Acquisition of delocalized information via classical and quantum carriers

TL;DR

This paper explores how spatial superposition and quantum interference can enhance information acquisition across distant sites, comparing classical and quantum strategies and analyzing their limitations and potential in information processing.

Contribution

It introduces a systematic comparison of classical and quantum strategies for information retrieval using spatial superposition, including bounds, symmetry analysis, and violation of inequalities.

Findings

Quantum particles in superposition can violate fingerprinting inequalities more than classical particles.

The violation of the inequality depends on the internal dimension d, with d=2 outperforming d=1.

The maximum violation cannot be increased for dimensions greater than 2.

Abstract

We investigate the information-theoretic power of spatial superposition by analyzing tasks in which infor- mation is locally encoded at multiple distant sites and must be acquired by a single information carrier, such as a particle. Within an operational framework, we systematically compare the statistical correlations that can be generated in such tasks using classical particles, quantum particles in spatial superposition, and more general "second-order interference" resources. We bound classical strategies via convex polytopes and present a study of their symmetry, demonstrating that the vertices are inherently connected to K-juntas as defined in the classical theory of Boolean functions, while their facet inequalities are in one-to-one correspondence with oracle games. We then analyze the violation of the "fingerprinting inequality" achievable by the use of one quantum particle, and we study the dependence of this violation on the dimension d of the particle's internal degree of freedom. In particular, we show that the case of d = 2 can achieve a higher violation of the inequality than the previously investigated case of d = 1. We also provide analytic and numerical evidence that this violation cannot be further increased for larger d > 2. Finally, we find that both quantum and any other (generalized) second-order interference models exhibit the same asymptotic scaling in violating the fingerprinting inequality. Our results thereby further articulate quantum interference and spatial superposition as a resource for information processing.