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Quantum Error Detection II: Bounds
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Quantum Error Detection II: Bounds
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In Part II we show that there exist quantum codes whose probability of undetected error falls exponentially with the length of the code and derive bounds on this exponent.The lower (existence) bound for stabilizer codes is proved by a counting argument for classical self-orthogonal quaternary codes. Upper bounds for any quantum codes are proved by linear programming. We present two general solutions of the LP problem. Together they give an upper bound on the exponent of undetected error. The upper and lower asymptotic bounds coincide for a certain interval of code rates close to 1.
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Cited by 1 Pith paper
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Asymptotic magic state distillation with almost linear rate
A new family of magic state distillation protocols based on logical Clifford error checking achieves near-linear asymptotic rate despite overhead exponent exceeding one, showing the quantities are not tightly coupled ...
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