Born’s rule in multiqubit Bohmian systems

Abstract

We study the Bohmian trajectories of a 4-qubit system made of coherent states of the quantum harmonic oscillator. We find, as in the 2-qubit and 3-qubit cases, that all the chaotic Bohmian trajectories are also ergodic. However, the chaotic trajectories are effectively ordered for longer times than in the 2 and 3-qubit cases. Then we study the long time dynamical establishing of Born’s rule with arbitrary initial distributions. We find that the higher the dimensionality of the system, the larger the proportion of the chaotic trajectories within the Born distribution, for any non-zero value; additionally, the proportion becomes practically total for a larger range of entanglements than in the 2-qubit and 3-qubit cases. Thus we conclude that in multiqubit systems Born’s rule will be accessible by practically all initial distributions.