Noninvasiveness and time symmetry of weak measurements

TL;DR

This paper explores the properties of weak measurements in classical and quantum systems, demonstrating that classical weak measurements are time symmetric while quantum ones can violate this symmetry, with an experimental proposal to observe this effect.

Contribution

It introduces a formal framework for noninvasive weak measurements in quantum systems and reveals their potential to violate time symmetry, unlike classical counterparts.

Findings

Classical weak measurements are time symmetric.

Quantum weak measurements can violate time symmetry.

Proposed experiment to detect time-symmetry violation in quantum dots.

Abstract

Measurements in classical and quantum physics are described in fundamentally different ways. Nevertheless, one can formally define similar measurement procedures with respect to the disturbance they cause. Obviously, strong measurements, both classical and quantum, are invasive -- they disturb the measured system. We show that it is possible to define general weak measurements, which are noninvasive: the disturbance becomes negligible as the measurement strength goes to zero. Classical intuition suggests that noninvasive measurements should be time symmetric (if the system dynamics is reversible) and we confirm that correlations are time-reversal symmetric in the classical case. However, quantum weak measurements -- defined analogously to their classical counterparts -- can be noninvasive but not time symmetric. We present a simple example of measurements on a two-level system which violates time symmetry and propose an experiment with quantum dots to measure the time-symmetry violation in a third-order current correlation function.