Title: Fidelity Lower Bounds for Stabilizer and CSS Quantum Codes,
Abstract: In this paper we estimate the fidelity of stabilizer and CSS codes. First, we
derive a lower bound on the fidelity of a stabilizer code via its quantum
enumerator. Next, we find the average quantum enumerators of the ensembles of
finite length stabilizer and CSS codes. We use the average quantum enumerators
for obtaining lower bounds on the average fidelity of these ensembles. We
further improve the fidelity bounds by estimating the quantum enumerators of
expurgated ensembles of stabilizer and CSS codes. Finally, we derive fidelity
bounds in the asymptotic regime when the code length tends to infinity.
These results tell us which code rate we can afford for achieving a target
fidelity with codes of a given length. The results also show that in symmetric
depolarizing channel a typical stabilizer code has better performance, in terms
of fidelity and code rate, compared with a typical CSS codes, and that balanced
CSS codes significantly outperform other CSS codes. Asymptotic results
demonstrate that CSS codes have a fundamental performance loss compared to
stabilizer codes.