Observing mixed-state Uhlmann winding numbers in integrated photonic quantum walks
Abstract
Integer winding numbers provide a well-established classification of topological phases protected by chiral symmetry at zero temperature, but extending this classification to thermal mixed states remains challenging. The Uhlmann phase, a mixed-state extension of the Berry phase, provides a geometric framework for characterizing finite-temperature topology. However, this geometric phase is restricted to two quantized values and therefore cannot resolve the multiple thermal regimes associated with high winding numbers. Here, we experimentally observe integer mixed-state winding numbers in a photonic quantum-walk chip. We prepare and reconstruct thermal states associated with high-winding chiral Hamiltonians and their spectrum-preserving dimensional extensions. The reconstructed Uhlmann overlaps form closed trajectories in the complex plane, and their integer windings around the zero-overlap point are directly observed. As temperature increases, the Uhlmann winding number undergoes multiple discrete changes, accompanied by switches of the Uhlmann phase and the successive disappearance of momentum-resolved topological kinks. These results highlight an integer-valued topological characterization alongside the mixed-state geometric phase.
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BibTeX
@misc{yu2026observing,
title = {{Observing mixed-state Uhlmann winding numbers in integrated photonic quantum walks}},
author = {Baichu Yu and Qin-Qin Wang and Huilong Huang and Bin-Tong Yin and Xiao-Ye Xu and Feng Gao and Xin Wang and Keren Li and Sen Yang and Yuan-Yuan Zhao},
howpublished = {arXiv},
year = {2026},
month = nov,
doi = {10.48550/arxiv.2611.07600},
eprint = {2611.07600},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2611.07600},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Observing mixed-state Uhlmann winding numbers in integrated photonic quantum walks
AU - Baichu Yu
AU - Qin-Qin Wang
AU - Huilong Huang
AU - Bin-Tong Yin
AU - Xiao-Ye Xu
AU - Feng Gao
AU - Xin Wang
AU - Keren Li
AU - Sen Yang
AU - Yuan-Yuan Zhao
PY - 2026
DA - 2026/11/05
PB - arXiv
DO - 10.48550/arxiv.2611.07600
UR - https://arxiv.org/abs/2611.07600
AB - Integer winding numbers provide a well-established classification of topological phases protected by chiral symmetry at zero temperature, but extending this classification to thermal mixed states remains challenging. The Uhlmann phase, a mixed-state extension of the Berry phase, provides a geometric framework for characterizing finite-temperature topology. However, this geometric phase is restricted to two quantized values and therefore cannot resolve the multiple thermal regimes associated with high winding numbers. Here, we experimentally observe integer mixed-state winding numbers in a photonic quantum-walk chip. We prepare and reconstruct thermal states associated with high-winding chiral Hamiltonians and their spectrum-preserving dimensional extensions. The reconstructed Uhlmann overlaps form closed trajectories in the complex plane, and their integer windings around the zero-overlap point are directly observed. As temperature increases, the Uhlmann winding number undergoes multiple discrete changes, accompanied by switches of the Uhlmann phase and the successive disappearance of momentum-resolved topological kinks. These results highlight an integer-valued topological characterization alongside the mixed-state geometric phase.
ER -