Entanglement of degenerate eigenstates superpositions

PONT, FEDERICO M.; SERRA, PABLO; GIOVENALE, NATALIA AGUSTINA; OSENDA, OMAR

Paraty - Rio de Janeiro

Otro; VI QUANTUM INFORMATION SCHOOL AND WORKSHOP; 2017

Universidad Federal de São João del-Rei

The entanglement content, or more generally, the information content of atomic-like, few-particle systems, has been intensely studied over the last decade. The study is twofold mired: by technical issues, how to obtain the few-particle wave functions to be studied, and the somewhat controversial interpretation of the entanglement when the system is composed of identical particles. Anyway, there has been great strides in the understanding of the subject. Most commonly, the ground state is the obvious subject of study since it contains the information relevant to quantum phase transitions (in large spin systems) or critical points (in atomic-like systems) and, for the majority of the systems already analyzed in the literature, it is non-degenerate. In some cases, the ground state is degenerate, a situation that is the norm in excited states. In any case, when a systems possess degenerate eigenstates they appear as a consequence of the symmetries of the system and, usually, the eigenstates are chosen to be simultaneous eigenfunctions of the Hamiltonian and the observables associated to the symmetries. Recently, there has been some speculation about the behaviour and entanglement content of superpositions of degenerate eigenstates, a problem that arise in photons eigenstates with spatial angular momentum and the Calogero model. We present some results about the entanglement of superpositions of degenerate eigenstates and analyze the problem in a quasi exactly solvable two-particle model.