Optical experiment to test negative probability in context of quantum-measurement selection

Abstract

Negative probability values have been widely employed as an indicator of the nonclassicality of quantum systems. Known as a quasiprobability distribution, they are regarded as a useful tool that provides significant insight into the underlying fundamentals of quantum theory when compared to the classical statistics. However, in this approach, an operational interpretation of these negative values with respect to the definition of probability—the relative frequency of occurred event—is missing. An alternative approach is therefore considered where the quasiprobability operationally reveals the negativity of measured quantities. We here present an experimental realization of the operational quasiprobability, which consists of sequential measurements in time. To this end, we implement two sets of polarization measurements of single photons. We find that the measured negativity can be interpreted in the context of selecting measurements, and it reflects the nonclassical nature of photons. Our results suggest a new operational way to unravel the nonclassicality of photons in the context of measurement selection.

Exploring entanglement resource in Si quantum dot systems with operational quasiprobability approach

“…where it has been shown theoretically and experimentally that a polarization of a single qubit system exhibits N > 0 [18,20].…”

“…Recently, an alternative method of entanglement verification, called as the operational quasiprobability (OQ), has been proposed. Employing a probability function that can generate negative values, the OQ method characterizes various quantum natures of a given logic state with negative probabilities that are fundamentally impossible to be obtained with classical probability density functions [18][19][20]. In principle, the OQ method is advantageous over the entanglement measures in a sense that the probability function can be determined only directly measurable quantities that can be easily tested in lab-oratory.…”

Necessary and sufficient condition for joint measurability

“…The test of OQ also identifies violation of macrorealism [35,36] and measurement-selection context [37] in given systems [24,25,28]. OQ can pave the way to reveal relations among non-JM and the quantum features, which is beyond this work.…”

“…For an operational test, we employ the indirect method based on operational quasiprobability [24,25], which is determined by the statistics from measurements, similarly to the device-independent approaches [26,27]. Negative operational quasiprobability is an indicator of nonclassicality such as entanglement [24], the violation of macrorealism [25], and the measurement-selection context [28].…”

Exploring entanglement resource in Si quantum dot systems with operational quasiprobability approach

“…Employing a probability function that can generate negative values, the OQ method characterizes various quantum natures of a given logic state with negative probabilities that are fundamentally impossible to be obtained with classical probability density functions [29,30]. In principle, the OQ method is advantageous over the entanglement measures in a sense that the probability function can be determined only directly measurable quantities that can be easily tested in laboratory [31]. Moreover, in general, the OQ method requires less number of measurements for entanglement verification, so the computational cost can be saved compared to the case of entanglement measures that involve a full-state tomography processes [17].…”