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Fidelity-based distance bounds for N-qubit approximate quantum error correction

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Autor(es):
Fiusa, Guilherme ; Soares-Pinto, Diogo O. ; Pires, Diego Paiva
Número total de Autores: 3
Tipo de documento: Artigo Científico
Fonte: PHYSICAL REVIEW A; v. 107, n. 3, p. 11-pg., 2023-03-24.
Resumo

The Eastin-Knill theorem is a central result of quantum error correction theory and states that a quantum code cannot correct errors exactly, possess continuous symmetries, and implement a universal set of gates transversely. As a way to circumvent this result, there are several approaches in which one gives up on either exact error correction or continuous symmetries. In this context, it is common to employ a complementary measure of fidelity as a way to quantify quantum state distinguishability and benchmark approximations in error correction. Despite having useful properties, evaluating fidelity measures stands as a challenging task for quantum states with a large number of entangled qubits. With that in mind, we address two distance measures based on the suband superfidelities as a way to bound error approximations, which in turn require a lower computational cost. We model the lack of exact error correction to be equivalent to the action of a single dephasing channel, evaluate the proposed fidelity-based distances both analytically and numerically, and obtain a closed-form expression for a general N-qubit quantum state. We illustrate our bounds with two paradigmatic examples, an N-qubit mixed GHZ state and an N-qubit mixed W state. (AU)

Processo FAPESP: 17/03727-0 - Características quânticas de sistemas compostos: geometria, dinâmica e termodinâmica
Beneficiário:Diogo de Oliveira Soares Pinto
Modalidade de apoio: Auxílio à Pesquisa - Regular