Quantum control without access to the controlling interaction

D. Janzing, F. Armknecht, R. Zeier, and Th. Beth
Phys. Rev. A 65, 022104 – Published 10 January 2002
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Abstract

In our model a fixed Hamiltonian acts on the joint Hilbert space of a quantum system and its controller. We show conditions under which measurements, state preparations, and unitary implementations on the system can be performed by quantum operations on the controller only. It turns out that a measurement of the observable A and an implementation of the one-parameter group exp(iAr) can be performed by almost the same sequence of control operations. Furthermore, measurement procedures for A+B, for (AB+BA), and for iA,B can be constructed from measurements of A and B. This shows that the algebraic structure of the set of observables can be explained by the Lie group structure of the unitary evolutions on the joint Hilbert space of the measuring device and the measured system. A spin chain model with nearest-neighborhood coupling shows that the border line between controller and system can be shifted consistently.

  • Received 9 March 2001

DOI:https://doi.org/10.1103/PhysRevA.65.022104

©2002 American Physical Society

Authors & Affiliations

D. Janzing*, F. Armknecht, R. Zeier, and Th. Beth

  • Institut für Algorithmen und Kognitive Systeme, Am Fasanengarten 3a, D-76131 Karlsruhe, Germany

  • *Electronic address: janzing@ira.uka.de

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Issue

Vol. 65, Iss. 2 — February 2002

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