• Rapid Communication

Maximum-likelihood estimation of the density matrix

K. Banaszek, G. M. D’Ariano, M. G. A. Paris, and M. F. Sacchi
Phys. Rev. A 61, 010304(R) – Published 8 December 1999
PDFExport Citation

Abstract

We present a universal technique for quantum-state estimation based on the maximum-likelihood method. This approach provides a positive-definite estimate for the density matrix from a sequence of measurements performed on identically prepared copies of the system. The method is versatile and can be applied to multimode radiation fields as well as to spin systems. The incorporation of physical constraints, which is natural in the maximum-likelihood strategy, leads to a substantial reduction of statistical errors. Numerical implementation of the method is based on a particular form of the Gauss decomposition for positive-definite Hermitian matrices.

  • Received 15 September 1999

DOI:https://doi.org/10.1103/PhysRevA.61.010304

©1999 American Physical Society

Authors & Affiliations

K. Banaszek1,2, G. M. D’Ariano1, M. G. A. Paris1, and M. F. Sacchi1

  • 1INFM and Dipartimento di Fisica “A. Volta,” Università di Pavia, via A. Bassi 6, I-27100 Pavia, Italy
  • 2Instytut Fizyki Teoretycznej, Uniwersytet Warszawski, Hoża 69, PL-00-681 Warszawa, Poland

References (Subscription Required)

Click to Expand
Issue

Vol. 61, Iss. 1 — January 2000

Reuse & Permissions
Access Options
Author publication services for translation and copyediting assistance advertisement

Authorization Required


×
×

Images

×

Sign up to receive regular email alerts from Physical Review A

Log In

Cancel
×

Search


Article Lookup

Paste a citation or DOI

Enter a citation
×