# Accession Number:

## ADA459294

# Title:

## Integration with Respect to Operator-Valued Measures with Applications to Quantum Estimation Theory

# Descriptive Note:

# Corporate Author:

## MASSACHUSETTS INST OF TECH CAMBRIDGE LAB FOR INFORMATION AND DECISION SYSTEMS

# Personal Author(s):

# Report Date:

## 1983-03-01

# Pagination or Media Count:

## 80.0

# Abstract:

The problem of quantum measurement has received a great deal of attention in recent years, both in the quantum physics literature and in the context of optical communications. An account of these ideas may be found in Davies 1976 and Holevo 1973. The development of a theory of quantum estimation requires a theory of integration with respect to operator-valued measures. Indeed, Holevo 1973 in his investigations on the Statistical Decision Theory for Quantum Systems develops such a theory which, however, is more akin to Riemann Integration. The objective of this paper is to develop a theory which is analogous to Lebesque integration and which is natural in the context of quantum physics problems and show how this can be applied to quantum estimation problems. The theory that we present has little overlap with the theory of integration with respect to vector measures nor the integration theory developed by Thomas 1970.

# Descriptors:

# Subject Categories:

- Quantum Theory and Relativity