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Description
Entanglement is a fundamental feature of quantum mechanics and a key resource in quantum information theory.
In this talk, I will give a self-contained introduction to quantum entanglement, starting from the minimal postulates of quantum mechanics needed to define quantum states, measurements, and composite systems.
I will explain why composite quantum systems are described by tensor products of Hilbert spaces and how this naturally leads to the notion of entanglement for pure states.
I will then introduce local operations as a way to compare and classify entangled states, focusing on local unitaries (LU) and local operations and classical communication (LOCC).
In the bipartite pure-state setting, I will show how the Schmidt decomposition provides a complete classification under LU and constrains possible LOCC transformations.
Finally, I will briefly discuss the multipartite case, where entanglement exhibits a much richer structure and many classification problems remain open.
