The Decision Problem for Entanglement

Paul M. Näger

Shion Maeda, Nicolas Chauvet, Hayato Saigo +4 more

Collective decision making is important for maximizing total benefits while preserving equality among individuals in the competitive multi-armed bandit (CMAB) problem, wherein multiple players try to gain higher rewards from multiple slot machines. The CMAB problem represents an essential aspect of applications such as resource management in social infrastructure. In a previous study, we theoretically and experimentally demonstrated that entangled photons can physically resolve the difficulty of the CMAB problem. This decision-making strategy completely avoids decision conflicts while ensuring equality. However, decision conflicts can sometimes be beneficial if they yield greater rewards than non-conflicting decisions, indicating that greedy actions may provide positive effects depending on the given environment. In this study, we demonstrate a mixed strategy of entangled- and correlated-photon-based decision-making so that total rewards can be enhanced when compared to the entangled-photon-only decision strategy. We show that an optimal mixture of entangled- and correlated-photon-based strategies exists depending on the dynamics of the reward environment as well as the difficulty of the given problem. This study paves the way for utilizing both quantum and classical aspects of photons in a mixed manner for decision making and provides yet another example of the supremacy of mixed strategies known in game theory, especially in evolutionary game theory.

Vijayaraj, Sujan, Nandakumar, S.

Binary decisions are the simplest form of decisions that are made in our daily lives. Examples include choosing a two-way path in a maze, accepting or declining an offer, etc. These decisions are also made by computers, machines and various electronic components. But decisions made on these devices can be partial and deterministic, and hence compromised. In this paper, a simple framework to implement binary decisions using one or many qubits is presented. Such systems are based on a separate hardware infrastructure rather than computer codes. This helps enable true randomness and impartial decision making. The multi-armed bandit problem is used to highlight the decision making ability of qubits by predictive modelling based on quantum Bayesianism. Bipartite and multipartite entangled states are also used to solve specific cases of the problem.

Bob Coecke

Michele Viscardi, Jessica Illiano, Angela Sara Cacciapuoti +1 more

The entanglement distribution process is widely en-visioned as one of the key functionalities of the Quantum Internet. Its engineering is, thus, foundational to effectively implement communication protocols in quantum networks. In this paper, we exploit the Markov Decision Process formalism to model the entanglement distribution as an optimal decision problem. Furthermore, we analyze the impact of reward functions on two key performance metrics, namely: the average distribution time and the average distributed cluster size. From this analysis, we gain some insights for choosing a reward function that meets suitable figures of merit for an overlaying communication protocol.