We study the circuit complexity for mixed bosonic Gaussian states in harmonic lattices in any number of dimensions. By employing the Fisher information geometry for the covariance matrices, we consider the optimal circuit connecting two states with vanishing first moments, whose length is identified with the complexity to create a target state from a reference state through the optimal circuit. Explicit proposals to quantify the spectrum complexity and the basis complexity are discussed. The purification of the mixed states is also analysed. In the special case of harmonic chains on the circle or on the infinite line, we report numerical results for thermal states and reduced density matrices.

Complexity of mixed Gaussian states from Fisher information geometry / Di Giulio, G.; Tonni, E.. - In: JOURNAL OF HIGH ENERGY PHYSICS. - ISSN 1029-8479. - 2020:12(2020), pp. 1-105. [10.1007/JHEP12(2020)101]

Complexity of mixed Gaussian states from Fisher information geometry

Di Giulio, G.
;
Tonni, E.
2020

Abstract

We study the circuit complexity for mixed bosonic Gaussian states in harmonic lattices in any number of dimensions. By employing the Fisher information geometry for the covariance matrices, we consider the optimal circuit connecting two states with vanishing first moments, whose length is identified with the complexity to create a target state from a reference state through the optimal circuit. Explicit proposals to quantify the spectrum complexity and the basis complexity are discussed. The purification of the mixed states is also analysed. In the special case of harmonic chains on the circle or on the infinite line, we report numerical results for thermal states and reduced density matrices.
2020
12
1
105
101
https://arxiv.org/abs/2006.00921
Di Giulio, G.; Tonni, E.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/20.500.11767/118256
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