Characterization of Local and Nonlocal Quantum Correlations

Quantum correlations, such as entanglement, are fundamental to quantum mechanics and a key resource for quantum technologies. However, their full quantitative description and axiomatic foundations remain unresolved. Recent studies suggest that the origin of nonlocal correlations lies in principles tied to quantum uncertainty. In particular, a recent paper [1] introduced the principle of Relativistic Independence (RI), which asserts that observers with spacelike separation cannot influence each other's uncertainty relations. This principle provides a novel bound intertwining local and nonlocal correlations: (Equation presented) where B = 〈Â1B1〉+ 〈Â1B2〉+ 〈Â2B1〉− 〈Â2B2〉 represents the CHSH-Bell parameter (nonlocal correlations), rQ = 〈Â2Â1〉−〈Â2〉〈Â1〉 quantifies the local correlations, and Âi and B j denote the observables measured by Alice and Bob, respectively. Testing this inequality requires measuring incompatible observables on the same quantum state, a task prohibited by the Heisenberg uncertainty principle when using traditional projective measurements. In this work, we present the first experimental verification of this bound [2] by combining sequential and joint weak measurements on entangled photon pairs (Fig. 1(a)). Our results reveal a fundamental bound for quantum correlations, highlighting the role of uncertainty in both enabling and constraining these correlations, demonstrating the interplay between local and nonlocal resources (Fig. 1(b)). The weak measurement approach permits the evaluation of quantum correlations without inducing the wavefunction collapse [3], as confirmed by tomographic reconstructions of the system's density matrix before (Figs. 1(c)-(d)) and after (Figs. 1(e)-(f)) four weak measurements. Our method enables the characterization of local and nonlocal quantum correlations by encoding measurements in ancillary degrees of freedom while preserving the entangled state, ensuring its usability for subsequent protocols.