Parallel Transport and “quantum Holonomy” along Density Operators
نویسندگان
چکیده
“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 e = WW*. There is an intrinsic nonlinearity in the parallel transport which dissolves for curves of projection operators. In the latter case one comes back to the Bott--Chern parallel transport.
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Uhlmann’s concept of quantum holonomy for paths of density operators is generalised to the off-diagonal case. This generalisation may provide information about the subjacent geometry of the space of density operators when the Uhlmann holonomy is undefined. Comparison with previous definitions of off-diagonal geometric phases for pure and mixed states is carried out. PACS numbers: 03.65.Vf ‡ Ele...
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