New Quantum Bounds for Inequalities involving Marginal Expectations

Abstract

We review, correct, and develop an algorithm which determines arbitrary Quantum Bounds, based on the seminal work of Tsirelson [Lett. Math. Phys. 4, 93 (1980)]. The potential of this algorithm is demonstrated by deriving both new number-valued Quantum Bounds, as well as identifying a new class of function-valued Quantum Bounds. Those results facilitate an 8-dimensional Volume Analysis of Quantum Mechanics which extends the work of Cabello [PRA 72 (2005)]. We contrast the Quantum Volume defined be these new bounds to that of Macroscopic Locality, defined by the inequalities corresponding to the first level of the hierarchy of Navascues et al [NJP 10 (2008)], proving our function-valued Quantum Bounds to be more complete.

6 pages. Now includes appendices containing a pseudo-code formulation of the algorithm as well as a discussion of general physical symmetries. A new lower bound to the quantum volume has been derived, and an error in the mapping of physical observables to variational parameters has been corrected

References in corpus (11)

• Information Causality as a Physical Principle
• A convergent hierarchy of semidefinite programs characterizing the set of quantum correlations
• Bounding the set of quantum correlations
• A glance beyond the quantum model
• Connes' embedding problem and Tsirelson's problem
• Recovering part of the quantum boundary from information causality
• Partial list of bipartite Bell inequalities with four binary settings
• Emergence of Quantum Correlations from Non-Locality Swapping
• Pentagrams and paradoxes
• Proposal of a two-qutrit contextuality test free of the finite precision and compatibility loopholes
• Bound on Hardy's non-locality from the principle of Information Causality

Cited by in corpus (14)

• Geometry of the set of quantum correlations
• Quantifying Bell: the Resource Theory of Nonclassicality of Common-Cause Boxes
• Identifying Nonconvexity in the Sets of Limited-Dimension Quantum Correlations
• Concentration phenomena in the geometry of Bell correlations
• Geometry of the quantum set on no-signaling faces
• Experimental Demonstration that No Tripartite-Nonlocal Causal Theory Explains Nature's Correlations
• Necessary and sufficient criterion for extremal quantum correlations in the simplest Bell scenario
• Naturally restricted subsets of nonsignaling correlations: typicality and convergence
• A Survey of Physical Principles Attempting to Define Quantum Mechanics
• Geometrical self-testing of partially entangled two-qubit states
• Tsirelson Polytopes and Randomness Generation
• Multipartite Composition of Contextuality Scenarios
• Certifying nonlocal properties of noisy quantum operations
• NPA Hierarchy and Extremal Criterion in the Simplest Bell Scenario