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.
Cite
@article{arxiv.1106.2169,
title = {New Quantum Bounds for Inequalities involving Marginal Expectations},
author = {Elie Wolfe and S. F. Yelin},
journal= {arXiv preprint arXiv:1106.2169},
year = {2013}
}
Comments
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