The entanglement fidelity and quantum error correction

TL;DR

This paper derives new formulas for entanglement fidelity, emphasizing its importance over general fidelity in quantum error correction for quantum computers.

Contribution

It introduces two new expressions for entanglement fidelity, highlighting its critical role in optimizing quantum error correction.

Findings

New formulas for entanglement fidelity derived

Entanglement fidelity should be maximized in quantum error correction

Clarifies the distinction between entanglement fidelity and general fidelity

Abstract

Two new expressions for the entanglement fidelity recently introduced by Schumacher (LANL e-print quant-ph/9604023, to appear in Phys. Rev. A) are derived. These expressions show that it is the entanglement fidelity which must be maximized when performing error correction on qubits for quantum computers, not the fidelity, which is the most-often used generalization of the probability for storing a qubit correctly.