Quantum Locality in Game Strategy

Abstract

Game theory is a well established branch of mathematics whose formalism has a vast range of applications from the social sciences, biology, to economics. Motivated by quantum information science, there has been a leap in the formulation of novel game strategies that lead to new (quantum Nash) equilibrium points whereby players in some classical games are always outperformed if sharing and processing joint information ruled by the laws of quantum physics is allowed. We show that, for a bipartite non zero-sum game, input local quantum correlations, and separable states in particular, suffice to achieve an advantage over any strategy that uses classical resources, thus dispensing with quantum nonlocality, entanglement, or even discord between the players’ input states. This highlights the remarkable key role played by pure quantum coherence at powering some protocols. Finally, we propose an experiment that uses separable states and basic photon interferometry to demonstrate the locally-correlated quantum advantage.

Experimental realisation of tunable ferroelectric/superconductor $$({\text {B}} {\text {T}} {\text {O}}/{\text {Y}} {\text {B}}{\text {C}} {\text {O}})_{{\text {N}}}/{\text {S}}{\text {T}}{\text {O}}$$ 1D photonic crystals in the whole visible spectrum

“…As it is well known, superconductors are materials characterised for low losses and better operating characteristics than normal metals. Nowadays, they are regarded as promising quantum materials, widely used in quantum computing networks 20 – 23 , quantum simulators 24 , 25 , loss-less microwave resonators 26 , and AC Josephson junction lasers 27 . Superconductors used as building blocks for PCs fabrication have mainly two advantages over traditional materials.…”

Pareto-optimal solution for the quantum battle of the sexes

“…In that sense, the Penny PQ flip over [4], gambling [5] and prisoner's dilemma [6] were the first games analyzed in the quantum regime. From those cited, the most versatile problem corresponds to the prisoner's dilemma, a symmetrical game successfully studied by the protocol proposed by Eisert-Wilkens-Lewenstein [6], which had its discussion extended to multiple players [7,8], concepts of non-locality [9,10,11], entanglement [12], concepts of symmetric and asymmetric games [13], or in the context of Bayesian games [14] and was verified experimentally by NMR techniques using a cytosine sample [15] and by optical quantum circuits on two and four-qubit systems [11,16,17] and using ion-trap setup on five-qubit system [18].…”

“…Specifically, we draw attention to the last two-qubit gate of the Eisert-Wilkens-Lewenstein protocol, the disentanglement operator J † , because it highlights the distinction between the Marinatto-Weber and the Eisert-Wilkens-Lewenstein protocols. This argument is underlined by Benjamin [20] who points out that the second inverse gate J † ensures that the classical game remains embedded within the quantum game [8], while Melo-Luna claims that it belongs to the measurement procedure [11].…”

Experimental realisation of tunable ferroelectric/superconductor (BTO/YBCO)N/STO 1D photonic crystals in the whole visible spectrum

“…As it is well known, superconductors are materials characterised for low losses and better operating characteristics than normal metals. Nowadays, they are considered as promising quantum materials, widely used in quantum computing networks [22][23][24][25] , quantum simulators 26,27 , loss-less microwave resonators 28 , and AC Josephson junction lasers 29 . Superconductors used as building blocks for PCs fabrication have mainly two advantages over traditional ones.…”