The Kirkwood-Dirac quasiprobability distribution, intimately connected with the quantum correlation function of two observables measured at distinct times, is becoming increasingly relevant for fundamental physics and quantum technologies. This quasiprobability distribution can take non-positive values, and its experimental reconstruction becomes challenging when expectation values of incompatible observables are involved. Here, we use an interferometric scheme aided by an auxiliary system to reconstruct the Kirkwood-Dirac quasiprobability distribution. We experimentally demonstrate this scheme in an electron-nuclear spin system associated with a nitrogen-vacancy center in diamond. By measuring the characteristic function, we reconstruct the quasiprobability distribution of work and analyze the behavior of its first and second moments. Our results clarify the physical meaning of the work quasiprobability distribution in the context of quantum thermodynamics. Finally, we study the uncertainty of measuring the Hamiltonian of the system at two times, via the Robertson-Schrödinger uncertainty relation, for different initial states.

Kirkwood-Dirac 准概率分布与在不同时间测量的两个可观察对象的量子相关函数密切相关，与基础物理学和量子技术越来越相关。这种准概率分布可以采用非正值，当涉及不兼容的可观察对象的期望值时，其实验重建变得具有挑战性。在这里，我们使用辅助系统的干涉方案来重建 Kirkwood-Dirac 准概率分布。我们在与金刚石中氮空位中心相关的电子核自旋系统中实验证明了这种方案。通过测量特征函数，我们重建了功的准概率分布，并分析了其第一和第二时刻的行为。我们的结果阐明了量子热力学背景下工作准概率分布的物理意义。最后，我们研究了通过 Robertson-Schrödinger 不确定性关系在不同初始状态下两次测量系统的哈密顿量的不确定性。