| Full text | |
| Author(s): |
Fiusa, Guilherme
;
Soares-Pinto, Diogo O.
;
Pires, Diego Paiva
Total Authors: 3
|
| Document type: | Journal article |
| Source: | PHYSICAL REVIEW A; v. 107, n. 3, p. 11-pg., 2023-03-24. |
| Abstract | |
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) | |
| FAPESP's process: | 17/03727-0 - Quantumness of composite systems: geometry, dynamics and thermodynamics |
| Grantee: | Diogo de Oliveira Soares Pinto |
| Support Opportunities: | Regular Research Grants |