Operational approach to Bell inequalities: applications to qutrits

Abstract

Bell inequalities can be studied both as constraints in the space of probability distributions and as expectation values of multipartite operators. The latter approach is particularly useful when considering outcomes as eigenvalues of unitary operators. This brings the possibility of exploiting the complex structure of the coefficients in the Bell operators. We investigate this avenue of though in the known case of two outcomes, and find new Bell inequalities for the cases of three outcomes and $n=3,4,5$ and $6$ parties. We find their corresponding classical bounds and their maximum violation in the case of qutrits. We further propose a novel way to generate Bell inequalities based on a mapping from maximally entangled states to Bell operators and produce examples for different outcomes and number of parties.

arXiv comment10 pages, no figures. A sign error in Eq.(10), appearing in the published version, has been corrected

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• Experimental high-dimensional Greenberger-Horne-Zeilinger entanglement with superconducting transmon qutrits
• Infinite violation of Bell inequalities in inflation
• Mermin's Inequalities of Multiple qubits with Orthogonal Measurements on IBM Q 53-qubit system
• Mermin inequalities for perfect correlations in many-qutrit systems
• Quantum Key-Distribution Protocols Based on a Quantum Version of the Monty Hall Game
• Avenues to generalising Bell inequalities
• Mermin's inequalities in Quantum Field Theory
• Mermin Polynomials for Entanglement Evaluation in Grover's algorithm and Quantum Fourier Transform
• The Degree of Quantum Contextuality in terms of Concurrence for the KCBS Scenario
• Deriving three-outcome permutationally invariant Bell inequalities
• Using Weyl operators to study Mermin's inequalities in Quantum Field Theory
• Semicoherent Symmetric Quantum Processes: Theory and Applications
• Probing Mermin's inequalities violations through pseudospin operators
• Freezing dynamics of entanglement and nonlocality for qutrit-qutrit ($3\otimes 3$) quantum systems
• Simulating Bell inequalities with Qibo
• Distribution of Non-Locality On Quantum Random Circuits