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By interpreting the well-known, qualitative criteria for the existence ofquantum error correction (QEC) codes by Knill and Laflamme from a quantitativeperspective, we propose a figure of merit for assessing a QEC scheme based onthe average fidelity between codewords. This enables us to quantify theperformance of a protocol as a whole, including errors beyond the correctableset. Various examples are calculated for photonic qubit codes dealing with theexperimentally relevant case of photon loss, demonstrating the advantages ofthe new measure. In the context of continuous-variable QEC, ourcodeword-overlap measure can be used to reproduce, in a different way with noneed for calculating entanglement measures, a previous result concerning theimpossibility of improving transmission of Gaussian states through Gaussianchannels via Gaussian operations alone.

Assessing quantum error correction: fidelity and entanglement measures with application to photonic codes