Quantum Covariance Scalar Products and Efficient Estimation of Max-Ent
Projections
- URL: http://arxiv.org/abs/2307.08683v2
- Date: Thu, 29 Feb 2024 17:27:39 GMT
- Title: Quantum Covariance Scalar Products and Efficient Estimation of Max-Ent
Projections
- Authors: F.T.B. P\'erez and J. M. Matera
- Abstract summary: The maximum-entropy principle (Max-Ent) is a valuable tool in statistical mechanics and quantum information theory.
It provides a method for inferring the state of a system by utilizing a reduced set of parameters associated with measurable quantities.
The computational cost of employing Max-Ent projections in simulations of quantum many-body systems is a significant drawback.
- Score: 0.0
- License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
- Abstract: The maximum-entropy principle (Max-Ent) is a valuable and extensively used
tool in statistical mechanics and quantum information theory. It provides a
method for inferring the state of a system by utilizing a reduced set of
parameters associated with measurable quantities. However, the computational
cost of employing Max-Ent projections in simulations of quantum many-body
systems is a significant drawback, primarily due to the computational cost of
evaluating these projections. In this work, a different approach for estimating
Max-Ent projections is proposed. The approach involves replacing the expensive
Max-Ent induced local geometry, represented by the Kubo-Mori-Bogoliubov (KMB)
scalar product, with a less computationally demanding geometry. Specifically, a
new local geometry is defined in terms of the quantum analog of the covariance
scalar product for classical random variables. Relations between induced
distances and projections for both products are explored. Connections with
standard variational and dynamical Mean-Field approaches are discussed. The
effectiveness of the approach is calibrated and illustrated by its application
to the dynamic of excitations in a XX Heisenberg spin-$\frac{1}{2}$ chain
model.
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