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arXiv:2010.03076 · Physical Review A

Decay of quantumness in a measurement process: Action of a coarse-graining channel

Gabriel Dias Carvalho, Pedro Silva Correia

Published Sep 16, 2020• 7 citations
arXivHTMLPDF

Abstract

A model of a quantum measurement process is presented: a system consisting of a qubit in a superposition interacts with a measuring apparatus consisting of a $N$ qubit state. Looking at the emerging, effective description of the apparatus given by the action of a coarse-graining channel, we have been able to recover information about the superposition coefficients of the system. We have also been able to visualize the death of quantum correlations between system and apparatus and the death of quantum coherences in the apparatus' effective state, in the limit of a strong coarse-graining action---a situation akin to decoherence, although it is not necessary to evoke any interaction with the surrounding environment.

DOI
10.1103/physreva.102.032217

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A model of a quantum measurement process is presented: a system consisting of a qubit in a superposition interacts with a measuring apparatus consisting of a NNN qubit state. Looking at the emerging, effective description of the apparatus given by the action of a coarse-graining channel, we have been able to recover information about the superposition coefficients of the system. We have also been able to visualize the death of quantum correlations between system and apparatus and the death of quantum coherences in the apparatus' effective state, in the limit of a strong coarse-graining action---a situation akin to decoherence, although it is not necessary to evoke any interaction with the surrounding environment.
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Abstract In the context of the century-long debate on quantum measurement problem, the current work proposes a model that describes the process of collapse of state by quantum interaction, which resolves the controversies of the framework of quantum mechanics and describes the entire domain of quantum-to-classical world including the weak measurement and partial collapse. ‘Measurement’, being the process of physically interacting with a system in order to extracting information from it, is theorized in the current model by synthesizing the quantum interaction between system and measuring apparatus with the information entropy of such process. The model assumes Schrödinger equation to be the only guiding equation for all physical systems including the measuring apparatus, and does not presuppose ‘superposition principle’, rather derives it theoretically from the formulation. The superposed state is shown to be independent of the choice of measurement operator (observable) or basis states (pointers) of the measuring apparatus. Most interestingly, the current model explains the non-observance of ‘superposition principle’ by classical systems as the classical limit of such quantum description of measurement. Along with solving the quantum measurement problem, the work also explains weak measurement and partial collapse, which can be further extended to investigate such several emerging critical phenomena.
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The measurement of a spin-$\half$ is modeled by coupling it to an apparatus, that consists of an Ising magnetic dot coupled to a phonon bath. Features of quantum measurements are derived from the dynamical solution of the measurement, regarded as a process of quantum statistical mechanics. Schrödinger cat terms involving both the system and the apparatus, die out very quickly, while the registration is a process taking the apparatus from its initially metastable state to one of its stable final states. The occurrence of Born probabilities can be inferred at the macroscopic level, by looking at the pointer alone. Apparent non-unitary behavior of the measurement process is explained by the arisal of small many particle correlations, that characterize relaxation.
A quantum-mechanical measurement process is analyzed in terms of a model Hamiltonian describing the interaction between a quantum system (a ``particle'') and a macroscopic apparatus (a ``detector''), which is assumed to be made up of N two-level elementary constituents (``molecules''). The description of the molecule locations introduces an effective fluctuating coupling constant, and this provokes a loss of quantum-mechanical coherence in the limit of large N. It is argued that coherence is lost statistically, as a result of the interaction: The collapse of the wave function is indeed obtained when the same experiment is performed many times, as a result of the microscopic differences among macroscopically identical initial states of the detector. In this way, insight is obtained into the mechanism engendering the loss of coherence suffered by a quantum-mechanical system when interacting with a macroscopic apparatus, and the concept of ``wave-function collapse'' is replaced by that of a statistically defined dephasing process. No classical behavior of the detection system is postulated and the presence of no external observer is required.