Experimental Test of Nonlocality Limits from Relativistic Independence
Francesco Atzori, Salvatore Virzì, Enrico Rebufello, Alessio Avella, Fabrizio Piacentini, Iris Cusini, Henri Haka, Federica Villa, Marco Gramegna, Eliahu Cohen, Ivo Pietro Degiovanni, Marco Genovese
Quantum correlations, like entanglement, represent the characteristic trait of quantum mechanics and pose essential issues and challenges to the interpretation of this pillar of modern physics. Although quantum correlations are largely acknowledged as a major resource to achieve quantum advantage in many tasks of quantum technologies, their full quantitative description and the axiomatic basis underlying them are still under investigation. Previous works have suggested that the origin of nonlocal correlations is grounded in principles capturing (from outside the quantum formalism) the essence of quantum uncertainty. In particular, the recently introduced principle of relativistic independence has given rise to a new bound intertwining local and nonlocal correlations. Here, we test such a bound by realizing together sequential and joint weak measurements on entangled photon pairs, allowing us to simultaneously quantify both local and nonlocal correlations by measuring incompatible observables on the same quantum system without collapsing its state, a task typically forbidden in the traditional (projective) quantum measurement framework. Our results demonstrate the existence of a fundamental limit on the extent of quantum correlations, shedding light on the profound role of uncertainty in both enabling and balancing them. Published by the American Physical Society 2024
Quantum correlations, like entanglement, represent the characteristic trait of quantum mechanics and pose essential issues and challenges to the interpretation of this pillar of modern physics. Although quantum correlations are largely acknowledged as a major resource to achieve quantum advantage in many tasks of quantum technologies, their full quantitative description and the axiomatic basis underlying them are still under investigation. Previous works have suggested that the origin of nonlocal correlations is grounded in principles capturing (from outside the quantum formalism) the essence of quantum uncertainty. In particular, the recently introduced principle of relativistic independence has given rise to a new bound intertwining local and nonlocal correlations. Here, we test such a bound by realizing together sequential and joint weak measurements on entangled photon pairs, allowing us to simultaneously quantify both local and nonlocal correlations by measuring incompatible observables on the same quantum system without collapsing its state, a task typically forbidden in the traditional (projective) quantum measurement framework. Our results demonstrate the existence of a fundamental limit on the extent of quantum correlations, shedding light on the profound role of uncertainty in both enabling and balancing them. Published by the American Physical Society 2024
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:
If nature allowed nonlocal correlations other than those predicted by quantum mechanics, would that contradict some physical principle? Various approaches have been put forward in the past two decades in an attempt to single out quantum nonlocality. However, none of them can explain the set of quantum correlations arising in the simplest scenarios. Here, it is shown that generalized uncertainty relations, as well as a specific notion of locality, give rise to both familiar and new characterizations of quantum correlations. In particular, we identify a condition, relativistic independence, which states that uncertainty relations are local in the sense that they cannot be influenced by other experimenters' choices of measuring instruments. We prove that theories with nonlocal correlations stronger than the quantum ones do not satisfy this notion of locality, and therefore, they either violate the underlying generalized uncertainty relations or allow experimenters to nonlocally tamper with the uncertainty relations of their peers.
