Quantum Description of Classical Apparatus:
Zeno Effect and Decoherence
S. A. Gurvitz
Received January 5, 2003; accepted May 5, 2003
We study the measurement process by treating classical detectors entirely quantum
mechanically. As a generic model we use a point-contact detector coupled to an
electron in a quantum dot and tunneling into the continuum. Transition to the
classical description and the mechanism of decoherence are investigated. We con-
centrate on the inﬂuence of the measurement on the electron decay rate to the
continuum. We demonstrate that the Zeno (or the anti-Zeno) effect requires a
nonuniform density of states in the continuum. In this case we show that the anti-
Zeno effect relates only to the average decay rate, whereas for sufﬁciently small
time the Zeno effect always takes place. We discuss the experimental consequences
of our results and the role of the projection postulate in a measurement process.
KEY WORDS: Quantum dots; quantum measurement; zeno effect; decoherence.
PACS: 73.21.La; 74.78.Na; 03.65.Ta; 03.65.Xp; 03.65.Yz.
The description of a measurement process has been a topic debated from the
early development of quantum mechanics.
Nevertheless, the under-
standing of quantum-mechanical measurements has not been achieved yet.
The main problem is still the nature of the projection postulate,
to which the wave-function of the observed system is projected onto an
eigenstate of the observable under consideration. During recent years the
measurement problem received a great deal of attention due to exiting
opportunities offered by developments in experimental techniques of optics
and mesoscopic structures. The problem also has close connections to the
rapidly growing ﬁelds of quantum cryptography and quantum computing.
Weizmann Institute of Science, Department of Particle Physics, 76100 Rehovot, Israel.
Quantum Information Processing, Vol. 2, Nos. 1–2, April 2003 (# 2003)
1570-0755/03/0400–0015/0 # 2003 Plenum Publishing Corporation