Harnessing Causal Indefiniteness for Accessing Locally Inaccessible Data

TL;DR

This paper explores how indefinite causal structures can enhance classical data retrieval tasks, demonstrating quantum advantages, super-activation phenomena, and the superiority of classical causally inseparable processes over quantum ones.

Contribution

It introduces a novel application of causal indefiniteness in classical data retrieval, establishing criteria for quantum process usefulness and revealing new phenomena like super-activation.

Findings

Quantum indefinite causal structures outperform definite ones in data retrieval.

Super-activation allows two ineffective processes to become useful together.

Classical causally inseparable processes can surpass quantum bi-causal processes.

Abstract

Recent studies suggest that physical theories can exhibit indefinite causal structures, where the causal order of events is fundamentally undefined yet logically consistent. Beyond its foundational appeal, causal indefiniteness has also emerged as a novel information-theoretic resource, offering advantages in various information processing tasks. Here, we investigate its utility in the classical Data Retrieval (DR) task. In its simplest version, a referee encodes classical messages into bipartite quantum states and distributes the local parts to two distant parties, ensuring that neither can independently extract any information about the encoded message. To retrieve their assigned data, parties must collaborate, and we show that those embedded in an indefinite causal structure generally outperform those operating within a definite causal framework. For the bipartite case, we establish a duality between the DR task and the well known Guess Your Neighbour's Input game and derive a criterion analogous to the Peres-Horodecki separability test to identify quantum processes that yield nontrivial success in the DR task. We also report an intriguing super-activation phenomenon, where two quantum processes, each individually inefficient for the DR task, become useful when combined. Extending the analysis to tripartite case, we show that classical causally inseparable processes can outperform quantum bi-causal processes in the DR task. Our study, thus, reveals several unexplored aspects of causal indefiniteness, inviting deeper investigation.