Nonlocal prediction of quantum measurement outcomes

TL;DR

This paper introduces the concept of nonlocal predictability in quantum mechanics, showing how entanglement influences the ability to predict measurement outcomes without communication, and revealing counterintuitive effects of dephasing.

Contribution

It defines nonlocal predictability, establishes bounds for product and entangled states, and explores how dephasing can enhance predictability in certain quantum states.

Findings

Product states meet the local bound.

Pure entangled states can exceed the bound.

Dephasing can enhance predictability in some states.

Abstract

We define nonlocal predictability as how well one observer can predict another's measurement outcomes without classical communication, given full knowledge of the shared quantum state and measurement settings. The local bound on nonlocal predictability is defined as the maximum probability with which one observer can correctly predict the other's measurement outcome prior to measurement. We show that product states always meet this bound, while all pure entangled states and some classically correlated states can exceed it. This demonstrates a nonlocal phenomenon since the predictability of measurement outcomes increases after the measurement. Perfect nonlocal predictability for arbitrary projective measurements occurs only for maximally entangled states among all pure states, underscoring their special role. Comparing pure entangled states with their dephased versions, we find that dephasing on one subsystem can enhance nonlocal predictability for a broad class of states and measurements - a counterintuitive, noise-induced advantage that vanishes for maximally entangled states under any projective measurement.