论文信息 - Parallel transport and “quantum holonomy” along density operators

Parallel transport and “quantum holonomy” along density operators

“Quantum holonomy” as defined by Berry and Simon, and based on the parallel transport of Bott and Chern, can be considerably extended. There is a natural “parallelity” W∗dW=(dW)∗W within the Hilbert-Schmidt operators W. This defines parallelity and holonomy along curves of density operators ϱ=WW∗. There is an intrinsic non-linearity in the parallel transport which dissolves for curves of projection operators. In the latter case one comes back to the Bott-Chern parallel transport.

Armin Uhlmann | A. Uhlmann

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