Measuring mixed-state topological invariant in open photonic quantum walk.

A photonic quantum walk enables direct measurement of the quantized Uhlmann geometric phase for topologically nontrivial mixed states, revealing a trivial-to-nontrivial transition linked to a topological kink structure.

• Why it matters: Mixed-state geometric phases and their possible topological character are largely untested experimentally, partly because Uhlmann parallel transport conflicts with Hamiltonian dynamics and preparing nontrivial mixed states is difficult.
• What they did: The protocol engineers controlled nonunitary dynamics in a photonic quantum walk to generate topologically nontrivial mixed states, then uses machine learning of the full density matrix in momentum space to extract the quantized geometric phase.
• The result: The quantized mixed-state topological invariant shifts from a trivial to a nontrivial value, and this change is closely associated with the emergence of a topological kink structure.

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