The Foundational Significance of Leggett’s Non-local Hidden-Variable Theories

Lee Smolin

Emilio Santos

Jacquiline Romero, Jonathan Leach, Barry Jack +3 more

We report an experimental test of Leggett's non-local hidden variable theory in an orbital angular momentum (OAM) state space of light. We show that the correlations we observe are in conflict with Leggett's model, thus excluding a particular class of non-local hidden variable theories for the first time in a non-polarization state space. It is known that the violation of the Leggett inequality becomes stronger as more detection settings are used. The required measurements become feasible in an OAM subspace, and we demonstrate this by testing the inequality using three and four settings. We observe excellent agreement with quantum predictions and a violation of five and six standard deviations, respectively, compared to Leggett's non-local hidden variable theory.

Abner Shimony

Michael Nauenberg

I impose previously neglected symmetry conditions in Leggett's non-local hidden variable theory that are required by the conditions in a recent experimental test of this theory. These conditions lead to an inequality for the polarization correlation function that has a maximal violation from the quantum predictions that is 2.5 times larger than reported in this article. Furthermore, when these symmetry conditions are applicable, Leggett's non-local theory also cannot model the observed quantum correlations in previous experiments.

Dongkai Zhang, Xiaodong Qiu, Lixiang Chen

Leggett inequality states that nonlocal hidden-variable models might still be incompatible with the predictions of quantum physics. However, its theoretical and experimental demonstration is only in the scenario of 2-dimensional maximally entangled systems. An open question remains as to whether the Leggett inequality can be violated by nonmaximally entangled states. Here, we answer this question both in theory and experiment. Specifically, from the point of view of geometry, we theoretically map the problem of maximizing the correlation measure in the Leggett inequality to maximizing the sum of an ellipse’s diameter and semi-diameter axes, accordingly, demonstrating that the violation of the Leggett inequality requires a more robust entanglement than that of Bell’s theory. Experimentally, by leveraging the controllable photonic orbital angular momentum entanglement, we demonstrate the violation of Leggett-type inequalities by more than 8.7 and 4.5 standard deviations under concurrence C = 0.95 and 0.9, respectively. Our observations indicate that, the requirement for quantum correlation should be increased to exclude a particular class of non-local hidden variable theories that abide by Leggett’s model, providing insights into the boundaries of quantum correlation and the limitations imposed by non-local hidden variables.