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arXiv:1003.5044 · Europhysics Letters (EPL)

Are Quantum Measurements on Macroscopic Bodies Feasible?

Roberto Onofrio

Published Apr 15, 1990• 6 citations
arXivHTMLPDF

Abstract

The possibility to test quantum measurement theories is discussed in the more phenomenological framework of the quantum nondemolition theory.A simple test of the hypothesis of the state vector collapse is proposed by looking for deviations from the Boltzmann distribution of the energy associated to only one complex amplitude of a macroscopic oscillator.

DOI
10.1209/0295-5075/11/8/001

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The possibility to test quantum measurement theories is discussed in the more phenomenological framework of the quantum nondemolition theory.A simple test of the hypothesis of the state vector collapse is proposed by looking for deviations from the Boltzmann distribution of the energy associated to only one complex amplitude of a macroscopic oscillator.
We establish an objective scheme to determine the macroscopicity of quantum superposition tests with mechanical degrees of freedom. It is based on the Bayesian hypothesis falsification of a class of macrorealist modifications of quantum theory, such as the model of continuous spontaneous localization. The measure uses the raw data gathered in an experiment, taking into account all measurement uncertainties, and can be used to directly assess any conceivable quantum mechanical test. We determine the resulting macroscopicity for three recent tests of quantum physics: double-well interference of Bose-Einstein condensates, Leggett-Garg tests with atomic random walks, and entanglement generation and read-out of nanomechanical oscillators.
Recent achievements in the isolation of macroscopic mechanical objects from a heat bath make it possible to implement quantum measurements with such systems. In this case, either a free mass or an oscillator can be used as a test object. The advantage of the first variant is in significantly longer relaxation times achieved for free masses. The advantage of the second variant is in the absence of restrictions on the limiting measurement accuracy associated with internal losses in the meter. This restriction can be bypassed, retaining a long relaxation time typical of free masses, if a test oscillator with a ponderomotive electromagnetic rigidity is used. Estimates show that the potential sensitivity of this test body for the modern level of technology may be considerably higher than the standard quantum limit.
The problem of chaotic behavior in quantum mechanics is investigated against the background of the theory of quantum-nondemolition (QND) measurements. The analysis is based on two relevant features: The outcomes of a sequence of QND measurements are unambiguously predictable, and these measurements actually can be performed on one single system without perturbing its time evolution. Consequently, QND measurements represent an appropriate framework to analyze the conditions for the occurrence of ``deterministic randomness'' in quantum systems. The general arguments are illustrated by a discussion of a quantum system with a time evolution that possesses nonvanishing algorithmic complexity.
The quantum effects on a cavity mode of the electromagnetic field caused by measuring one of its quadrature components is analyzed. We consider three measurement schemes: an intracavity quantum-nondemolition coupling to another mode, simple homodyne detection, and balanced homodyne detection. It is shown that, for suitable initial conditions, the first scheme has an effect which approaches that of a projective collapse of the state vector for long measurement times. However, the two homodyne schemes (which are shown to be equivalent for large local-oscillator amplitudes) do not approximate a projective measurement in any limit. In particular, it is shown that homodyne measurement cannot produce a squeezed state from a classical initial state. All three schemes are analyzed in terms of ``quantum trajectories'' which link measurement theory with stochastic quantum-jump processes.