Consequences and Limits of Nonlocal Strategies
CCC '04 Proceedings of the 19th IEEE Annual Conference on Computational Complexity
Strict Hierarchy of Bell Theorems
ICQNM '08 Proceedings of the Second International Conference on Quantum, Nano and Micro Technologies (ICQNM 2008)
Minimum entangled state dimension required for pseudo-telepathy
Quantum Information & Computation
Quantum Information & Computation
| Hi-index | 5.23 |
As demonstrated by John Bell, quantum mechanics exhibits correlations in spacelike separated bipartite systems that are impossible to reproduce by classical means. There are three levels of ''Bell Theorems'', depending on which aspects of the quantum correlations can or cannot be reproduced classically. The original ''Bell Inequalities'' (BI) require a perfect classical simulation of all quantum probabilities. With ''Bell Theorems Without Inequalities'' (BTWI), we ask the classical simulation to be able to produce precisely the outcomes that could occur according to quantum mechanics, but we do not worry about their exact probabilities. With ''Pseudotelepathy'' (PT), we are satisfied if the classical simulation produces only outcomes allowed by quantum mechanics, but not necessarily all of them. Bell's original proof of BI involved a maximally entangled 2x2 bipartite state such as the singlet state. Hardy proved that BTWI are possible in dimension 2x2, but his construction used a non-maximally entangled state. Here, we prove that no 2x2 maximally entangled state can serve to produce BTWI. Combining this with our earlier result that 2x2 entangled states cannot be used at all for the purpose of PT, it follows a strict hierarchy on the quantum resources that are required to exhibit the various levels of Bell Theorems.