Foundations 3

Abstract: Attempts to understand multipartite quantum nonlocality are thwarted by the difficulty of devising quantum Bell inequalities (QBI) for systems composed of more than a few separate parties. In this work, we introduce the notion of ``tight connectors", a class of tensors which, if contracted according to some simple rules, result in tight QBIs. The new inequalities are saturated by tensor network states, whose structure mimics the corresponding network of connectors. Some tight connectors are furthermore ``fully self-testing'', which implies that the QBI they generate through contractions can only be maximized with such a tensor network state and specific measurement operators (modulo local isometries). We provide large analytic families of tight, fully self-testing connectors that allow the generation, via contraction, of N-partite QBIs with a ratio between the maximum quantum and classical values that grows exponentially with N. In turn, our method provides a modular recipe for the generation of extremal quantum behaviours and associated tight bounds in arbitrarily large systems.

Abstract: Device-independent self-testing refers to the certification of quantum states based entirely on the correlations exhibited by measurements on separate subsystems. The fact that such a certification is possible at all is remarkable in its own right, and is intimately connected to the violation Bell’s inequalities by entangled quantum systems. In the bipartite case, self-testing of states has been completely characterized, up to local isometries, as there exist protocols that self-test arbitrary pure states of any local dimension. Despite the growing interest in device-independent certification protocols, an analogous result in the general multipartite case has remained elusive. In this work, we give a complete characterization of the qubit case, showing that any multipartite entangled state of qubits can be self-tested.

Abstract: As a striking manifestation of quantum entanglement, nonlocality has long played a pivotal role in shaping our understanding of the quantum world. When considering a Bell test involving three parties, we may even find a remarkable situation where the nonlocality in two bipartite subsystems forces the remaining bipartite subsystem to exhibit nonlocality. This intriguing effect, dubbed nonlocality transitivity, was first identified in the non-quantum non-signaling world in 2011. However, whether such transitivity could manifest within quantum theory has remained unresolved—until now. Here, we provide the first affirmative answer to this open problem at the level of quantum states, thereby showing that there exists a quantum-realizable notion of nonlocality transitivity. Specifically, by leveraging the possibility of Bell-inequality violation by tensoring, we analytically construct a pair of nonlocal bipartite states such that simultaneously realizing them in a tripartite system induces nonlocality in the remaining bipartite subsystem. En route to showing this, we also prove that multiple copies of the W-state marginals uniquely determine the global compatible state, thus establishing another instance when the parts determine the whole. Surprisingly, the nonlocality transitivity of quantum states also occurs among the reduced states of Haar-random three-qutrit pure states. We further show that the transitivity of quantum steering can already be demonstrated with the marginals of a three-qubit W state, showing again another noteworthy difference between the two forms of quantum correlations. Finally, we present a simple method to construct quantum states and correlations that are nonlocal in all their non-unipartite marginals, which may be of independent interest.

Abstract: Violations of Bell inequalities are often regarded as evidence that quantum nonlocality guarantees intrinsic randomness, effectively playing the role of a “dice” at the heart of device-independent (DI) cryptographic protocols. Yet the precise connection between nonlocality and randomness is more nuanced. We first show that there exist nontrivial Bell inequalities that are maximally violated by quantum correlations while certifying no randomness for any fixed input pair, rendering them ineffective for a large class of standard DI schemes. Moreover, we construct maximally nonlocal quantum correlations that remain deterministic for every fixed input pair, in the sense that for any chosen inputs they can be decomposed into strategies with fixed outputs. Conversely, we show when all input pairs are used for randomness generation, any amount of quantum nonlocality suffices to certify randomness, implying that no form of bound randomness exists in quantum nonlocality: every nonlocal behavior can be useful for DI randomness generation under an appropriately designed protocol. Building on this, we introduce the average guessing probability over all inputs, in contrast to the hitherto considered fixed-input guessing probability, as a faithful and monotonic quantifier of nonlocality. Using this measure, we prove that, contrary to recent findings in PRL 134, 090201, the detection efficiency threshold for certifying randomness is never lower than that required for detecting nonlocality. Finally, we analytically compute the average guessing probability by a quantum adversary in the standard CHSH test and show how this leads to improved generation rates in state-of-the-art amplification protocols. Together, our results precisely delineate the limits of determinism compatible with quantum nonlocality and establish average guessing probability as the correct operational bridge between nonlocality and DI randomness.