrictions
Determinant
Restriction
operators
Scenarios
matrices

Keywords

  • Complementarity
  • Experiment design
  • Measurement
  • Quadratic error
  • Qubit
  • State estimation
  • Symmetric informationally complete POVM

ASJC Scopus subject areas

  • Mathematical Physics
  • Statistical and Nonlinear Physics

Cite this

Efficient quantum tomography needs complementary and symmetric measurements. / Petz, D.; Ruppert, László.

In: Reports on Mathematical Physics, Vol. 69, No. 2, 04.2012, p. 161-177.

Research output: Contribution to journalArticle

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