Towards Grothendieck Constants and LHV Models in Quantum Mechanics

Abstract

We adopt a continuous model to estimate the Grothendieck constants. An analytical formula to compute the lower bounds of Grothendieck constants has been explicitly derived for arbitrary orders, which improves previous bounds. Moreover, our lower bound of the Grothendieck constant of order three gives a refined bound of the threshold value for the nonlocality of the two-qubit Werner states.

arXiv comment5 pages

References in corpus (3)

• Nonsequential positive-operator-valued measurements on entangled mixed states do not always violate a Bell inequality
• Grothendieck's constant and local models for noisy entangled quantum states
• More efficient Bell inequalities for Werner states

Cited by in corpus (13)

• Better local hidden variable models for two-qubit Werner states and an upper bound on the Grothendieck constant $K_G(3)$
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• Trade-off Relations of Bell Violations among Pairwise Qubit Systems
• Improved local models and new Bell inequalities via Frank-Wolfe algorithms
• Exact Steering Bound for Two-Qubit Werner States
• EPR Steering inequalities with Communication Assistance
• Certification of qubits in the prepare-and-measure scenario with large input alphabet and connections with the Grothendieck constant
• Discovering Local Hidden-Variable Models for Arbitrary Multipartite Entangled States and Arbitrary Measurements
• Revealing the Boundary between Quantum Mechanics and Classical Model by EPR-Steering Inequality
• Better bounds on finite-order Grothendieck constants
• Platonic Bell inequalities for all dimensions
• On an optimal problem of bilinear forms