Sequential measurements of non-commuting observables with quantum controlled interactions

TL;DR

This paper demonstrates how quantum controlled interactions can measure non-commuting observables, revealing intrinsic joint probabilities and imaginary correlations, thus providing new insights into quantum non-classical correlations.

Contribution

It introduces a method using quantum controlled measurements to directly observe complex joint probabilities and imaginary correlations between non-commuting observables.

Findings

Measurement statistics explained by resolution and back-action errors.

Intrinsic joint probabilities include complex-valued correlations.

Experimental observation of imaginary correlations in quantum systems.

Abstract

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, where the measurement is described by a 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. These intrinsic joint probabilities are consistent with the complex-valued joint probabilities recently observed in weak measurements of quantum systems and provide direct evidence of non-commutativity in the form of imaginary correlations between the non-commuting operators. In quantum controlled measurements, these imaginary correlations can be converted into well-defined contributions to the real measurement statistics, allowing a direct experimental observation of the less intuitive aspects of quantum theory.