Simulating indefinite causal order with Rindler observers

TL;DR

This paper proposes a method to simulate indefinite causal order using Rindler observers in superposition of accelerations, with potential experimental realization via optomechanical resonators, advancing quantum causality research.

Contribution

It introduces a novel simulation approach for indefinite causal order using superposed Rindler observers, linking black hole physics to quantum information processing.

Findings

Rindler observers in superposition can simulate ICO space-time.

Entangled accelerations of Rindler observers mimic entangled ICO observers.

Potential experimental implementation with optomechanical resonators.

Abstract

Realization of indefinite causal order (ICO), a theoretical possibility that even causal relations between physical events can be subjected to quantum superposition, apart from its general significance for the fundamental physics research, would also enable quantum information processing that outperforms protocols in which the underlying causal structure is definite. In this paper, we start with a proposition that an observer in a state of quantum superposition of being at two different relative distances from the event horizon of a black hole, effectively resides in ICO space-time generated by the black hole. By invoking the fact that the near-horizon geometry of a Schwarzschild black hole is that of a Rindler space-time, we propose a way to simulate an observer in ICO space-time by a Rindler observer in a state of superposition of having two different proper accelerations. By extension, a pair of Rindler observers with entangled proper accelerations simulates a pair of entangled ICO observers. Moreover, these Rindler-systems might have a plausible experimental realization by means of optomechanical resonators.