A geometric invariant in entanglement
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In this thesis we offer a quick introduction to entanglement. Then we propose a gedanken experiment that is designed to showcase the limitations, if any, of the concept of indistinguishability of particles. We use a Bose-Einstein Condensation scheme to make any such limitations experimentally testable. The outcome of the gedanken experiment is subjected to analysis of two kinds. First, we interpret our system in terms of macroscopic quantum states and their Josephson-like interference. Then we analyze the possible entanglement in our quantum system. The mode entanglement found is interpreted in physical as well as geometric terms. The resulting wedge product machinery is generalized to high dimensional Hilbert spaces. Finally, an entanglement measure is proposed in the form of a geometric invariant, and compared to a measure of particle entanglement, concurrence.