arXiv subjects

Shoto Aoki

Publications and source records attributed to Shoto Aoki.

22 records · Page 2Linked to original sources

arXiv2021

Infinitely Repeated Quantum Games and Strategic Efficiency

Repeated quantum game theory addresses long term relations among players who choose quantum strategies. In the conventional quantum game theory, single round quantum games or at most finitely repeated games have been widely studied, however less is known for infinitely repeated quantum games. Investigating infinitely repeated games is crucial since finitely repeated games do not much differ from single round games. In this work we establish the concept of general repeated quantum games and show the Quantum Folk Theorem, which claims that by iterating a game one can find an equilibrium strategy of the game and receive reward that is not obtained by a Nash equilibrium of the corresponding single round quantum game. A significant difference between repeated quantum prisoner's dilemma and repeated classical prisoner's dilemma is that the classical Pareto optimal solution is not always an equilibrium of the repeated quantum game when entanglement is sufficiently strong. When entanglement is sufficiently strong and reward is small, mutual cooperation cannot be an equilibrium of the repeated quantum game. In addition we present several concrete equilibrium strategies of the repeated quantum prisoner's dilemma.

quant-ph↗

arXiv2021

Theory of Quantum Games and Quantum Economic Behavior

The quest of this work is to present discussions of some fundamental questions of economics in the era of quantum technology, which require a treatment different from economics studied thus far in the literature. A study of quantum economic behavior will become the center of attention of economists in the coming decades. We analyze a quantum economy in which players produce and consume quantum goods. They meet randomly and barter with neighbors bilaterally for quantum goods they produced. We clarify the conditions where certain quantum goods emerge endogenously as media of exchange, called quantum commodity money. As quantum strategies are entangled, we find distinctive aspects of quantum games that cannot be explained by conventional classical games. In some situations a quantum player can acquire a quantum good from people regardless of their strategies, while on the other hand people can find quantum strategies that improve their welfare based on an agreement. Those novel properties imply that quantum games also shed new light on theories of mechanism design, auction and contract in the quantum era.

quant-ph↗

arXiv2021

Chiral fermion on curved domain-wall

We consider a massive fermion system having a curved domain-wall embedded in a square lattice. In a similar way to the conventional flat domain-wall fermion, chiral massless modes appear at the domain-wall but these modes feel "gravity" through the induced spin connections. In this work, we embed $S^1$ and $S^2$ domain-walls into a Euclidean space and show how the gravity is detected from the spectrum of the Dirac operator.

hep-lat↗

arXiv2021

Hyperbolic Band Theory under Magnetic Field and Dirac Cones on a Higher Genus Surface

We explore the hyperbolic band theory under a magnetic field for the first time. Our theory is a general extension of the conventional band theory defined on a Euclidean lattice into the band theory on a general hyperbolic lattice/Riemann surface. Our methods and results can be confirmed experimentally by circuit quantum electrodynamics (cQED), which enables us to create novel materials in a hyperbolic space. To investigate the band structures, we construct directly the hyperbolic magnetic Bloch states and find that they form Dirac cones on a coordinate neighborhood, by which they can be regarded as a global quantum gravity solution detectable in a laboratory. Besides this is the first explicit example of a massless Dirac state on a higher genus surface. Moreover we show that the energy spectrum exhibits an unusual fractal structure refracting the negative curvature, when plotted as a function of a magnetic flux.

cond-mat.mes-hall↗