A complementary relation between classical bits and randomness in local part in simulating singlet state

TL;DR

This paper explores the relationship between classical bits and randomness in simulating singlet state statistics, proposing a new correlation resource that unifies existing models and explains their limitations.

Contribution

It introduces a novel signaling correlation resource that demonstrates a complementary relation between classical communication and randomness in local outputs for singlet simulation.

Findings

Classical communication of 1 cbit can simulate singlet statistics without nonlocal correlation.

Using a non-local box allows simulation with no classical cost but fully random outputs.

The proposed model unifies existing simulation approaches as extreme cases.

Abstract

Recently Leggett's proposal of non-local model generates new interest in simulating the statistics of singlet state. Singlet state statistics can be simulated by 1 bit of classical communication without using any further nonlocal correlation. But, interestingly, singlet state statistics can also be simulated with no classical cost if a non-local box is used. In the first case, the output is completely unbiased whereas in second case outputs are completely random. We suggest a new (possibly) signaling correlation resource which successfully simulates singlet statistics and this result suggests a new complementary relation between required classical bits and randomness in local output when the classical communication is limited by 1 cbit. This result reproduces the above two models of simulation as extreme cases. This also explains why Leggett's non-local model and the model presented by Branciard et.al. should fail to reproduce the statistics of a singlet.