Violations of Local Realism by Two EntangledN-Dimensional Systems Are Stronger than for Two Qubits

Abstract

Tests of local realism versus quantum mechanics based on Bell's inequality employ two entangled qubits. We investigate the general case of two entangled quantum systems defined in N-dimensional Hilbert spaces, or " quNits." Via a numerical linear optimization method we show that violations of local realism are stronger for two maximally entangled quNits ( 3</=N</=9) than for two qubits and that they increase with N. The two quNit measurements can be experimentally realized using entangled photons and unbiased multiport beam splitters.

Superpositions of the orbital angular momentum for applications in quantum experiments

“…Since orbital angular momentum entangled photons can be used as However the ultimate confirmation of the entanglement of the orbital angular momentum will be a Bell inequality experiment generalized to more states [14]. Such an experiment will also give a quantitative measure of the multi-dimensional entanglement produced by parametric down-conversion.…”

Concurrence vectors for entanglement of high-dimensional systems

“…The qutrit system was also suggested to be realized by nuclear magnetic resonance (NMR) utilizing deuterium nuclei partially oriented in liquid crystalline phase [4] or by trapped ions [5]. The use of qutrits instead of qubits was shown [6] to be more secure against symmetric attacks on a quantum key distribution protocol while the violation of local realism for two maximally entangled N -dimensional state is stronger than for qubits [7]. Thus an effective measurement of entanglement for high dimensional Hilbert space become useful.…”

Solving large-scale optimization problems related to Bell’s Theorem

“…These problems were described in detail in [2,3] and are, in fact, two-level optimization problems. The higher level problem is a non-convex non-linear optimization task.…”