Uncertainty characteristics of generalized quantum measurements

Holger F. Hofmann
Phys. Rev. A 67, 022106 – Published 13 February 2003
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Abstract

The effects of any quantum measurement can be described by a collection of measurement operators {Mm} acting on the quantum state of the measured system. However, the Hilbert space formalism tends to obscure the relationship between the measurement results and the physical properties of the measured system. In this paper, a characterization of measurement operators in terms of measurement resolution and disturbance is developed. It is then possible to formulate uncertainty relations for the measurement process that are valid for arbitrary input states. The motivation of these concepts is explained from a quantum communication viewpoint. It is shown that the intuitive interpretation of uncertainty as a relation between measurement resolution and disturbance provides a valid description of measurement back action. Possible applications to quantum cryptography, quantum cloning, and teleportation are discussed.

  • Received 29 September 2002

DOI:https://doi.org/10.1103/PhysRevA.67.022106

©2003 American Physical Society

Authors & Affiliations

Holger F. Hofmann*

  • PRESTO, Japan Science and Technology Corporation (JST), Research Institute for Electronic Science, Hokkaido University, Kita-12 Nishi-6, Kita-ku, Sapporo 060-0812, Japan

  • *Electronic address: h.hofmann@osa.org

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Issue

Vol. 67, Iss. 2 — February 2003

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