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Seminário de Óptica e Informação Quântica

Data: Sexta-Feira 05/10/2012 Sala A5-01, 11:00

Palestrante: Fernando Lemini (UFMG)

Título: Medidas de Emaranhamento em Sistemas de Partículas Indistinguíveis

Resumo: Despite being a subject widely studied in systems of non-identical particles, or whose particles, though identical, are well separated from each other, being thus distinguishable, less attention was given to the case where this separation is very small, such that the overlap of  their wave functions is no longer negligible. In this case we have to take into account the indistinguishability of the particles, being the space of quantum states restricted to symmetric or antisymmetric subspaces of the Hilbert space, depending on the bosonic or fermionic nature of the system. The study of entanglement for systems of indistinguishable particles has been, however, a subject of great controversy, leading to different approaches in its treatment. Among the most mentioned we have: quantum correlations and the entanglement of modes. We will review these different approaches and deal with the somewhat more subtle notion of quantum correlations.

We'll see how to quantify such quantum correlations in general states, pure or mixed, of fermionic/bosonic indistinguishable particles. We'll show that any sensitive measure to the purity of the single-particle reduced state (e.g. Von Neumann entropy) can be used when dealing with pure states, and for the general case we show how to employ the Negativity and the concepts of entanglement witnesses as quantifiers of quantum correlations. We'll also show how to employ some of these tools of quantification in homogeneous D-dimensional Hamiltonian models with certain symmetries, obtaining analytical measures of quantum correlations for its eigenstates.