Quantum advantage in postselected metrology

Abstract

In every parameter-estimation experiment, the final measurement or the postprocessing incurs a cost. Postselection can improve the rate of Fisher information (the average information learned about an unknown parameter from a trial) to cost. We show that this improvement stems from the negativity of a particular quasiprobability distribution, a quantum extension of a probability distribution. In a classical theory, in which all observables commute, our quasiprobability distribution is real and nonnegative. In a quantummechanically noncommuting theory, nonclassicality manifests in negative or nonreal quasiprobabilities. Negative quasiprobabilities enable postselected experiments to outperform optimal postselection-free experiments: postselected quantum experiments can yield anomalously large information-cost rates. This advantage, we prove, is unrealizable in any classically commuting theory. Finally, we construct a preparation-and-postselection procedure that yields an arbitrarily large Fisher information. Our results establish the nonclassicality of a metrological advantage, leveraging our quasiprobability distribution as a mathematical tool.

Certifying Quantum Signatures in Thermodynamics and Metrology via Contextuality of Quantum Linear Response

“…I show that, given the phenomenology of the phase estimation experiment, a nonzero Fisher information is incompatible with all classical (noncontextual) models. This complements a recent result showing that certain features of postselected metrology are nonclassical [17], but in my case I do not have to consider any postselection.…”

“…These examples show that noncontextual OMs allow one to reproduce features normally attributed to quantum measurement disturbance, superposition, and entanglement. In this Letter, I will hence adopt the same stringent notion of quantum signature used to analyze several quantum information primitives [17,[24][25][26][27]: a set of operational features that unavoidably require contextuality.…”

Weak Measurement of a Superconducting Qubit Reconciles Incompatible Operators

“…In bridging entropic uncertainty relations with weak measurements and superconducting qubits, this Letter unites several subfields of quantum-information physics, which can benefit from the synergy introduced here. For example, in addition to the fundamental contribution to weak values mentioned above, this Letter paves the path toward detecting quantum chaos with weak measurements experimentally, being the first experiment to sprout from the considerable theoretical work on leveraging weak measurements to identify chaos [22,[30][31][32][33][34][35][36][37].…”

“…Quantum information scrambles by spreading through many-body entanglement, during a nonclassical stage of equilibration [53][54][55][56]. The entropic uncertainty relation for quantum-information scrambling occupies a recent line of theoretical applications of weak measurements to scrambling [22,[30][31][32][33][34][35][36][37]. Our experiment is the first to arise from this theory.…”

Multiphoton quantum metrology without pre-and post-selected measurements

“…Thus far, all demonstrations of quantum metrology for phase estimation have relied on either pre-or postselected measurements or have lacked photon-number resolution [27,28,[31][32][33][34][35][36][37][38][39]. Nevertheless, theoretical studies suggest that counting of resources only when pre-or post-selection is successful may lead to enhanced sensitivities beyond the shot-noise limit [40][41][42].…”