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We propose an operational quasiprobability function for qudits, enabling a comparison between quantum and hidden-variable theories. We show that the quasiprobability function becomes positive semidefinite if consecutive measurement results are described by a hidden-variable model with locality and noninvasive measurability assumed. Otherwise, it is negative valued. The negativity depends on the observables to be measured as well as a given state, as the quasiprobability function is operationally defined. We also propose a marginal quasiprobability function and show that it plays the role of an entanglement witness for two qudits. In addition, we discuss an optical experiment of a polarization qubit to demonstrate its nonclassicality in terms of the quasiprobability function.
We generalize the operational quasiprobability involving sequential measurements proposed by Ryu {em et al.} [Phys. Rev. A {bf 88}, 052123] to a continuous-variable system. The quasiprobabilities in quantum optics are incommensurate, i.e., they repre
We report on the first experimental reconstruction of an entanglement quasiprobability. In contrast to related techniques, the negativities in our distributions are a necessary and sufficient identifier of separability and entanglement and enable a f
Presently, one of the most ambitious technological goals is the development of devices working under the laws of quantum mechanics. One prominent target is the quantum computer, which would allow the processing of information at quantum level for pur
We investigate the interplay between mutual unbiasedness and product bases for multiple qudits of possibly different dimensions. A product state of such a system is shown to be mutually unbiased to a product basis only if each of its factors is mutua
We discuss how the internal structure of ultracold molecules, trapped in the motional ground state of optical tweezers, can be used to implement qudits. We explore the rotational, fine and hyperfine structure of $^{40}$Ca$^{19}$F and $^{87}$Rb$^{133}