The problem of computing the quantum dynamical entropy introduced by Alicki and Fannes requires the trace of the operator function \$F(\Omega) = - \Omega \log \Omega\$, where \$\Omega\$ is a non-negative, Hermitean operator. Physical significance demands that this operator be a matrix of large order. We study its properties and we derive efficient algorithms to solve this problem, also implementable on parallel machines with distributed memory. We rely on a Lanczos technique for large matrix computations developed by Gene Golub.

### Quantum dynamical entropy and an algorithm by Gene Golub

#### Abstract

The problem of computing the quantum dynamical entropy introduced by Alicki and Fannes requires the trace of the operator function \$F(\Omega) = - \Omega \log \Omega\$, where \$\Omega\$ is a non-negative, Hermitean operator. Physical significance demands that this operator be a matrix of large order. We study its properties and we derive efficient algorithms to solve this problem, also implementable on parallel machines with distributed memory. We rely on a Lanczos technique for large matrix computations developed by Gene Golub.
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Quantum dynamical entropy; large matrices; Lanczos method; Montecarlo techniques.
Mantica, GIORGIO DOMENICO PIO
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Utilizza questo identificativo per citare o creare un link a questo documento: `https://hdl.handle.net/11383/10435`
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