Envariance, or environment-assisted invariance, is a recently identified symmetry for maximally entangled states in quantum theory with important ramifications for quantum measurement, specifically for understanding Born's rule. We benchmark the degree to which nature respects this symmetry by using entangled photon pairs. Our results show quantum states can be (99.66 ± 0.04)% envariant as measured using the quantum fidelity, and (99.963 ± 0.005)% as measured using a modified Bhattacharya coefficient, as compared with a perfectly envariant system which would be 100% in either measure. The deviations can be understood by the less-than-maximal entanglement in our photon pairs.

Bell's inequalities are important to our understanding of quantum foundations and critical to several quantum technologies. A recent work [E. Wolfe and S. F. Yelin, Phys. Rev. A 86, 012123 (2012)] derived three parametrized families of two-particle, two-setting Bell inequalities. These inequalities are important as they theoretically explore a larger volume of allowed quantum correlations over local hidden-variable models than previous results [A. Cabello, Phys. Rev. A 72, 012113 (2005)] by exploiting marginal, or single particle measurements. In this work we subject those predictions to experimental test using nonmaximally entangled photon pairs to optimize the expected violation. We find excellent agreement with the upper bounds predicted by quantum mechanics with violations of the limits imposed by local hidden-variable models as large as almost 30σ for the optimal parameters and a significant violation over a wide range of parameters.

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