Local Quantum Measurement and No-Signaling Imply Quantum Correlations

2009/10/31 by Howard Barnum, H. Barnum, S. Beigi +7 · 4 citations
Computer Science · Mathematics · Physics and Astronomy · #Advanced Thermodynamics and Statistical Mechanics #Classical mechanics #Hilbert space #Mathematical formulation of quantum mechanics #Mathematics #Open quantum system #POVM #Physics #Pure mathematics #Quantum #Quantum Information and Cryptography #Quantum Mechanics and Applications #Quantum discord #Quantum dynamics #Quantum mechanics #Quantum operation #Quantum process #Quantum state #Quantum statistical mechanics #SIC-POVM #Tensor product #quant-ph

paper · pdf · doi:10.1103/physrevlett.104.140401

published as Phys. Rev. Lett. 104, 140401 (2010) · Published version. 5 pages, 1 figures

openalex publication_date 2010/04/06 · arxiv created 2010/04/26 · arxiv updated 2010/04/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

Abstract

We show that, assuming that quantum mechanics holds locally, the finite speed of information is the principle that limits all possible correlations between distant parties to be quantum mechanical as well. Local quantum mechanics means that a Hilbert space is assigned to each party, and then all local positive-operator-valued measurements are (in principle) available; however, the joint system is not necessarily described by a Hilbert space. In particular, we do not assume the tensor product formalism between the joint systems. Our result shows that if any experiment would give nonlocal correlations beyond quantum mechanics, quantum theory would be invalidated even locally.

Citations

• Tsirelson bounds for generalized Clauser-Horne-Shimony-Holt inequalities
• Experimental violation of a Bell's inequality with efficient detection
• Quantum states and generalized observables: a simple proof of Gleason's theorem
• Violation of Bell's inequality under strict Einstein locality conditions
• Quantum nonlocality as an axiom
• Discussion of Probability Relations between Separated Systems
• Limit on Nonlocality in Any World in Which Communication Complexity Is Not Trivial
• Long-distance quantum communication with atomic ensembles and linear optics
• Scalable multi-particle entanglement of trapped ions
• On the Einstein Podolsky Rosen paradox

Cited by

• Quantum correlations with no causal order
• Dimension of physical systems, information processing, and thermodynamics
• QBism and the Ithaca Desiderata
• Perfect discrimination of non-orthogonal separable pure states on bipartite system in general probabilistic theory

Related

• Local Broadcasting of Quantum Correlations
• No-local-broadcasting theorem for quantum correlations
• Quantum correlations and causal structures
• No-signaling versus quantum constraints for spatio-temporal correlations caused by weak measurement
• No Disturbance Without Uncertainty as a Physical Principle