Entanglement criteria for general (pure or mixed) states of systems consisting of two identical fermions are introduced. These criteria are based on appropriate inequalities involving the entropy of the global density matrix describing the total syst
em, on the one hand, and the entropy of the one particle reduced density matrix, on the other one. A majorization-related relation between these two density matrices is obtained, leading to a family of entanglement criteria based on Renyis entropic measure. These criteria are applied to various illustrative examples of parametrized families of mixed states. The dependence of the entanglement detection efficiency on Renyis entropic parameter is investigated. The extension of these criteria to systems of $N$ identical fermions is also considered.
A simple expression is obtained for the low temperature behavior of the energy and entropy of finite nuclei for $20leq Aleq 250$. The dependence on $A$ of these quantities is for the most part due to the presence of the asymmetry energy.
Entanglement is closely related to some fundamental features of the dynamics of composite quantum systems: quantum entanglement enhances the speed of evolution of certain quantum states, as measured by the time required to reach an orthogonal state.
The concept of speed of quantum evolution constitutes an important ingredient in any attempt to determine the fundamental limits that basic physical laws impose on how fast a physical system can process or transmit information. Here we explore the relationship between entanglement and the speed of quantum evolution in the context of the quantum brachistochrone problem. Given an initial and a final state of a composite system we consider the amount of entanglement associated with the brachistochrone evolution between those states, showing that entanglement is an essential resource to achieve the alluded time-optimal quantum evolution.
