Quantum magic of strongly correlated fermions $-$ the Hubbard dimer

TL;DR

This paper analyzes the quantum magic resource in the Hubbard dimer, revealing its unique properties and limitations compared to other quantum resources, across various states and dynamics.

Contribution

It provides a detailed evaluation of non-stabilizerness in the Hubbard dimer, highlighting the effectiveness of robustness of magic over stabilizer Renyi entropy.

Findings

Non-stabilizerness offers unique insights into quantum resources.

Stabilizer Renyi entropy often fails to detect mixed stabilizer states.

Non-stabilizerness differs fundamentally from other quantum resources.

Abstract

We study the non-stabilizerness (quantum magic) content of the Hubbard dimer, an analytically solvable, yet completely non-trivial, model of strongly correlated fermions. We can access zero- and finite-temperature properties as well as the time evolution in a quantum quench protocol. We evaluate local and nonlocal non-stabilizerness using both the robustness of magic and the stabilizer Renyi entropy, demonstrating how the latter often fails in detecting the mixed stabilizer states that are typically found in this kind of systems. Finally, we compare the non-stabilizerness with other genuine resources of quantum-state complexity, i.e., the fermionic non-Gaussianity and the superselected two-site entanglement. Our findings corroborate the notion of non-stabilizerness as a fundamentally different quantum resource, able to give profound insights that are missed by more traditional information-theoretic quantities.