Entropy Power Inequality in Fermionic Quantum Computation

Abstract

We study quantum computation relations on unital finite-dimensional CAR $C^{\ast }$-algebras. We prove an entropy power inequality (EPI) in a fermionic setting, which presumably will permit understanding the capacities in fermionic linear optics. Similar relations to the bosonic case are shown, and alternative proofs of known facts are given. Clifford algebras and the Grassmann representation can thus be used to obtain mathematical results regarding coherent fermion states.

arXiv comment32 pages

References in corpus (6)

• Density Operators for Fermions
• Optimal Hypercontractivity for Fermi Fields and Related Non-Commutative Integration
• The entropy power inequality for quantum systems
• A generalization of the Entropy Power Inequality to Bosonic Quantum Systems
• The conductivity measure for the Anderson model
• Ac-conductivity and electromagnetic energy absorption for the Anderson model in linear response theory

Cited by in corpus (1)

• Curvature-dimension conditions for symmetric quantum Markov semigroups