Probing quantumness with joint continuous measurements of non-commuting qubit observables

TL;DR

This paper investigates the quantum nature of a qubit through joint continuous measurements of non-commuting observables, revealing violations of macrorealistic inequalities and highlighting fundamental quantum measurement effects.

Contribution

It demonstrates that simultaneous continuous measurements violate macrorealistic inequalities even without Hamiltonian evolution, challenging classical interpretations.

Findings

Violations of macrorealistic inequalities observed in measurements

Classical stochastic model can emulate quantum violations with unphysical noise

Violations occur even in the absence of Hamiltonian dynamics

Abstract

We analyze the continuous measurement of two non-commuting observables for a qubit, and investigate whether the simultaneously observed noisy signals are consistent with the evolution of an equivalent classical system. Following the approach outlined by Leggett and Garg, we show that the readouts violate macrorealistic inequalities for arbitrarily short temporal correlations. Moreover, the derived inequalities are manifestly violated even in the absence of Hamiltonian evolution, unlike for Leggett-Garg inequalities that use a single continuous measurement. Such a violation should indicate the failure of at least one postulate of macrorealism: either physical quantities do not have well defined values at all times, or the measurement process itself disturbs what is being measured. For measurements of equal strength we are able to construct a classical stochastic model for a spin that perfectly emulates both the qubit evolution and the observed noisy signals, thus emulating the violations; interestingly, this model also requires an unphysical noise to emulate the readouts, which effectively restricts the ability of an observer to learn information about the spin.