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

Published Jan 1, 2004• 0 citations
OpenAlex

Abstract

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:

Related papers

Comment on Geometric phases for mixed states during cyclic evolutions

Erik Sjöqvist

It is shown that a recently suggested concept of mixed state geometric phase in cyclic evolutions (Fu L-B and Chen J-L 2004 J. Phys. A: Math. Gen. 37 3699 ) is gauge dependent.

arXiv:quant-ph/0404174•Journal of Physics A Mathematical and General•Jul 8, 2004•4 citations

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

L-B Fu, J-L Chen

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.

arXiv:quant-ph/0407076•Journal of Physics A Mathematical and General•Jul 8, 2004•2 citations

Geometric phases for mixed states during cyclic evolutions

Li-Bin Fu, Jing-Ling Chen

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.

arXiv:quant-ph/0403070•Journal of Physics A Mathematical and General•Mar 2, 2004•4 citations

Geometric phases for mixed states during cyclic evolutions

Fu, L. B., Chen, J. L.

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.

•Jan 1, 2004•4 citations

Comment on ``Cyclic quantum-evolution dependence on the Hamiltonian and geometric phase''

Ali Mostafazadeh

It is shown that the analysis and the main result of the article by L-A. Wu [Phys. Rev. A 53, 2053 (1996)] are completely erroneous.

arXiv:quant-ph/9606022•Physical Review A•Jun 1, 1997•4 citations

Geometric phase for mixed states

L. C. Kwek, D. M. Tong, J. L. Chen +5 more

We present a kinematic approach for obtaining the geometric phase of a mixed state under nonunitary evolution. This phase is gauge-invariant and measurable and leads to well-known results for unitary evolution.

Laser Physics•Feb 1, 2006•8 citations
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.