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Register a new userViolation of a Bell inequality in two-dimensional spin-orbit hypoentangled subspaces
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Based on spin-orbit coupling induced by q-plates, we present a feasible experimental proposal for preparing two-dimensional spatially inhomogeneous polarizations of light. We further investigate the quantum correlations between these inhomogeneous polarizations of photon pairs generated by spontaneous parametric down-conversion, which in essence describe the so-called hypoentanglement that is established between composite spin-orbit variables of photons. The violation of the Clauser-Horne-Shimony-Holt-Bell inequality is predicted with S=2sqrt2 to illustrate the entangled nature of the cylindrical symmetry of spatially inhomogeneous polarizations.
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In this paper, we use Bell inequality and nonlocality to study the bipartite correlation in an exactly soluble two-dimensional mixed spin system. Bell inequality turns out to be a valuable detector for phase transitions in this model. It can detect not only the quantum phase transition, but also the thermal phase transitions, of the system. The property of bipartite correlation in the system is also analyzed. In the quantum anti-ferromagnetic phase, the Bell inequality is violated thus nonlocality is present. It is interesting that the nonlocality is enhanced by thermal fluctuation, and similar results have not been observed in anti-ferromagnetic phase. In the ferromagnetic phase, the quantum correlation turns out to be very novel, which cannot be captured by entanglement or nonlocality.
We observe violation of a Bell inequality between the quantum states of two remote Yb ions separated by a distance of about one meter with the detection loophole closed. The heralded entanglement of two ions is established via interference and joint detection of two emitted photons, whose polarization is entangled with each ion. The entanglement of remote qubits is also characterized by full quantum state tomography.
Single photons emerging from q-plates (or Pancharatnam-Berry phase optical element) exhibit entanglement in the degrees of freedom of spin and orbital angular momentum. We put forward an experimental scheme for probing the spin-orbit correlations of single photons. It is found that the Clauser-Horne-Shimony-Holt (CHSH) parameter S for the single-photon spin-orbit entangled state could be up to 2.828, evidently violating the Bell-like inequality and thus invalidating the noncontextual hidden variable (NCHV) theories.
The original formula of Bell inequality (BI) in terms of two-spin singlet has to be modified for the entangled-state with parallel spin polarization. Based on classical statistics of the particle-number correlation, we prove in this paper an extended BI, which is valid for two-spin entangled states with both parallel and antiparallel polarizations. The BI and its violation can be formulated in a unified formalism based on the spin coherent-state quantum probability statistics with the state-density operator, which is separated to the local and non-local parts. The local part gives rise to the BI, while the violation is a direct result of the non-local quantum interference between two components of entangled state. The Bell measuring outcome correlation denoted by $P_{B}$ is always less than or at most equal to one for the local realistic model ($P_{B}^{lc}leq1$) regardless of the specific superposition coefficients of entangled state. Including the non-local quantum interference the maximum violation of BI is found as $P_{B}^{max}$ $=2$, which, however depends on state parameters and three measuring directions as well. Our result is suitable for entangled photon pairs.
A finite non-classical framework for physical theory is described which challenges the conclusion that the Bell Inequality has been shown to have been violated experimentally, even approximately. This framework postulates the universe as a deterministic locally causal system evolving on a measure-zero fractal-like geometry $I_U$ in cosmological state space. Consistent with the assumed primacy of $I_U$, and $p$-adic number theory, a non-Euclidean (and hence non-classical) metric $g_p$ is defined on cosmological state space, where $p$ is a large but finite Pythagorean prime. Using number-theoretic properties of spherical triangles, the inequalities violated experimentally are shown to be $g_p$-distant from the CHSH inequality, whose violation would rule out local realism. This result fails in the singular limit $p=infty$, at which $g_p$ is Euclidean. Broader implications are discussed.
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