Quantum Advantage in Information Retrieval

TL;DR

This paper introduces the Torpedo Game, demonstrating a quantum advantage surpassing traditional random access codes, and links this advantage to sequential contextuality in quantum systems, with practical implications demonstrated through a quantum Battleship variant.

Contribution

It presents a new information retrieval task, the Torpedo Game, showing quantum advantage via prepare-and-measure protocols and linking advantage to sequential contextuality.

Findings

Quantum advantage exceeds that of random access codes.

Sequential contextuality is necessary and sufficient for quantum advantage.

Perfect qutrit strategies reveal logical paradoxes with non-contextual hidden variables.

Abstract

Random access codes have provided many examples of quantum advantage in communication, but concern only one kind of information retrieval task. We introduce a related task - the Torpedo Game - and show that it admits greater quantum advantage than the comparable random access code. Perfect quantum strategies involving prepare-and-measure protocols with experimentally accessible three-level systems emerge via analysis in terms of the discrete Wigner function. The example is leveraged to an operational advantage in a pacifist version of the strategy game Battleship. We pinpoint a characteristic of quantum systems that enables quantum advantage in any bounded-memory information retrieval task. While preparation contextuality has previously been linked to advantages in random access coding we focus here on a different characteristic called sequential contextuality. It is shown not only to be necessary and sufficient for quantum advantage, but also to quantify the degree of advantage. Our perfect qutrit strategy for the Torpedo Game entails the strongest type of inconsistency with non-contextual hidden variables, revealing logical paradoxes with respect to those assumptions.