Internal one degree of freedom is sufficient to induce exact decoherence

Theoretical Physics Group, National Institute of Physics, University of the Philippines Diliman Quezon City, 1101 Philippines

^(a) eagalapon@up.edu.ph

Received: 7 February 2016
Accepted: 4 April 2016

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 measurement time and the pointer states are exactly orthogonal after a sufficiently longer time of measurement. Furthermore, it is shown that the measurement scheme reproduces the main result of the environment-induced decoherence theory that coherences decay asymptotically in time for a general initial state of the probe.