Quantum strategies in moving frames

Salman Khan, Majid Khan

We study the influence of the Unruh effect on quantum non-zero sum games. In particular, we investigate the quantum Prisoners’ Dilemma both for entangled and unentangled initial states and show that the acceleration of the noninertial frames disturbs the symmetry of the game. It is shown that for the maximally entangled initial state, the classical strategy (cooperation) becomes the dominant strategy. Our investigation shows that any quantum strategy does no better for any player against the classical strategies. The miracle move of Eisert et al (1999 Phys. Rev. Lett. 83 3077) is no more a superior move. We show that the dilemma-like situation is resolved in favor of one player or the other.

Pierre Clairambault, Marc de Visme, Glynn Winskel

Salman Khan, Majid Khan

The influence of noise and of Unruh effect on quantum Prisoners’ dilemma is investigated both for entangled and unentangled initial states. The noise is incorporated through amplitude damping channel. For unentangled initial state, the decoherence compensates for the adverse effect of acceleration of the frame and the effect of acceleration becomes irrelevant provided the game is fully decohered. It is shown that the inertial player always out scores the noninertial player by choosing defection. For maximally entangled initially state, we show that for fully decohered case every strategy profile results in either of the two possible equilibrium outcomes. Two of the four possible strategy profiles become Pareto optimal and Nash equilibrium and no dilemma is leftover. It is shown that other equilibrium points emerge for different region of values of decoherence parameter that are either Pareto optimal or Pareto inefficient in the quantum strategic spaces. It is shown that the Eisert et al. (Phys Rev Lett 83:3077, 1999) miracle move is a special move that leads always to distinguishable results compare to other moves. We show that the dilemma like situation is resolved in favor of one player or the other.

Chuan‐Feng Li, Yong-Sheng Zhang, Yun‐Feng Huang +1 more

Josef Janyška, Marco Modugno

Simone Zuccher, Marco Caliari A

Abstract We compute simultaneously the translational speed, the magnitude and the phase of a quantum vortex ring for a wide range of radii, within the Gross–Pitaevskii model, by imposing its self preservation in a co-moving reference frame. By providing such a solution as the initial condition for the time-dependent Gross–Pitaevskii equation, we verify a posteriori that the ring’s radius and speed are well maintained in the reference frame moving at the computed speed. Convergence to the numerical solution is fast for large values of the radius, as the wavefunction tends to that of a straight vortex, whereas a continuation technique and interpolation of rough solutions are needed to reach convergence as the ring tends to a disk. Comparison with other strategies for generating a quantum ring reveals that all of them seem to capture quite well the translational speed, whereas none of them seems to preserve the radius with the accuracy reached in the present work.