Exactly decohering quantum measurement without environment

TL;DR

This paper demonstrates a measurement scheme that achieves exact decoherence without environmental interaction by using a decomposable meter with a probe and pointer, challenging the traditional environment-induced decoherence paradigm.

Contribution

It introduces a novel measurement scheme where decoherence occurs internally without external environment, relying on the probe-pointer decomposition and initial state conditions.

Findings

Coherences die out within finite time under the scheme.

Pointer states become exactly orthogonal.

Decoherence can occur with a single internal degree of freedom.

Abstract

Current quantum orthodoxy claims that the statistical collapse of the wave-function arises from the interaction of the measuring instrument with its environment through the phenomenon known as environment induced decoherence. Here it is shown that there exists a measurement scheme that is exactly decohering without the aid of an environment. The scheme relies on the assumption that the meter is decomposable into probe and pointer, with the probe taken to be inaccessible for observation. Under the assumption that the probe and the pointer initial states are momentum limited, it is shown that coherences die out within a finite interval of time and the pointer states are exactly orthogonal. These lead to the fundamental realization that dispersion of correlation does not require an external infinite number of degrees of freedom. An internal one degree of freedom is already sufficient to delocalize the correlations and leave its subparts in a classical mixed state, so that decoherence may occur even for isolated measuring instruments.