Quantum coding with finite resources.

摘要: The quantum capacity of a memoryless channel determines the maximal rate at which we can communicate reliably over asymptotically many uses channel. Here illustrate that this asymptotic characterization is insufficient in practical scenarios where decoherence severely limits our ability to manipulate large systems encoder and decoder. In settings, should instead focus on optimal trade-off between three parameters: code, size devices decoder, fidelity transmission. We find approximate exact characterizations for various channels interest, including dephasing, depolarizing erasure channels. each case, parameterized by second parameter, dispersion. process, develop several bounds are valid general be computed small instances.