We study in detail the critical points of Bohmian flow, both in the inertial frame of reference (Y-points) and in the frames centered at the moving nodal points of the guiding wavefunction (X-points), and analyze their role in the onset of chaos in a system of two entangled qubits. We find the distances between these critical points and a moving Bohmian particle at varying levels of entanglement, with particular emphasis on the times at which chaos arises. Then, we find why some trajectories are ordered, without any chaos. Finally, we examine numerically how the Lyapunov Characteristic Number (LCN) depends on the degree of quantum entanglement. Our results indicate that increasing entanglement reduces the convergence time of the finite-time LCN of the chaotic trajectories toward its final positive value.
We discuss quantum entanglement in the context of the thermodynamic arrow of time. We review the role of correlations in entropy-decreasing events and prove that the occurrence of a transformation between two thermodynamic states constitutes a new type of entanglement witness, one not defined as a separating plane in state space between separable and entangled states, but as a physical process dependent on the local initial properties of the states. Extending work by Partovi, we consider a general entangled multipartite system that allows large reversals of the thermodynamic arrow of time. We describe a hierarchy of arrows that arises from the different correlations allowed in a quantum state and examine these features in the context of Maxwell's Demon. We examine in detail the case of three qubits, and also propose some simple experimental demonstrations possible with small numbers of qubits.
Quantum entanglement has played a pivotal role in both theoretical investigations and practical applications within quantum information science. In this study, we explore the connection between entanglement and geometric structures, specifically manifolds and their associated geometric properties such as curvature. We focus on the manifolds formed by the product states of three qubits, examining the induced metric derived from the Euclidean metric, the Levi-Civita connection, and, where computationally tractable, the scalar curvature. Consequently, separable states can be characterized as convex combinations of points residing on these manifolds, whereas non-separable states exhibit entanglement.