Quantum Probability assignment limited by relativistic causality

TL;DR

This paper introduces a new causality condition based on the independence of space-like events, deriving the Born rule and explaining the limits of quantum nonlocality through relativistic causality constraints.

Contribution

It proposes a causality condition stronger than no-signaling and derives the Born rule from relativistic causality, clarifying quantum nonlocality limits.

Findings

New causality condition is stronger than no-signaling.

Born rule derived from relativistic causality constraints.

Quantum nonlocality is limited by causality principles.

Abstract

The quantum nonlocality is limited by relativistic causality, however, the reason is not fully understood yet. The relativistic causality condition on nonlocal correlations has been usually accepted as a prohibition of faster-than-light signaling, called no-signaling condition. We propose another causality condition from the observation that space-like separate events should have no causal relationship. It is proved that the new condition is stronger than no-signaling condition for a pair of binary devices. We derive the standard probability assignment rule, so-called Born rule, on quantum measurement, which determines the degree of quantum nonlocality, by using relativistic causality constraint. This shows how the causality limits the upper bound of quantum nonlocality through quantum probability assignment.