Bipartite qutrit local realist inequalities and the robustness of their quantum mechanical violation

Abstract

Distinct from the type of local realist inequality (known as the Collins-Gisin-Linden-MassarPopescu or CGLMP inequality) usually used for bipartite qutrit systems, we formulate a new set of local realist inequalities for bipartite qutrits by generalizing Wigner's argument that was originally formulated for the bipartite qubit singlet state. This treatment assumes existence of the overall joint probability distributions in the underlying stochastic hidden variable space for the measurement outcomes pertaining to the relevant trichotomic observables, satisfying the locality condition and yielding the measurable marginal probabilities. Such generalized Wigner inequalities (GWI) do not reduce to Bell-CHSH type inequalities by clubbing any two outcomes, and are violated by quantum mechanics (QM) for both the bipartite qutrit isotropic and singlet states using trichotomic observables defined by six-port beam splitter as well as by the spin-1 component observables. The efficacy of GWI is then probed in these cases by comparing the QM violation of GWI with that obtained for the CGLMP inequality. This comparison is done by incorporating white noise in the singlet and isotropic qutrit states. It is found that for the six-port beam splitter observables, QM violation of GWI is more robust than that of the CGLMP inequality for singlet qutrit states, while for isotropic qutrit states, QM violation of the CGLMP inequality is more robust. On the other hand, for the spin-1 component observables, QM violation of GWI is more robust for both the type of states considered.

Sharing of tripartite nonlocality by multiple observers measuring sequentially at one side

“…Secondly, in the same spirit of the present work, it would be interesting to investigate sharing of multipartite quantum steering [50][51][52] by multiple observers measuring sequentially on the same particle. Thirdly, exploring the concept of nonlocality sharing for higher dimensional quantum systems by using different many-outcome local realist inequalities [53,54] remains open till date. Another interesting direction is to explore the pos-sibility of sharing tripartite nonlocal correlations between (i) single Alice -multiple Bobs -multiple Charlies, (ii) multiple Alices -multiple Bobs -multiple Charlies and finding a connection of these sharing phenomena with some information processing task(s).…”

Pearson correlation coefficient as a measure for certifying and quantifying high-dimensional entanglement

“…This is similar to the case of nonlocality studies using Bell-type inequalities involving measurements pertaining to mutually noncommuting bases which do not necessarily need to be MUBs [46]. Here we may also mention that apart from its other applications, the procedure of entanglement characterization and quantification using PCCs in the qutrit case, together with the results of studies on the nonlocality of bipartite qutrit states can provide a powerful experimental platform for a comprehensive probing of hitherto unexplored quantitative aspects of the relationship between entanglement and nonlocality [44][45][46][58][59][60][61][62][63].…”

Experimentally Demonstrate the Spin-1 Information Entropic Inequality Based on Simulated Photonic Qutrit States

“…All mentioned above information and entropic schemes for quantum systems open a new prospective for implementation of quantum technologies, e.g., realization of quantum memory, quantum algorithms, and many-level quantum simulation [ 16 ]. However, in order to prove the inequality and study its application experimentally, especially the higher-dimensional inequality, the quality requirement of the entangled system is very strict [ 17 , 18 , 19 ]. To our knowledge, experimental reports on quantum entanglement entropy are very few [ 18 , 19 , 20 , 21 ].…”