Entanglement and nonlocality are studied in the framework of pre-/postselected ensembles with the aid of weak measurements and the two-state-vector formalism. In addition to the EPR–Bohm experiment, we revisit the Hardy and Cheshire Cat experiments, whose entangled pre- or postselected states give rise to curious phenomena. We then turn to even more peculiar phenomenon suggesting “emerging correlations” between independent preand postselected ensembles of particles. This can be viewed as a quantum violation of the classical “pigeonhole principle.” Introduction It is seldom acknowledged that seven years before the celebrated Bell paper [1], Bohm and Aharonov [2] published an analysis of the EPR paradox [3]. They suggested an experimental setup, based on Compton scattering, for testing nonlocal correlations between the polarizations of two annihilation photons. In 1964, Bell proposed his general inequality, thereby excluding local realism. During the same time, Aharonov et al. constructed the foundations of a time-symmetric formalism of quantum mechanics [4]. While Bell's proof utilizes entanglement to demonstrate nonlocal correlations,wewill describe inwhat follows the emergence of nonlocal correlations between product states. For this purpose, however, we shall invoke weak measurements of pre- and postselected ensembles. In classical mechanics, initial conditions of position and velocity for every particle fully determine the time evolution of the system. Therefore, trying to impose an additional final condition would lead either to redundancy or to inconsistency with the initial conditions. This is radically different in quantum mechanics. Because of the uncertainty principle, an initial state vector does not fully determine, in general, the outcome of a future measurement. However, adding a final (backward-evolving) state vector results in a more complete description of the quantum system in between these two boundary conditions, which has a bearing on the determination of measurement outcomes. The basis for this time-symmetric formulation of quantum mechanics was laid down by Aharonov, Bergman, and Lebowitz (ABL), who derived a symmetric probability rule concerning measurements performed on systems, while taking into account the final state of the system, in addition to the usual initial state [4].
In quantum mechanics, joint measurements of noncommuting observables are only possible if a minimal unavoidable measurement uncertainty is accepted. On the other hand, correlations between noncommuting observables can exceed classical limits, as demonstrated by the violation of Bell's inequalities. Here, the relation between the uncertainty-limited statistics of joint measurements and the limits on expectation values of possible input states is analyzed. It is shown that the experimentally observable statistics of joint measurements explain the uncertainty limits of local states, but result in less restrictive bounds when applied to identify the limits of nonlocal correlations between two separate quantum systems. A tight upper bound is obtained for the four correlations that appear in the violation of Bell's inequalities and the statistics of pure states saturating the bound is characterized. The results indicate that the limitations of quantum nonlocality are a necessary consequence of the local features of joint measurements, suggesting the possibility that quantum nonlocality could be explained in terms of the local characteristics of quantum statistics.
Multipartite quantum correlations are complex and intricate, posing challenges for their detection and quantification. Nevertheless, they are central to both fundamental quantum science and its numerous applications. We discuss several approaches for analyzing quantum correlations, with an emphasis on the Relativistic Independence framework which allows one to detect and differentiate classes of multipartite entangled states, while also yielding refined quantum bounds on multipartite systems. This framework is shown to rely on a recently demonstrated tradeoff between local and nonlocal correlations, signifying the enabling power of quantum uncertainty. Furthermore, we examine these notions from the broader perspective of quantum reference frames (QRFs), attempting to see which of the above concepts are perspective-dependent and which are not. Large parts of the current discussion, as well as many of the quantitative results presented, specifically rely on the structure of the covariance matrix, whose determinant remains invariant under QRF changes, thereby signaling its fundamental significance.
Recent works in foundations of quantum (field) theory and relativistic quantum information try to better grasp the interplay between the structure of quantum correlations and the constraints imposed by causality on physical operations. Chapter 1 is dedicated to the study of the conceptual implications of quantum nonlocality, a concept that subsumes that of entanglement in a certain way. We detail the recent information-theoretic approaches to understanding the structure of nonlocal correlations, and the issues the latter raise concerning the ability of local observers to isolate a system from its environment. Chapter 2 reviews in what sense imposing Poincare invariance affects entanglement detection and quantification procedures. This invariance ultimately forces a description of all quantum systems within the framework of quantum field theory, which leads to the impossibility of localized finite-energy states and to the divergence of all entanglement measures for local observers. We provide a solution to these two problems by showing that there exists a generic equivalence between a finite spatial resolution of the measurement apparatus and the exclusion of high-energy degrees of freedom from the definition of the observed system. This equivalence allows for an epistemic interpretation of the standard quantum formalism describing nonrelativistic localized systems and their correlations, hence a clarification of the origin of the finite measures of entanglement between such systems. Chapter 3 presents a recent theoretical framework that predicts the existence of correlations with indefinite causal order. In analogy to the information-theoretic approaches to nonlocal correlations, we introduce some principles that constrain the structure of such correlations, which is a first step toward a clear understanding of their physical origin.