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I'm wondering whether or not we can construct quantum deletion error correcting codes. The quantum deletion error is defined by the partial trace. If we can, could anyone give an example?

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It is well known that quantum error correction can also correct erasure errors. In fact, a code which can correct $k$ general errors (in arbitrary locations) can correct erasure errors in $2k$ locations. Thus, any quantum error correction code serves as an example.

To learn more about that, you could e.g. consult Preskill's lecture notes or the book by Nielsen and Chuang.

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  • $\begingroup$ Thanks, but I think I led you to misunderstanding. In my sentence, "deletion error" is not "erasure error". A deletion error is an error that some quantum particles disappear. In classical coding theory, an erasure error is like 010→0e0, where e is the erasure symbol, and a deletion error is like 010→00. $\endgroup$ – user225954 Mar 26 at 6:19
  • $\begingroup$ I think this is not commonly considered, as usually one knows when a particle is lost. (Say, when you send photons you'd send them at a fixed rate, or - if the runtime is varying - you could accompany each by a classical "carrier" pulse e.g. on a different frequency.) $\endgroup$ – Norbert Schuch Mar 26 at 11:14

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