The study of measurements in quantum mechanics exposes many of the ways in which the quantum world is different. For example, one of the hallmarks of quantum mechanics is that observables may be incompatible, implying among other things that it is not always possible to find joint probability distributions which fully capture the joint statistics of multiple measurements. Instead, one must employ more general tools such as the Kirkwood-Dirac quasiprobability (KDQ) distribution, which may exhibit negative or nonreal values heralding nonclassicality. In this paper, we consider the KDQ distributions describing arbitrary collections of measurements on disjoint components of some generic multipartite system. We show that the system dynamics ensures that these distributions are classical if and only if the Hamiltonian supports quantum Darwinism. Thus, we demonstrate a fundamental relationship between these two notions of classicality and their emergence in the quantum world.
The study of measurements in quantum mechanics exposes many of the ways in which the quantum world is different. For example, one of the hallmarks of quantum mechanics is that observables may be incompatible, implying among other things that it is not always possible to find joint probability distributions which fully capture the joint statistics of multiple measurements. Instead, one must employ more general tools such as the Kirkwood-Dirac quasiprobability (KDQ) distribution, which may exhibit negative or nonreal values heralding nonclassicality. In this paper, we consider the KDQ distributions describing arbitrary collections of measurements on disjoint components of some generic multipartite system. We show that the system dynamics ensures that these distributions are classical if and only if the Hamiltonian supports quantum Darwinism. Thus, we demonstrate a fundamental relationship between these two notions of classicality and their emergence in the quantum world.
Abstract Quantum Darwinism explains how tenets of classical reality, such as objectivity and repeatability, emerge within a quantum Universe. As a mathematical framework, quantum Darwinism also provides guiding principles that determine what physical models support emergent classical behavior, what specific observables obey classical laws, and much more. Recently, we demonstrated that in the regime where a quantum model exhibits quantum Darwinism, the Kirkwood–Dirac quasiprobability distributions for all disjoint multiparty measurement protocols become effectively classical. In the present work, we use this connection as a tool to study how the breaking of quantum Darwinism in a specific model translates to non-classical measurement statistics. Interestingly, this provides effective tools for benchmarking the genuine quantum characteristics of NISQ hardware, which we demonstrate with IonQ’s trapped-ion and IBM’s superconducting quantum computing platforms.
The Kirkwood–Dirac (KD) quasiprobability distribution describes any quantum state with respect to the eigenbases of two incompatible observables. While the KD quasiprobability distribution behaves similarly to a classical probability distribution, it can take on negative or nonreal values. Recently, the framework of the temporal Kirkwood–Dirac quasiprobability distribution has been proposed, generalizing the KD quasiprobability distribution to arbitrary multi-time quantum processes. In this work, we specifically focus on the temporal KD quasiprobability distribution within the context of two-time dynamics. We begin by constructing a nonclassicality measure derived from the real and imaginary parts of the temporal KD quasiprobability distribution. Next, we establish two uncertainty relations closely linked to this nonclassicality measure, one of which shows that the nonclassicality measure is bounded below by the measurement disturbance caused by the first measurement. Finally, we elucidate the relationships among temporal KD nonclassicality, the spatiotemporal Born rule, and spatiotemporal compatibility.
Recent work has revealed the central role played by the Kirkwood-Dirac quasiprobability (KDQ) as a tool to properly account for 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, our aim is two-fold: First, we highlight the role played by quasiprobabilities in characterizing the statistics of quantum observables and processes in the presence of measurement incompatibility. In this way, we show how the KDQ naturally underpins and unifies quantum correlators, quantum currents, Loschmidt echoes, and weak values. Second, we provide novel theoretical and experimental perspectives by discussing a wide variety of schemes to access the KDQ and its non-classicality features.
Quantum Darwinism explains how tenets of classical reality, such as objectivity and repeatability, emerge within a quantum universe. As a mathematical framework, Quantum Darwinism also provides guiding principles that determine what physical models support emergent classical behavior, what specific observables obey classical laws, and much more. For instance, in a recent work we elucidated that the limit under which Kirkwood-Dirac quasiprobability distributions become effectively classical coincides with the regime where the underlying physical model obeys the rules of Quantum Darwinism. In the present work, we study the breaking of Quantum Darwinism in a specific model and how that translates to non-classical measurement statistics. Interestingly, this provides effective tools for benchmarking the genuine quantum characteristics of NISQ hardware, which we demonstrate with IonQ's trapped-ion and IBM's superconducting quantum computing platforms.
The Kirkwood-Dirac (KD) quasiprobability describes measurement statistics of joint quantum observables, and has generated great interest as prominent indicators of non-classical features in various quantum information processing tasks. It relaxes the Kolmogorov axioms of probability by allowing for negative and even imaginary probabilities, and thus incorporates the classical probability theory as its inner boundary. In this work, we introduce the postquantum quasiprobability under mild assumptions to provide an outer boundary for KD quasiprobability. Specifically, we present qualitative and quantitative evidence to show that the classical, KD, and postquantum quasiprobabilities form a strict hierarchy, in the sense that joint probability distributions are a strict subset of KD quasiprobability distributions that are a strict subset of postquantum ones. Surprisingly, we are able to derive some nontrivial bounds valid for both classical probability and KD quasiprobability, and even valid for the KD quasiprobability generated by an arbitrary number of measurements. Finally, other interesting bounds are obtained, and their implications are noted. Our work solves the fundamental problems of what and how to bound the KD quasiprobability, and hence provides a deeper understanding of utilizing it in quantum information processing.
Abstract Kirkwood discovered in 1933, and Dirac discovered in 1945, a representation of quantum states that has undergone a renaissance recently. The Kirkwood–Dirac (KD) distribution has been employed to study nonclassicality across quantum physics, from metrology to chaos to the foundations of quantum theory. The KD distribution is a quasiprobability distribution, a quantum generalization of a probability distribution, which can behave nonclassically by having negative or nonreal elements. Negative KD elements signify quantum information scrambling and potential metrological quantum advantages. Nonreal elements encode measurement disturbance and thermodynamic nonclassicality. KD distributions’ nonclassicality has been believed to follow necessarily from pairwise noncommutation of operators in the distribution’s definition. We show that noncommutation does not suffice. We prove sufficient conditions for the KD distribution to be nonclassical (equivalently, necessary conditions for it to be classical). We also quantify the KD nonclassicality achievable under various conditions. This work resolves long-standing questions about nonclassicality and may be used to engineer quantum advantages.