Physics Colloquium: Why entanglement needs topology

Zoom: https://tau-ac-il.zoom.us/j/84097289852?pwd=bj3ZxsNaOBpvlemc35waxxSLLZ541f.1

Abstract: 

Quantum entanglement and topological phases of matter are usually presented as distinct chapters of modern physics. I will argue they are the same chapter. The Wootters concurrence, the standard measure of two-qubit entanglement, is built from the time-reversal operator, the very antiunitary symmetry that underlies the tenfold classification of topological matter. This is no coincidence: entangling Hamiltonians fall into disconnected topological sectors, and only topologically nontrivial ones can generate entanglement. The connection is measurable: geometric phases of a quantum gate obey a topological sum rule, so two implementations of the same gate acquire measurably different phases. For indistinguishable fermions the correspondence deepens: particle–hole conjugation replaces time reversal, the two-fermion space splits into exactly two entanglement channels, spin and orbital, and free fermions cannot entangle at all. Interacting fermionic matter, graphene vacancies among others, realizes both channels robustly.

Event Organizer: Dr. Tobias Holder