If Mixed States Are Secretly Quickly Oscillating Pure States, Weak Measurements Can Detect It

TL;DR

This paper shows that weak measurements with postselection can distinguish mixed states from rapidly oscillating pure states, providing a new experimental approach to probe high-energy phenomena like black hole radiation.

Contribution

It introduces a method using weak measurements with postselection to differentiate mixed states from fast oscillating pure states, which is not possible with strong nonpostselected measurements.

Findings

Weak measurements can detect differences between mixed and oscillating pure states.

Strong nonpostselected measurements cannot distinguish these states in practice.

Proposed experimental procedure applicable to blackbody radiation, Hawking radiation, and other high-energy phenomena.

Abstract

The apparent nonunitary evolution in the black hole information paradox and recent work on describing wavefunction collapse via nonunitary nonlinear stochastic operators has motivated us to analyze whether mixed states can be distinguished from quickly oscillating pure states. We have demonstrated that the answer is no for all practical purposes if only strong nonpostselected measurements are performed. However, if weak measurements in postselected systems are used, mixed states and quickly oscillating states produce different results. An experimental procedure is proposed which could in principle determine the nature of mixed states stemming from blackbody radiation, decoherence, thermalization in solid state materials, Unruh radiation and Hawking radiation, among others. The analysis in this work applies to all fast oscillations, including those at Planck scale. As such, tabletop weak measurements can be used to probe (very specific) potential high energy behavior, where strong nonpostselected measurements cannot be applied. This work also demonstrates that weak measurements are not equivalent to a set of strong measurements without postselection since measurements which are impossible for all practical purposes need to be excluded.