Simulating Bell inequality violations with classical optics encoded qubits

Abstract

We present here a classical optics device based on an imaging architecture as analogy of a quantum system where the violation of the Bell inequality can be evidenced. In our case, the two qbits entangled state needed to obtain non classical correlations is encoded using an electromagnetic wave modulated in amplitude and phase. Computational states are represented in a way where each one of the two qbits is associated with two orthogonal directions in the input plane. In addition, unitary operations involved in the measurement of the observables are simulated with the use of a coherent optical processor. The images obtained in the output of the process, contain all the information about the joint, marginal and conditional probabilities. By measuring the intensity distribution in the image plane we evaluate the mean values of the simulated observables. The obtained experimental results show, in an illustrative manner, how some correlations of Clauser-Horne-Shimony-Holt type exceed the upper bound imposed by the local realism hypothesis as a consequence of the joint effect of entanglement and two-particle interference.

Quantum−like nonseparable structures in optical beams

“…A second way to encode two qubits in optical beams was proposed by Puentes et al [35] (a similar method to process optical beams was previously proposed by Caulfield and Shamir [36] and by Spreeuw and coworkers [37]) and found numerous applications in recent years [38][39][40][41][42]. The key idea is to encode two qubits in the transverse positions of four non-overlapping beams of light propagating along a common axis, say z.…”

Bell-like inequality for the spin-orbit separability of a laser beam

“…(7). With the description of the inequality above, we can calculate the theoretical value of S for different input quantum states.…”

“…We have proposed a similar setup to investigate the spin-orbit separability of a laser beam in [5]. Simulations of Bell inequalities in classical optics have also been discussed in waveguides [6] and imaging systems [7]. The combination of the polarization and spatial photonic degrees of freedom open interesting possibilities in the quantum optics and quantum-information domains [8][9][10].…”

Experimental realization of the analogy of quantum dense coding in classical optics

“…An interesting recent development is the identification of classical wave-optics analogies of some quantum information-related processes, such as quantum entanglement and quantum teleportation. [14][15][16][17][18][19][20][21][22][23][24][25][26] By exploiting the local classical optical correlation among different degrees of freedom from the same classical vector beam, dense coding has been demonstrated for classical optical communication. 27 However, the question remains whether or not it is possible to realize the analogy of quantum dense coding in the classical communication system, which is similar to quantum dense coding using pairs of photons entangled in polarization.…”