Operational quasiprobabilities for continuous variables

Abstract

We generalize the operational quasiprobability involving sequential measurements proposed by Ryu et al. [Phys. Rev. A 88, 052123] to a continuous-variable system. The quasiprobabilities in quantum optics are incommensurate, i.e., they represent a given physical observation in different mathematical forms from their classical counterparts, making it difficult to operationally interpret their negative values. Our operational quasiprobability is commensurate, enabling one to compare quantum and classical statistics on the same footing. We show that the operational quasiprobability can be negative against the hypothesis of macrorealism for various states of light. Quadrature variables of light are our examples of continuous variables. We also compare our approach to the Glauber-Sudarshan P function. In addition, we suggest an experimental scheme to sequentially measure the quadrature variables of light.

Quasiprobability representation of quantum coherence

“…In general, the technique of quasiprobability distributions presents a remarkably successful approach in modern quantum physics. For example, quasiprobabilities can be applied to confirm fundamental predictions of quantum physics, such as nonlocality [2,3], macrorealism [4], and contextuality [5]. Moreover, negative quasiprobabilities serve as a resource for quantum information protocols [6,7].…”

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

“…Furthermore, their comparison to classical statistics reveals the subtlety that quasiprobabilities require different physical interpretations for the same form of functionals as their classical counterparts. This is described as “incommensurability” of quasiprobabilities 31,32 . Therefore, it is more natural to employ quasiprobability that compares quantum and classical statistics on the same footing.…”

Necessary and sufficient condition for joint measurability

“…Thus, the positivity condition of the OQ (or that of Wmeasure) fully and operationally characterizes the JM of 2-outcome unbiased POVMs in the SSM scenario. 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.…”

“…Selective and Sequential Measurements.-JM and non-JM can operationally be tested by using the operational quasiprobability (OQ) [24,25]. OQ is constructed with probabilities by the measurements, A, B, and C: Q(i, j) = p C (i, j) + (p A (i) − j p C (i, j))/2 + (p B (j) − i p C (i, j))/2, where p X (x) is a probability of obtaining outcome x by measurement X.…”

“…The non-JM test now involves the sequential measurement, C, and the individual A and B. We call these selective and sequential measurements (SSM) [24,25]. Our test in the SSM scenario is also sufficient for non-JM in case of the 2-outcome unbiased measurements A and B. AssumingK i = Â i , the W -measure is given bŷ…”