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Zeitschrift für Physik A Hadrons and Nuclei

Quasiprobabilities and correlation functions in quantum systems

Richard Bausch, F. Schlögl, Á. Stáhl

Published Oct 1, 1969• 1 citation
Publisher
DOI
10.1007/bf01394787

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We introduce a method for testing quantum correlations in terms of quasiprobability functions in the presence of noise. We analyze the effects of measurement imperfection and thermal environment on quantum correlations and show that their noise effects can be well encapsulated into the change of the order parameter of the generalized quasiprobability function. We then formulate a noise-adaptive entanglement witness in the form of a Bell-type inequality by using the generalized quasiprobability function. Remarkably, it allows us to observe quantum correlations under severe noise. Our method provides a useful tool to test quantum correlations in near-term noisy quantum processors with continuous-variable systems.
Abstract 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.
The presence of unique quantum correlations is the core of quantum-information processing and general quantum theory. We address the fundamental question of how quantum correlations of a generic quantum system can be probed using correlation functions defined for quasiprobability distributions. In particular, we discuss the possibility of probing the negativity of a quasiprobability by comparing moments of the Wigner function. We show that one must take at least the fourth moments to find the negativity in general and the eighth moments for states with a rotationally invariant Wigner function.