Noninvasiveness and time symmetry of weak measurements

Abstract

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