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The European Physical Journal Special Topics

Relativistic independence and multipartite quantum correlations

Rain Lenny, Amit Te’eni, Michael Suleymanov, Eliahu Cohen

Published Aug 11, 2025• 1 citation
Publisher

Abstract

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.

DOI
10.1140/epjs/s11734-025-01836-0

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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.
Viewing frames of reference as physical systems, subject to the same laws as the systems they describe, is central to the relational approach in physics. Under the assumption that quantum mechanics universally governs all physical entities, this perspective naturally leads to the concept of quantum reference frames (QRFs). We investigate the perspective-dependence of position and momentum uncertainties, correlations, covariance matrices, and entanglement within the QRF formalism. We show that the Robertson-Schrödinger uncertainty relations are frame-dependent, and so are correlations and variances, which satisfy various constraints described as inequalities. However, the determinant of the total covariance matrix, linked to the uncertainty volume in phase space, as well as variance-based entanglement criteria, remains invariant under changes of reference frame. Under specific conditions, the purities of subsystems are also invariant for different QRFs, but in general, they are perspective-dependent. These invariants suggest fundamental, robust measures of uncertainty and entanglement that persist despite changes in observational perspective, potentially inspiring dedicated quantum information protocols as well as further foundational studies.
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:
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.
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Quantum reference frames provide a relational description of multipartite quantum systems in which physical states and observables are defined relative to quantum observers. Yet different observers can assign different entropies to the same system, raising the question of how such observer-dependence is constrained. We identify a family of frame-independent diagonal Rényi entropies for arbitrary subsystems, yielding a generalized multipartite coherence-entanglement tradeoff. For ideal frames, the observer-dependence of subsystem entropy admits an exact decomposition into a sum of single-frame coherences and inter-frame correlations; for non-ideal frames, it is instead bounded by the dimension of an effective relational Hilbert space determined by the representation structure of the frames. Our results place quantitative limits on how much quantum observers can disagree about subsystem entropy, with potential implications for observer-dependent entropy assignments in gravitational settings.