Fermionic Quasi-free States and Maps in Information Theory

Abstract

This paper and the results therein are geared towards building a basic toolbox for calculations in quantum information theory of quasi-free fermionic systems. Various entropy and relative entropy measures are discussed and the calculation of these reduced to evaluating functions on the one-particle component of quasi-free states. The set of quasi-free affine maps on the state space is determined and fully characterized in terms of operations on one-particle subspaces. For a subclass of trace preserving completely positive maps and for their duals, Choi matrices and Jamiolkowski states are discussed.

19 pages

References in corpus (4)

• Unknown Quantum States: The Quantum de Finetti Representation
• Multiplicativity of maximal output purities of Gaussian channels under Gaussian inputs
• Introduction to representations of the canonical commutation and anticommutation relations
• Quantum computation algorithm for many-body studies

Cited by in corpus (18)

• Spectral theorem for the Lindblad equation for quadratic open fermionic systems
• Entanglement Entropy of Eigenstates of Quadratic Fermionic Hamiltonians
• Average eigenstate entanglement entropy of the XY chain in a transverse field and its universality for translationally invariant quadratic fermionic models
• Spectral properties of reduced fermionic density operators and parity superselection rule
• Asymptotic distinguishability measures for shift-invariant quasi-free states of fermionic lattice systems
• Second-order asymptotics for quantum hypothesis testing in settings beyond i.i.d. - quantum lattice systems and more
• Two approaches to obtain the strong converse exponent of quantum hypothesis testing for general sequences of quantum states
• Absence of localization in two-dimensional Clifford circuits
• Connecting the von Neumann and Renyi entropies for Fermions
• Degradability of Fermionic Gaussian Channels
• On optimal currents of indistinguishable particles
• On Fermionic walkers interacting with a correlated structured environment
• Thermalization of Fermionic Quantum Walkers
• Fermionic walkers driven out of equilibrium
• Maximally entangled fermions
• Correlations in Free Fermionic States
• Super-exponential distinguishability of correlated quantum states
• On sampling determinantal and Pfaffian point processes on a quantum computer