Optimal quantum-state tomography with known parameters

D. Petz, László Ruppert

Research output: Contribution to journalArticle

8 Citations (Scopus)

Abstract

It is a well-known fact that the optimal positive operator valued measure (POVM) for quantum-state tomography is the symmetric, informationally complete POVM (SIC-POVM). We investigate the same problem only in the case when there is some a priori information about the state, specifically when some parameters are known. In this paper, we mainly focus on solving a three-dimensional optimization problem, which gives us a non-trivial example for the so-called conditional SIC-POVMs, a straightforward generalization of the concept of SIC-POVMs. We also present other special cases to show further applications of the proposed numerical methods and to illustrate the complexity of this topic.

Original languageEnglish
Article number085306
JournalJournal of Physics A: Mathematical and Theoretical
Volume45
Issue number8
DOIs
Publication statusPublished - Mar 2 2012

Fingerprint

structural influence coefficients
Positive Operator
Quantum State
Tomography
Numerical methods
tomography
operators
Numerical Methods
Optimization Problem
Three-dimensional
optimization
Generalization
Concepts

ASJC Scopus subject areas

  • Mathematical Physics
  • Physics and Astronomy(all)
  • Statistical and Nonlinear Physics
  • Modelling and Simulation
  • Statistics and Probability

Cite this

Optimal quantum-state tomography with known parameters. / Petz, D.; Ruppert, László.

In: Journal of Physics A: Mathematical and Theoretical, Vol. 45, No. 8, 085306, 02.03.2012.

Research output: Contribution to journalArticle

@article{960352bac901492ca79ca1fa0bcfc72a,
title = "Optimal quantum-state tomography with known parameters",
abstract = "It is a well-known fact that the optimal positive operator valued measure (POVM) for quantum-state tomography is the symmetric, informationally complete POVM (SIC-POVM). We investigate the same problem only in the case when there is some a priori information about the state, specifically when some parameters are known. In this paper, we mainly focus on solving a three-dimensional optimization problem, which gives us a non-trivial example for the so-called conditional SIC-POVMs, a straightforward generalization of the concept of SIC-POVMs. We also present other special cases to show further applications of the proposed numerical methods and to illustrate the complexity of this topic.",
author = "D. Petz and L{\'a}szl{\'o} Ruppert",
year = "2012",
month = "3",
day = "2",
doi = "10.1088/1751-8113/45/8/085306",
language = "English",
volume = "45",
journal = "Journal of Physics A: Mathematical and Theoretical",
issn = "1751-8113",
publisher = "IOP Publishing Ltd.",
number = "8",

}

TY - JOUR

T1 - Optimal quantum-state tomography with known parameters

AU - Petz, D.

AU - Ruppert, László

PY - 2012/3/2

Y1 - 2012/3/2

N2 - It is a well-known fact that the optimal positive operator valued measure (POVM) for quantum-state tomography is the symmetric, informationally complete POVM (SIC-POVM). We investigate the same problem only in the case when there is some a priori information about the state, specifically when some parameters are known. In this paper, we mainly focus on solving a three-dimensional optimization problem, which gives us a non-trivial example for the so-called conditional SIC-POVMs, a straightforward generalization of the concept of SIC-POVMs. We also present other special cases to show further applications of the proposed numerical methods and to illustrate the complexity of this topic.

AB - It is a well-known fact that the optimal positive operator valued measure (POVM) for quantum-state tomography is the symmetric, informationally complete POVM (SIC-POVM). We investigate the same problem only in the case when there is some a priori information about the state, specifically when some parameters are known. In this paper, we mainly focus on solving a three-dimensional optimization problem, which gives us a non-trivial example for the so-called conditional SIC-POVMs, a straightforward generalization of the concept of SIC-POVMs. We also present other special cases to show further applications of the proposed numerical methods and to illustrate the complexity of this topic.

UR - http://www.scopus.com/inward/record.url?scp=84857171446&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84857171446&partnerID=8YFLogxK

U2 - 10.1088/1751-8113/45/8/085306

DO - 10.1088/1751-8113/45/8/085306

M3 - Article

AN - SCOPUS:84857171446

VL - 45

JO - Journal of Physics A: Mathematical and Theoretical

JF - Journal of Physics A: Mathematical and Theoretical

SN - 1751-8113

IS - 8

M1 - 085306

ER -