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Register a new userSpin-parity effect in violation of bells inequalities for entangled states of parallel polarization
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Bell inequalities (BIs) derived in terms of quantum probability statistics are extended to general bipartite-entangled states of arbitrary spins with parallel polarization. The original formula of Bell for the two-spin singlet is slightly modified in the parallel configuration, while, the inequality for- mulated by Clauser-Horne-Shimony-Holt remains not changed. The violation of BIs indeed resulted from the quantum non-local correlation for spin-1=2 case. However, the inequalities are always satisfied for the spin-1 entangled states regardless of parallel or antiparallel polarizations of two spins. The spin parity effect originally demonstrated with the antiparallel spin-polarizations (Mod. Phys. Lett. B28, 145004) still exists for the parallel case. The quantum non-locality does not lead to the violation for integer spins due to the cancellation of non-local interference effects by the quantum statistical-average. Again the violation of BIs seems a result of the measurement induced nontrivial Berry-phase for half-integer spins.
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We present a scheme for demonstrating violation of Bells inequalities using a spin-1/2 system entangled with a pair of classically distinguishable wave packets in a harmonic potential. In the optical domain, such wave packets can be represented by coherent states of a single light mode. The proposed scheme involves standard spin-1/2 projections and measurements of the position and the momentum of the harmonic oscillator system, which for a light mode can be realized by means of homodyne detection. We discuss effects of imperfections, including non-unit efficiency of the homodyne detector, and point out a close link between the visibility of interference and violation of Bells inequalities in the described scheme.
The experimental test of Bells inequality is mainly focused on Clauser-Horne-Shimony-Holt (CHSH) form, which provides a quantitative bound, while little attention has been pained on the violation of Wigner inequality (WI). Based on the spin coherent state quantum probability statistics we in the present paper extend the WI and its violation to arbitrary two-spin entangled states with antiparallel and parallel spin-polarizations. The local part of density operator gives rise to the WI while the violation is a direct result of non-local interference between two components of the entangled states. The Wigner measuring outcome correlation denoted by $W$ is always less than or at most equal to zero for the local realist model ($% W_{lc_{{}}}leq 0$) regardless of the specific initial state. On the other hand the violation of WI is characterized by any positive value of $W$, which possesses a maximum violation bound $W_{max }$ $=1/2$. We conclude that the WI is equally convenient for the experimental test of violation by the quantum entanglement.
The robustness of Bells inequality (in CHSH form) violation by entangled state in the simultaneous presence of colored and white noise in the system is considered. A twophoton polarization state is modeled by twoparameter density matrix. Setting parameter values one can vary the relative fraction of pure entangled Bells state as well as white and colored noise fractions. Bells operator-parameter dependence analysis is made. Computational results are compared with experimental data [quant-ph/0511265] and with results computed using a oneparameter density matrix [doi: 10.1103/PhysRevA.72.052112], which one can get as a special case of the model considered in this work.
Bells inequality for continuous-variable bipartite systems is studied. The inequality is expressed in terms of pseudo-spin operators and quantum expectation values are calculated for generic two-mode squeezed states characterized by a squeezing parameter $r$ and a squeezing angle $varphi$. Allowing for generic values of the squeezing angle is especially relevant when $varphi$ is not under experimental control, such as in cosmic inflation, where small quantum fluctuations in the early Universe are responsible for structures formation. Compared to previous studies restricted to $varphi=0$ and to a fixed orientation of the pseudo-spin operators, allowing for $varphi eq 0$ and optimizing the angular configuration leads to a completely new and rich phenomenology. Two dual schemes of approximation are designed that allow for comprehensive exploration of the squeezing parameters space. In particular, it is found that Bells inequality can be violated when the squeezing parameter $r$ is large enough, $rgtrsim 1.12$, and the squeezing angle $varphi$ is small enough, $varphilesssim 0.34,e^{-r}$.
Newtons second law aids us in predicting the location of a classical object after knowing its initial position and velocity together with the force it experiences at any time, which can be seen as a process of continuous iteration. When it comes to discrete problems, e.g. building Bell inequalities, as a vital tool to study the powerful nonlocal correlations in quantum information processing. Unless having known precisely the general formula of associated inequalities, iterative formulas build a bridge from simple examples to all elements in the set of Bell inequalities. Although exhaust all entities in the set, even in the subset of tight individuals, is a NP hard problem, it is possible to find out the evolution law of Bell inequalities from few-body, limited-setting and low-dimension situations to arbitrary $(n,k,d)$ constructions, i.e. $n$ particles, $k$ measurements per particle, and $d$ outcomes per measurement. In this work, via observing Sliwas 46 tight (3,2,2) Bell inequalities [{Phys. Lett. A}. 317, 165-168 (2003)], uniting the root method [{Phys. Rev. A}. 79, 012115, (2009)] and the idea of degeneration, we discover an iterative formula of Bell inequalities containing all $(n,k,2)$ circumstances, which paves a potential way to study the current Bell inequalities in terms of iterative relations combining root method on the one hand, and explore more interesting inequalities on the other.
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