Spin-bounded correlations: rotation boxes within and beyond quantum theory
arXiv:2312.09278 · doi:10.1007/s00220-024-05123-2
Abstract
How can detector click probabilities respond to spatial rotations around a fixed axis, in any possible physical theory? Here, we give a thorough mathematical analysis of this question in terms of "rotation boxes", which are analogous to the well-known notion of non-local boxes. We prove that quantum theory admits the most general rotational correlations for spins 0, 1/2, and 1, but we describe a metrological game where beyond-quantum resources of spin 3/2 outperform all quantum resources of the same spin. We prove a multitude of fundamental results about these correlations, including an exact convex characterization of the spin-1 correlations, a Tsirelson-type inequality for spins 3/2 and higher, and a proof that the general spin-J correlations provide an efficient outer SDP approximation to the quantum set. Furthermore, we review and consolidate earlier results that hint at a wealth of applications of this formalism: a theory-agnostic semi-device-independent randomness generator, an exact characterization of the quantum (2,2,2)-Bell correlations in terms of local symmetries, and the derivation of multipartite Bell witnesses. Our results illuminate the foundational question of how space constrains the structure of quantum theory, they build a bridge between semi-device-independent quantum information and spacetime physics, and they demonstrate interesting relations to topics such as entanglement witnesses, spectrahedra, and orbitopes.
29+21 pages, 9 figures. V2: Minor corrections, close to published version
References in corpus (32)
- Advances in Quantum Metrology
- Bell nonlocality
- Device-independent security of quantum cryptography against collective attacks
- No Signalling and Quantum Key Distribution
- Quantum metrology from a quantum information science perspective
- One-sided Device-Independent Quantum Key Distribution: Security, feasibility, and the connection with steering
- A convergent hierarchy of semidefinite programs characterizing the set of quantum correlations
- Contextuality for preparations, transformations, and unsharp measurements
- From Classical to Quantum Shannon Theory
- Quantum steering: a review with focus on semidefinite programming
- Self-testing of quantum systems: a review
- Device-independent tests of classical and quantum dimensions
- Semi-device-independent security of one-way quantum key distribution
- Quantum speed limits, coherence and asymmetry
- Bell Correlations in a Bose-Einstein Condensate
- Almost quantum correlations
- Memory Attacks on Device-Independent Quantum Cryptography
- Maximal violation of the I3322 inequality using infinite dimensional quantum systems
- Local Quantum Measurement and No-Signaling Imply Quantum Correlations
- Semi-device-independent framework based on natural physical assumptions
- General probabilistic theories: An introduction
- The structure of reversible computation determines the self-duality of quantum theory
- Semi-device-independent bounds on entanglement
- Unified Framework for Correlations in Terms of Local Quantum Observables
- Orbitopes
- The Characterization of Noncontextuality in the Framework of Generalized Probabilistic Theories
- Semidefinite Programming in Quantum Information Science
- Semidefinite programming relaxations for quantum correlations
- Extensions of the Mandelstam-Tamm quantum speed limit to systems in mixed states
- Rotational invariance as an additional constraint on local realism
- Typical local measurements in generalised probabilistic theories: emergence of quantum bipartite correlations
- How dynamics constrains probabilities in general probabilistic theories