Perturbation Theory for Quantum Information
- URL: http://arxiv.org/abs/2106.05533v3
- Date: Thu, 23 Mar 2023 16:26:10 GMT
- Title: Perturbation Theory for Quantum Information
- Authors: Michael R Grace and Saikat Guha
- Abstract summary: We develop theories for two classes of quantum state perturbations, perturbations that preserve the vector support of the original state and perturbations that extend the support beyond the original state.
We apply our perturbation theories to find simple expressions for four of the most important quantities in quantum information theory.
- Score: 1.2792576041526287
- License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
- Abstract: We report lowest-order series expansions for primary matrix functions of
quantum states based on a perturbation theory for functions of linear
operators. Our theory enables efficient computation of functions of perturbed
quantum states that assume only knowledge of the eigenspectrum of the zeroth
order state and the density matrix elements of a zero-trace, Hermitian
perturbation operator, not requiring analysis of the full state or the
perturbation term. We develop theories for two classes of quantum state
perturbations, perturbations that preserve the vector support of the original
state and perturbations that extend the support beyond the support of the
original state. We highlight relevant features of the two situations, in
particular the fact that functions and measures of perturbed quantum states
with preserved support can be elegantly and efficiently represented using
Fr\'echet derivatives. We apply our perturbation theories to find simple
expressions for four of the most important quantities in quantum information
theory that are commonly computed from density matrices: the Von Neumann
entropy, the quantum relative entropy, the quantum Chernoff bound, and the
quantum fidelity.
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