1212.2683 (Holger F. Hofmann)

Sequential measurements of non-commuting observables with quantum
controlled interactions    [PDF]

Holger F. Hofmann

The origin of non-classical correlations is difficult to identify since the uncertainty principle requires that information obtained about one observable invariably results in the disturbance of any other non-commuting observable. Here, this problem is addressed by investigating the uncertainty trade-off between measurement errors and disturbance for measurement interactions controlled by the state of a single qubit that can realize any quantum coherent superposition of a fully projective measurement and the identity operation. It is shown that the measurement statistics obtained from a quantum controlled measurement of A followed by a projective measurement of B can be explained in terms of a simple combination of resolution and back-action errors acting on an intrinsic joint probability of the non-commuting observables defined by the input state of the system. This complex-valued joint probability is consistent with the complex-valued probabilities that have been derived from weak measurement statistics, indicating that the results of weak measurements are also valid at intermediate measurement strengths once the effects of back-action are properly taken into account.

View original: http://arxiv.org/abs/1212.2683