Brassard, Theoretical Computer Science 560, 7 (2014), reprint of 1984. Brassard, in International Conference on Computers, Systems & Signal Processing, Vol. While we here focus on the case of losses, our methodology is applicable whenever the errors in a system can be characterized by a known linear map. This allows us to arrive at new codes ideal for the distribution of entangled states in this particular setting, and also to investigate if encoding in qudits or allowing for non-deterministic correction proves advantageous compared to known QECCs. We develop a numerical set of tools that allows to optimize an encoding specifically for recovering lost particles both deterministically and probabilistically, where some knowledge about $what$ was lost is available, and demonstrate its capabilities. In this paper, we investigate the loss channel, which plays a key role in quantum communication, and in particular in quantum key distribution over long distances. This does not necessarily give rise to the most efficient protection possible given a certain known error or a particular application for which the code is employed. ![]() In particular, once found, a QECC is typically used in very diverse contexts, while its resilience against errors is captured in a single figure of merit, the distance of the code. By now, a plethora of families of codes is known, but there is no universal approach to finding new or optimal codes for a certain task and subject to specific experimental constraints. Quantum error correcting codes (QECCs) are the means of choice whenever quantum systems suffer errors, e.g., due to imperfect devices, environments, or faulty channels.
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