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Physical Review A

Dynamical analysis of seemingly interaction-free measurements

Alfredo Luis, Luis Lorenzo Sánchez-Soto

Published Aug 1, 1998• 10 citations
Publisher

Abstract

A full quantum analysis of $100%$ efficient interaction-free measurements is presented. It is shown that it is possible to describe consistently the phenomenon in terms of an effective interaction between object and apparatus that disturbs measurable quantities of the observed system.

DOI
10.1103/physreva.58.836

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A full quantum analysis of 100100%100 efficient interaction-free measurements is presented. It is shown that it is possible to describe consistently the phenomenon in terms of an effective interaction between object and apparatus that disturbs measurable quantities of the observed system.
It is now well established that the presence of an opaque classical object can be unambiguously determined by an "interaction-free" measurement (IFM), where the object and the probe never directly interact. For quantum objects, we examine "interaction-free" measurement (the object wavefunction is unchanged) and "interaction-free" preparation (the object wavefunction is changed without physical interaction) and find that in general, neither is possible. We propose using high efficiency IFM's as a quantum information bus to connect disjoint quantum systems.
It is now well-understood that the complementary wave- and particle-like natures of quanta enable one to make measurements that are “interaction-free” -- one can determine the presence or absence of an object, even a completely absorbing object, without any photons being absorbed. The first proposal of such a scheme was limited to an efficiency of 50% -- at most half of the measurements could be interaction free [1]. By using an application of the Quantum Zeno effect, one can in fact have the fraction of interaction-free measurements arbitrarily close to one [2].
We investigate the extent to which ``interaction-free'' measurements perturb the state of quantum systems. We show that the absence of energy exchange during the measurement is not a sufficient criterion to preserve that state, as the quantum system is subject to measurement-dependent decoherence. While it is possible in general to design interaction-free measurement schemes that do preserve that state, the requirement of quantum coherence preservation rapidly leads to a very low efficiency. Our results, which have a simple interpretation in terms of ``which-way'' arguments, open up the way to novel quantum nondemolition techniques.
We use the term ‘measurement’ to refer to the interaction between an object and an apparatus on the basis of which information concerning the initial state of the object may be obtained from information on the resulting state of the apparatus. The quantum theory of measurement is a quantum theoretic investigation of such interactions in order to analyse the correlations between object and apparatus that measurement must establish. Although there is a sizeable literature on quantum measurements there appear to be just two sorts of interactions that have been employed. There are the ‘disturbing’ interactions consistent with the analysis of Landau and Peierls (8) as developed by Pauli (11) and by Landau and Lifshitz (7), and there are the ‘non-disturbing’ interactions explicitly set out by von Neumann ((10), chs. 5, 6), and that dominate the literature. In this paper we shall investigate the most general types of interactions that could possibly constitute measurements and provide a precise mathematical characterization (section 2). We shall then examine an interesting subclass, corresponding to Landau's ideas, that contains both of the above sorts of measurements (section 3). Finally, we shall discuss von Neumann measurements explicitly and explore the purported limitations suggested by Wigner(12) and Araki and Yanase (2). We hope, in this way, to provide a comprehensive basis for discussions of quantum measurements.