Quantum Information Processing, Vol. 5, No. 3, June 2006 (© 2006)
Further Results on the Observability of Quantum
Systems Under General Measurement
and Raffaele Romano
Received October 29, 2005; accepted March 16, 2006; Published online May 10, 2006
In this paper, we present a collection of results on the observability of quantum
mechanical systems, in the case the output is the result of a discrete nonselective
measurement. By deﬁning an effective observable, we extend previous results, on
the Lie algebraic characterization of observable systems, to general measurements.
Further results include the characterization of a ‘best probe’ (i.e. a minimally
disturbing probe) in indirect measurement and a study of the relation between
disturbance and observability in this case. We also discuss how the observabil-
ity properties of a quantum system relate to the problem of state reconstruction.
Extensions of the formalism to the case of selective measurements are also given.
KEY WORDS: Observability of quantum systems; generalized measurement
in quantum mechanics; quantum state reconstruction and observers.
PACS: 03.65.-w; 03.65.wj; 02.30.Yy.
The structural properties of controllability and observability have been
studied in depth for deterministic control systems (see, e.g. Ref. 20) of the
˙x = f (t, x, u) (1)
y = y(x). (2)
Department of Mathematics at Iowa State University, Ames IA-50011, USA.
To whom correspondence should be addressed. E-mail: email@example.com
1570-0755/06/0600-0139/0 © 2006 Springer Science+Business Media, Inc.