Spooky action at a distance in general probabilistic theories

TL;DR

This paper explores the nature of complete probabilistic theories, revealing that such theories are inherently spooky if they admit pure steering states, and discusses paradoxes akin to Schrödinger's cat.

Contribution

It establishes a precise link between completeness, spookiness, and the existence of pure steering states in probabilistic theories.

Findings

Complete theories are spooky if they admit pure steering states.

Steering of complementary states can lead to Schrödinger's cat-like paradox.

The paper characterizes when a probabilistic theory exhibits nonlocal hidden-variable features.

Abstract

We call a probabilistic theory "complete" if it cannot be further refined by no-signaling hidden-variable models, and name a theory "spooky" if every equivalent hidden-variable model violates Shimony's Outcome Independence. We prove that a complete theory is spooky if and only if it admits a pure steering state in the sense of Schr\"odinger. Finally we show that steering of complementary states leads to a Schr\"odinger's cat-like paradox.