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. 2019 Dec 13;9(1):19021.
doi: 10.1038/s41598-019-53121-5.

Optical Experiment to Test Negative Probability in Context of Quantum-Measurement Selection

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Free PMC article

Optical Experiment to Test Negative Probability in Context of Quantum-Measurement Selection

Junghee Ryu et al. Sci Rep. .
Free PMC article

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.

Conflict of interest statement

The authors declare no competing interests.

Figures

Figure 1
Figure 1
Experimental scheme for measuring the polarization of single photons. (a) A sequential polarization measurement was implemented. Two knobs denoted by n1 and n2 indicate the selective polarization measurements at the times t1 and t2, respectively. Such configurations are implemented in a laboratory setting, as shown (b). When the PBS1 is in position, the H polarization is measured by taking the sum of clicks on D0,0 and D0,1 and the V polarization is obtained from the sum of D1,0 and D1,1. If the PBS1 is out, then the input light travels directly to the PBS2 corresponding to the D/A polarization measurement (see Methods for more details).
Figure 2
Figure 2
Negativity with a source by spontaneous parametric down conversion. (a) Negativity as a function of θ with a fixed value of φ=0 of the state |Ψ(θ,φ)=cos(θ/2)|H+eiφsin(θ/2)|V. The black line shows the theoretical values and the i experimental results are denoted by the red circles with the error estimation. (b) A contour plot of the measured negativity for 0θ,φ90. The inset represents the theoretical values. The experimental maximum negativity N0.103 is obtained at θ=45 and φ=0.
Figure 3
Figure 3
Negativity of the mixed states. (a) Simulation of the negativity in a cross-sectional plane of a Bloch sphere for φ=0. The points on the surface of the circle corresponds to the pure state as Ψ(θ,φ=0)=cos(θ/2)H+sin(θ/2)V. The inner points correspond to the mixed states which can be represented by a probabilistic mixture of the pure states as ϱ^(θ1,θ2,α)=1+α2|Ψ(θ1)Ψ(θ1)|+ 1α2|Ψ(θ2)Ψ(θ2)|with a mixing parameter α. The yellow dotted lines denote the mixture of two pure states among the four measuring bases which results in zero negativity for each case. All points inside the dotted square, therefore, give a zero negativity. The centre position corresponds to a completely depolarized state. (b) Experimental results for the heralded single photons and (c) for single photons from a molecule. We plotted the data for the different conditions of the parameters as 0θ1180, θ2=θ1+180, and α1 with resolution values of Δθ1=1 and Δα=1/30. The slightly distorted shape is due to the imperfect alingment and response of the wave-plate in the experiments.

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