Ergodicity and Born's rule in an entangled three-qubit Bohmian system

We study in detail the interplay between chaos and entanglement in the Bohmian trajectories of three entangled qubits, made of coherent states of the quantum harmonic oscillator. We find that all the three-dimensional (3D) chaotic trajectories are ergodic; namely, they have a common long time distribution of points regardless of the initial conditions, and for any nonzero entanglement, their number is much larger than in the corresponding two-qubit system. Furthermore, the range of entanglements for which practically all the trajectories are chaotic and ergodic is much larger than in the two-qubit case. Thus, as the dimensionality of the system increases, Born's rule becomes accessible to a wider range of arbitrary initial distributions than in the 2D case. Our numerical results lead to the conjecture that, for multiqubit systems, Born's rule is the limit of almost all initial distributions of particles.