Nonlocality of Quantum States can be Transitive
arXiv:2412.10505 · doi:10.1038/s41534-025-01173-z
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 {\em 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 -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 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.
Please see the published open-access version for the final paper; v2: Substantially rewritten to improve clarity, and with various new results added; v1: 8+ pages, 1 figure; this is Ref. [86] of arXiv:2202.03523
References in corpus (49)
- Quantum entanglement
- Three qubits can be entangled in two inequivalent ways
- Bell nonlocality
- Distributed Entanglement
- Efficient classical simulation of slightly entangled quantum computations
- Device-independent security of quantum cryptography against collective attacks
- Steering, Entanglement, Nonlocality, and the EPR Paradox
- Information Causality as a Physical Principle
- On the role of entanglement in quantum computational speed-up
- Non-local correlations as an information theoretic resource
- Quantum Steering
- Fully device independent quantum key distribution
- A limit on nonlocality in any world in which communication complexity is not trivial
- General properties of Nonsignaling Theories
- A Relevant Two Qubit Bell Inequality Inequivalent to the CHSH Inequality
- Quantum Communication between N partners and Bell's inequalities
- Optimal spin squeezing inequalities detect bound entanglement in spin models
- Monogamy of nonlocal quantum correlations
- The completeness of quantum theory for predicting measurement outcomes
- Introduction to the book "Quantum Theory: Informational Foundations and Foils"
- Quantum from principles
- Quasi-quantization: classical statistical theories with an epistemic restriction
- Quantum nonlocality based on finite-speed causal influences leads to superluminal signaling
- Super-activation of quantum non-locality
- Local Hidden Variable Theories for Quantum States
- All quantum states useful for teleportation are nonlocal resources
- General method for constructing local-hidden-variable models for entangled quantum states
- Monogamy of Bell's inequality violations in non-signaling theories
- Algorithmic construction of local hidden variable models for entangled quantum states
- Correlation complementarity yields Bell monogamy relations
- Uniqueness of Quantum States Compatible with Given Measurement Results
- Bounds on Quantum Correlations in Bell Inequality Experiments
- Tripartite quantum state violating the hidden influence constraints
- Superluminal influences, hidden variables, and signaling
- Bell nonlocality is not sufficient for the security of standard device-independent quantum key distribution protocols
- Quantum steerability: characterization, quantification, superactivation and unbounded amplification
- Nonlocality is transitive
- N-Qubit W States are Determined by their Bipartite Marginals
- Useful multipartite correlations from useless reduced states
- Persistency of entanglement and nonlocality in multipartite quantum systems
- Almost quantum correlations violate the no-restriction hypothesis
- Anonymous Quantum Nonlocality
- Strong monogamies of no-signaling violations for bipartite correlation Bell inequalities
- Upper bounds on device-independent quantum key distribution
- Unmasking the Polygamous Nature of Quantum Nonlocality
- Verification of Bell Nonlocality by Violating Quantum Monogamy Relations
- Monogamy of Nonlocal Games
- Large Parts are Generically Entangled Across All Cuts
- The additivity of states uniquely determined by marginals