Eur. Phys. J. Special Topics 203, 185-192 (2012)
https://doi.org/10.1140/epjst/e2012-01542-2

Regular Article

Quantum estimation of states and operations from incomplete data

¹ Dipartimento di Fisica, Università degli Studi di Trieste, 34151 Trieste, Italy
² Dipartimento di Fisica dell’Università di Milano, 20133 Milano, Italy
³ CNISM, UdR Milano Statale, 20133 Milano, Italy

^a e-mail: stefano.olivares@ts.infn.it
^b e-mail: matteo.paris@fisica.unimi.it

Received: 13 January 2012
Revised: 21 February 2012
Published online: 11 April 2012

Abstract

We review minimum Kullback entropy principle for estimation of quantum states and operations and discuss its application to qubit and harmonic oscillator systems. In particular, we address the estimation of displacement and squeezing operations from incomplete data and show how to estimate the displacement or squeezing amplitude starting from photon-number resolving or on/off photodetection.