Kirkwood-Dirac quasiprobability approach to quantum fluctuations: Theoretical and experimental perspectives

Abstract

Recent work has revealed the central role played by the Kirkwood-Dirac quasiprobability (KDQ) as a tool to encapsulate non-classical features in the context of condensed matter physics (scrambling, dynamical phase transitions) metrology (standard and post-selected), thermodynamics (power output and fluctuation theorems), foundations (contextuality, anomalous weak values) and more. Given the growing relevance of the KDQ across the quantum sciences, the aim of this work is twofold: first, we clarify the role played by quasiprobabilities in characterising dynamical fluctuations in the presence of measurement incompatibility, and highlight how the KDQ naturally underpins and unifies quantum correlators, quantum currents, Loschmidt echoes and weak values; second, we discuss several schemes to access the KDQ and its non-classicality features, and assess their experimental feasibility in NMR and solid-state platforms. Finally, we analyze the possibility of a 'thermodynamics with quasiprobabilities' in the light of recent no-go theorems limiting traditional treatments.

Experimental assessment of non-classicality in a solid-state spin qutrit

“…Introduced as a characterization of the quantum state for discrete quantum systems [4,5], the KDQ and its real part, the Margenau-Hill quasiprobability (MHQ), have been recently brought back into the spotlight by a series of papers showing their ubiquity in quantum physics. As we survey in [7], these quasiprobabilities underpin analyses of perturbation theory [8][9][10], quantum currents [11], dynamical phase transitions [12,13], quantum information scrambling beyond out-of-time ordered cor-relators [14,15], non-classical heat-flows between locallythermal systems [16], fluctuation theorems [17,18] and more. KDQ and MHQ are also closely related to the concept of weak values, and they have been used in tomographic reconstructions of the quantum density matrix in optical experiments [19,20].…”

“…In this letter we report the experimental implementation of a weak two-point measurement (wTPM) scheme [7,34] in a solid-state spin qutrit at room temperature. The scheme allows to directly access the MHQ encoding the statistics of energy fluctuations via projective measurements only.…”

“…where q(ρ) denotes the KDQ vector containing all the elements of {q if (ρ)} [7]. For the MHQ distribution, the relevant measure of non-classicality is the negativity.…”

“…Here, NS stands for "non-selective", and the state ρ NS,i can be obtained by performing non-selective projective measurements with projectors Π i and I − Π i or, equivalently, by the preparation of the states ρ i and ρ i with the corresponding probabilities. This joint probability is related to the MHQ by [7,34] Re…”

“…Given the initial and final non-commuting observables, it is always possible to find an initial state ρ such that the corresponding MHQ distribution entails non-classicality [7]. We follow this logic to find an initial pure state to witness non-classicality when the MHQ work distribution is measured.…”