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A Second Measurement Problem

Elemér Elad Rosinger

Published Dec 1, 2010• 0 citations
OpenAlex

Abstract

Within quantum measurement there is the sharp di erence in the dynamics between the case when the eigenstate of the prepared quantum system is different from any of those of the measuring device, and on the other and, when it is the same with one of those of the measuring devices. It is argued that here one may face a second measurement problem.

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Within quantum measurement there is the sharp di erence in the dynamics between the case when the eigenstate of the prepared quantum system is different from any of those of the measuring device, and on the other and, when it is the same with one of those of the measuring devices. It is argued that here one may face a second measurement problem.
Based on an analysis of protective measurements, we show that the quantum state represents the physical state of a single quantum system. This result is more definite than the PBR theorem [Pusey, Barrett, and Rudolph, Nature Phys. 8, 475 (2012)]. The physical meaning of the quantum state is an important interpreta-tive problem of quantum mechanics. A long-standing question is whether a pure state relates only to an ensemble of identically prepared systems or di-rectly to the state of a single system. Recently, Pusey, Barrett and Rudolph (PBR) demonstrated that under an independence assumption, the quantum state is a representation of the physical state of a single quantum system [1]. This poses a further interesting question, namely whether ψ-ontology can be argued without resorting to nontrivial assumptions such as the in-dependence assumption (cf. Ref. [2-4]). In this Letter, we will show that protective measurements [5,6] already provide such an argument. The meaning of the quantum state is usually analyzed in the context of conventional impulsive measurements of an ensemble of identically prepared systems. However, it has been known that the quantum state of a single prepared system can be protectively measured [5-9]. During a protective measurement, the measured system is protected by an appropriate procedure (e.g. via the quantum Zeno effect) so that its quantum state neither changes nor becomes entangled with the quantum state of the measuring device appreciably. In this way, such protective measurements can measure the expectation values of observables from a single quantum system, even if the system is initially not in an eigenstate of the measured observable, and in particular, the quantum state of the system can also be measured as expectation values of certain observables. It is expected that protective measurements will be realized in the near future with the rapid development of quantum technologies.
In quantum computer implementation using resonance phenomena in quantum waveguides coupled through small windows is suggested. It has some interesting features, but faces some objectives. There are two variants of such devices. In the first one we have two quantum waveguides for each qubit, and the state of the qubit is determined by the position of the electron. In the second variant we have one waveguide for each qubit and the state of the qubit is determined by the electron spin projection ("up" or "down"). In each case, to perform many-qubit operations successfully, we need to solve the two-electrons problem in the area of waveguide and to synchronize the electrons in different waveguides. Also preparation of the initial state is here very important problem. In the present paper we study the Green function for the simplest cases of two noninteracting particles in two-dimensional infinite straight waveguide and three-dimensional infinite layer with Neumann boundary conditions. We use the convolution method based on known representation of the one-particle Green function