Quantum advantage in decentralized control of POMDPs: A control-theoretic view of the Mermin-Peres square

TL;DR

This paper demonstrates that entangled quantum states can provide a performance advantage in decentralized POMDPs, revealing a novel quantum advantage in dynamic control scenarios through a control-theoretic interpretation of the Mermin-Peres square.

Contribution

It introduces a new perspective linking quantum entanglement with decentralized control, showing quantum advantage in dynamic POMDPs where prior results focused on static cases.

Findings

Quantum entanglement improves decentralized control performance.

Quantum advantage can vanish in static but not in dynamic scenarios.

The work connects quantum information theory with control theory via the Mermin-Peres square.

Abstract

Consider a decentralized partially-observed Markov decision problem (POMDP) with multiple cooperative agents aiming to maximize a long-term-average reward criterion. We observe that the availability, at a fixed rate, of entangled states of a product quantum system between the agents, where each agent has access to one of the component systems, can result in strictly improved performance even compared to the scenario where common randomness is provided to the agents, i.e. there is a quantum advantage in decentralized control. This observation comes from a simple reinterpretation of the conclusions of the well-known Mermin-Peres square, which underpins the Mermin-Peres game. While quantum advantage has been demonstrated earlier in one-shot team problems of this kind, it is notable that there are examples where there is a quantum advantage for the one-shot criterion but it disappears in the dynamical scenario. The presence of a quantum advantage in dynamical scenarios is thus seen to be a novel finding relative to the current state of knowledge about the achievable performance in decentralized control problems. This paper is dedicated to the memory of Pravin P. Varaiya.