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

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.