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Entanglement Theory Quantum Correlations Topological Quantum Computing Quantum Simulation Quantum State Preparation Representation

Cumulants associated with geometric phases

arXiv
Authors: Balázs Hetényi, Mohammad Yahyavi

Year

2013

Paper ID

32761

Status

Preprint

Abstract Read

~2 min

Abstract Words

114

Citations

N/A

Abstract

The Berry phase can be obtained by taking the continuous limit of a cyclic product -mbox{Im} ln prodI=0M-1 langle Ψ0\({boldsymbol ξ}I\)|Ψ0\({boldsymbol ξ}I+1\)rangle, resulting in the circuit integral i oint mbox{d}{boldsymbol ξ} cdot langle Ψ0\({boldsymbol ξ}\)|nablaboldsymbol ξ|Ψ0\({boldsymbol ξ}rangle. Considering a parametrized curve {boldsymbol ξ}(χ\) we show that the product prodI=0M-1 langle Ψ0\(χI\)|Ψ0\(χI+1\)rangle can be equated to a cumulant expansion. The first contributing term of this expansion is the Berry phase itself, the other terms are the associated spread, skew, kurtosis, etc. The cumulants are shown to be gauge invariant. It is also shown that these quantities can be expressed in terms of an operator.

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  • The Berry phase can be obtained by taking the continuous limit of a cyclic product -mboxIm ln prodI=0^M-1 langle Ψ0(boldsymbol ξI)|Ψ0(boldsymbol ξI+1)rangle, resulting in the...

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References & Citation Signals

[1] DOI https://doi.org/arXiv:1309.2962 [2] arXiv https://arxiv.org/abs/1309.2962 [3] Publisher https://arxiv.org/abs/1309.2962

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