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arXiv:quant-ph/0407076 · Journal of Physics A Mathematical and General

Reply to Comment on Geometric phases for mixed states during cyclic evolutions

L-B Fu, J-L Chen

Published Jul 8, 2004• 2 citations
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Abstract

We show that the geometric phase for mixed state during a cyclic evolution suggested in 2004 J. Phys. A 37 3699 is U(1) invariant and can be observed by nowaday techniques.
DOI
10.1088/0305-4470/37/29/n02

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Comment on “Geometric phases for mixed states during cyclic evolutions”

Abstract. It is shown that a recently suggested concept of mixed state geometric phase in cyclic evolutions [2004 J. Phys. A 37 3699] is gauge dependent. PACS numbers: 03.65.Vf, 03.67.Lx ‡ Electronic address:

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The geometric phases of cyclic evolutions for mixed states are discussed in the framework of unitary evolution. A canonical 1-form is defined whose line integral gives the geometric phase, which is gauge invariant. It reduces to the Aharonov and Anandan phase in the pure state case. Our definition is consistent with the phase shift in the proposed experiment (Sjöqvist et al 2000 Phys. Rev. Lett. 85 2845) for a cyclic evolution if the unitary transformation satisfies the parallel transport condition. A comprehensive geometric interpretation is also given. It shows that the geometric phases for mixed states share the same geometric sense with the pure states.
The geometric phases of cyclic evolutions for mixed states are discussed in the framework of unitary evolution. A canonical 1-form is defined whose line integral gives the geometric phase, which is gauge invariant. It reduces to the Aharonov and Anandan phase in the pure state case. Our definition is consistent with the phase shift in the proposed experiment (Sjöqvist et al 2000 Phys. Rev. Lett. 85 2845) for a cyclic evolution if the unitary transformation satisfies the parallel transport condition. A comprehensive geometric interpretation is also given. It shows that the geometric phases for mixed states share the same geometric sense with the pure states.