Estimation of Quantum Channels with Finite Resources
Markus A. Cirone,
Dietmar G. Fischer,
and Michael Mussinger
Received July 3, 2002; accepted October 28, 2002
We examine the problem of determining the parameters that describe a quantum
channel. It is assumed that the users of the channel have at best only partial
knowledge of it and make use of a ﬁnite amount of resources to estimate it. We
discuss simple protocols for the estimation of the parameters of several classes of
channels that are studied in the current literature. A quantitative measures of the
quality of the estimation schemes can be given on the basis of the standard deviation
or of the ﬁdelity. Protocols that employ entangled particles are also discussed. The
use of entangled particles as a nonclassical resource enhances the estimation quality
of some classes of quantum channel. Further, the methods presented here can be
extended to higher dimensional quantum systems.
KEY WORDS: Quantum information; quantum channel; entanglement.
Quantum information processing has attracted a lot of interest in recent
years, following Deutsch’s investigations
concerning the potentiality of a
quantum computer, i.e., a computer where information is stored and pro-
cessed in quantum systems. Their application as quantum information
carriers gives rise to outstanding possibilities, like secret communication
(quantum cryptography) and the implementation of quantum networks and
quantum algorithms that are more eﬃcient than classical ones.
Many investigations concern the transmission of quantum informa-
tion from one party (usually called Alice) to another (Bob) through a
1570-0755/02/1000-0303/0 # 2003 Plenum Publishing Corporation
r Quantenphysik, Universita
t Ulm, D-89069 Ulm, Germany.
To whom correspondence should be addressed. E-mail: email@example.com-
Quantum Information Processing, Vol. 1, No. 5, October 2002 (# 2003)