Eur. Phys. J. D 59, 521-523 (2010)
https://doi.org/10.1140/epjd/e2010-00195-3

Parameter estimation with mixed quantum states

¹ Université de Toulouse, UPS, Laboratoire de Physique Théorique (IRSAMC), 31062 Toulouse, France
² CNRS, LPT (IRSAMC), 31062 Toulouse, France

Corresponding author: ^a braun@irsamc.ups-tlse.fr

Received: 15 March 2010
Revised: 9 June 2010
Published online: 27 July 2010

Abstract

We consider quantum enhanced measurements with initially mixed states. We show very generally that for any linear propagation of the initial state that depends smoothly on the parameter to be estimated, the sensitivity is bound by the maximal sensitivity that can be achieved for any of the pure states from which the initial density matrix is mixed. This provides a very general proof that purely classical correlations cannot improve the sensitivity of parameter estimation schemes in quantum enhanced measurement schemes.