Kirkwood-Dirac (KD) quasiprobability is a quantum analog of phase space probability of classical statistical mechanics, allowing negative or/and nonreal values. It gives an informationally complete representation of a quantum state. Recent works have revealed the important roles played by the KD quasiprobability in the broad fields of quantum science and quantum technology. In the present work, we use the KD quasiprobability to access the quantum coherence in a quantum state. We show that the ${l}_{1}$ norm of the imaginary part of the KD quasiprobability over an incoherent reference basis and a second basis, maximized over all possible choices of the latter, can be used to quantify quantum coherence, satisfying certain desirable properties. It is upper bounded by the quantum uncertainty, i.e., the quantum standard deviation, of the incoherent basis in the state. It gives a lower bound to the ${l}_{1}$ norm quantum coherence, and for a single qubit, they are identical. We discuss the measurement of the KD coherence based on the measurement of the KD quasiprobability and an optimization procedure in hybrid quantum-classical schemes, and suggest statistical interpretations. We also discuss its relevance in the physics of linear response regime.Kirkwood-Dirac (KD) quasiprobability is a quantum analog of phase space probability of classical statistical mechanics, allowing negative or/and nonreal values. It gives an informationally complete representation of a quantum state. Recent works have revealed the important roles played by the KD quasiprobability in the broad fields of quantum science and quantum technology. In the present work, we use the KD quasiprobability to access the quantum coherence in a quantum state. We show that the ${l}_{1}$ norm of the imaginary part of the KD quasiprobability over an incoherent reference basis and a second basis, maximized over all possible choices of the latter, can be used to quantify quantum coherence, satisfying certain desirable properties. It is upper bounded by the quantum uncertainty, i.e., the quantum standard deviation, of the incoherent basis in the state. It gives a lower bound to the ${l}_{1}$ norm quantum coherence, and for a single qubit, they are identical. We discuss the measurement of the KD coherence based on the measurement of the KD quasiprobability and an optimization procedure in hybrid quantum-classical schemes, and suggest statistical interpretations. We also discuss its relevance in the physics of linear response regime.

arXiv:2309.09152Physical Review AFeb 8, 202371 citations

Quantum Non-Markovianity via the Covariance Matrix

Yajing Fan, Liang Chen, Huaixin Cao +1 more

International Journal of Theoretical PhysicsJun 8, 20181 citation

Kirkwood-Dirac quasiprobability approach to the statistics of incompatible observables

Matteo Lostaglio, Alessio Belenchia, Amikam Levy +3 more

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.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.

arXiv:2206.11783QuantumOct 9, 202379 citations

Interpolating Kirkwood-Dirac quasiprobabilities and their complex conjugates:characterization and quantification

Yajing Fan, Yutong Zhang

Abstract Kirkwood-Dirac (KD) quasiprobability distributions serve as quantum analog representations of the classical phase-space probability, capable of exhibiting nonclassical behavior through negativity or nonreal values. Recent studies have demonstrated that the nonclassicality of KD quasiprobability distributions plays a crucial role in quantum information tasks and provides deep insights into foundational aspects of quantum mechanics. In this work, we introduce an interpolated KD quasiprobability distribution parametrized by a continuous variable α , which smoothly connects different KD quasiprobability representations. Based on the interpolated KD quasiprobability distribution, we propose a quantitative measure of nonclassicality and rigorously analyze its key properties, including unitary covariance, convexity, and monotonicity. Furthermore, we derive an upper bound for this measure and conduct a comparison with other nonclassicality measures. Finally, we evaluate the nonclassicality measures for several prototypical interpolated KD quasiprobability distributions, illustrating their applicability in quantum information theory.Abstract Kirkwood-Dirac (KD) quasiprobability distributions serve as quantum analog representations of the classical phase-space probability, capable of exhibiting nonclassical behavior through negativity or nonreal values. Recent studies have demonstrated that the nonclassicality of KD quasiprobability distributions plays a crucial role in quantum information tasks and provides deep insights into foundational aspects of quantum mechanics. In this work, we introduce an interpolated KD quasiprobability distribution parametrized by a continuous variable α , which smoothly connects different KD quasiprobability representations. Based on the interpolated KD quasiprobability distribution, we propose a quantitative measure of nonclassicality and rigorously analyze its key properties, including unitary covariance, convexity, and monotonicity. Furthermore, we derive an upper bound for this measure and conduct a comparison with other nonclassicality measures. Finally, we evaluate the nonclassicality measures for several prototypical interpolated KD quasiprobability distributions, illustrating their applicability in quantum information theory.

Physica ScriptaOct 1, 20250 citations

{l}_{1}

norm of the imaginary part of the KD quasiprobability over an incoherent reference basis and a second basis, maximized over all possible choices of the latter, can be used to quantify quantum coherence, satisfying certain desirable properties. It is upper bounded by the quantum uncertainty, i.e., the quantum standard deviation, of the incoherent basis in the state. It gives a lower bound to the

{l}_{1}

norm quantum coherence, and for a single qubit, they are identical. We discuss the measurement of the KD coherence based on the measurement of the KD quasiprobability and an optimization procedure in hybrid quantum-classical schemes, and suggest statistical interpretations. We also discuss its relevance in the physics of linear response regime.