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arXiv:1305.5322 · Physical Review A

Nonclassical features of the polarization quasiprobability distribution

Maria V. Chekhova, Farid Ya Khalili

Published Aug 13, 2013• 5 citations
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Abstract

Polarization quasiprobability distribution is defined in the space of the Stokes observables. It can be reconstructed with the help of polarization quantum tomography and provides a full description of the so-called polarization sector of quantum states of light. We show here that due to its definition in terms of the discrete-valued Stokes operators, polarization quasiprobability distribution has singularities at integer values of the Stokes observables and takes negative values even for the quantum states typically considered as ``classical'' ones. In experiments with ``bright'' multiphoton states, the photon-number resolution is smeared due to the photodetectors' technical limitations. In this case, nonclassical features of the explored quantum states can be revealed by adding a strong coherent beam into the orthogonal polarization.

DOI
10.1103/physreva.88.023822

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Polarization quasiprobability distribution is defined in the space of the Stokes observables. It can be reconstructed with the help of polarization quantum tomography and provides a full description of the so-called polarization sector of quantum states of light. We show here that due to its definition in terms of the discrete-valued Stokes operators, polarization quasiprobability distribution has singularities at integer values of the Stokes observables and takes negative values even for the quantum states typically considered as classical'' ones. In experiments with bright'' multiphoton states, the photon-number resolution is smeared due to the photodetectors' technical limitations. In this case, nonclassical features of the explored quantum states can be revealed by adding a strong coherent beam into the orthogonal polarization.
Polarization quasiprobability distribution defined in the Stokes space shares many important properties with the Wigner function for position and momentum. Most notably, they both give correct one-dimensional marginal probability distributions and therefore represent the natural choice for the probability distributions in classical hidden-variable models. In this context, negativity of the Wigner function is considered as proof of nonclassicality for a quantum state. On the contrary, the polarization quasiprobability distribution demonstrates negativity for all quantum states. This feature comes from the discrete nature of Stokes variables; however, it was not observed in previous experiments, because they were performed with photon-number averaging detectors. Here we reconstruct the polarization quasiprobability distribution of a coherent state with photon-number resolving detectors, which allows us to directly observe for the first time its negativity. Furthermore we derive a theoretical polarization quasiprobability distribution for any linearly polarized quantum state.
The polarization properties of macroscopic Bell states are characterized using three-dimensional quantum polarization tomography. This method utilizes three-dimensional (3D) inverse Radon transform to reconstruct the polarization quasiprobability distribution function of a state from the probability distributions measured for various Stokes observables. The reconstructed 3D distributions obtained for the macroscopic Bell states are compared with those obtained for a coherent state with the same mean photon number. The results demonstrate squeezing in one or more Stokes observables.
Quantum features of correlated optical modes define a major aspect of the nonclassicality in quantized radiation fields. However, the phase-sensitive detection of a two-mode light field is restricted to interferometric setups and local intensity measurements. Even the full reconstruction of the quantum state of a single radiation mode relies on such detection layouts and the preparation of a well-defined reference light field. In this work, we establish the notion of the essential quantum correlations of two-mode light fields. It refers to those quantum correlations which are measurable by a given device, i.e., the accessible part of a nonclassical Glauber-Sudarshan phase-space distribution, which does not depend on a global phase. Assuming a simple four-port interferometer and photon-number-resolving detectors, we derive the reconstruction method and nonclassicality criteria based on the Laplace-transformed moment-generating function of the essential quasiprobability. With this technique, we demonstrate that the essential quantum correlations of a polarization tomography scheme are observable even if the detectors are imperfect and cannot truly resolve the photon statistics.
Quantum features of correlated optical modes define a major aspect of the nonclassicality in quantized radiation fields. However, the phase-sensitive detection of a two-mode light field is restricted to interferometric setups and local intensity measurements. Even the full reconstruction of the quantum state of a single radiation mode relies on such detection layouts and the preparation of a well-defined reference light field. In this work, we establish the notion of the essential quantum correlations of two-mode light fields. It refers to those quantum correlations which are measurable by a given device, i.e., the accessible part of a nonclassical Glauber-Sudarshan phase-space distribution, which does not depend on a global phase. Assuming a simple four-port interferometer and photon-number-resolving detectors, we derive the reconstruction method and nonclassicality criteria based on the Laplace-transformed moment-generating function of the essential quasiprobability. With this technique, we demonstrate that the essential quantum correlations of a polarization tomography scheme are observable even if the detectors are imperfect and cannot truly resolve the photon statistics.
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.