Weak Measurement of Superconducting Qubit Reconciles Incompatible Operators

TL;DR

This paper experimentally demonstrates that weak measurements on a superconducting qubit can reduce the uncertainty caused by incompatible measurements, supporting the interpretation of weak values as a means to reconcile quantum incompatibility.

Contribution

It provides the first experimental validation that weak measurements can lower entropic uncertainty bounds in superconducting qubits, highlighting the role of weak values in quantum measurement theory.

Findings

Weak measurements can reduce uncertainty bounds in superconducting qubits.

Weak values influence the ability of measurements to reconcile incompatibility.

Experimental support for weak values as determinants of measurement reconciliation.

Abstract

Traditional uncertainty relations dictate a minimal amount of noise in incompatible projective quantum measurements. However, not all measurements are projective. Weak measurements are minimally invasive methods for obtaining partial state information without projection. Recently, weak measurements were shown to obey an uncertainty relation cast in terms of entropies. We experimentally test this entropic uncertainty relation with strong and weak measurements of a superconducting transmon qubit. A weak measurement, we find, can reconcile two strong measurements' incompatibility, via backaction on the state. Mathematically, a weak value -- a preselected and postselected expectation value -- lowers the uncertainty bound. Hence we provide experimental support for the physical interpretation of the weak value as a determinant of a weak measurement's ability to reconcile incompatible operations.