# Two-qubit pure entanglement as optimal social welfare resource in Bayesian game

## Article Type

Research Article

## Publication Title

Quantum

## Abstract

Entanglement is of paramount importance in quantum information theory. Its supremacy over classical correlations has been demonstrated in a numerous information theoretic protocols. Here we study possible adequacy of quantum entanglement in Bayesian game theory, particularly in social welfare solution (SWS), a strategy which the players follow to maximize sum of their payoffs. Given a multi-partite quantum state as an advice, players can come up with several correlated strategies by performing local measurements on their parts of the quantum state. A quantum strategy is called quantum-SWS if it is advantageous over a classical equilibrium (CE) strategy in the sense that none of the players has to sacrifice their CE-payoff rather some have incentive and at the same time it maximizes sum of all players' payoffs over all possible quantum advantageous strategies. Quantum state yielding such a quantum-SWS is called a quantum social welfare advice (SWA). We show that any two-qubit pure entangled state, even if it is arbitrarily close to a product state, can serve as quantum-SWA in some Bayesian game. Our result, thus, gives cognizance to the fact that every two-qubit pure entanglement is the best resource for some operational task.

## DOI

10.22331/q-2019-09-09-185

## Publication Date

1-1-2019

## Recommended Citation

Banik, Manik; Bhattacharya, Some Sankar; Ganguly, Nirman; Guha, Tamal; Mukherjee, Amit; Rai, Ashutosh; and Roy, Arup, "Two-qubit pure entanglement as optimal social welfare resource in Bayesian game" (2019). *Journal Articles*. 986.

https://digitalcommons.isical.ac.in/journal-articles/986

## Comments

Open Access, Gold, Green