Abstract
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. 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. 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. 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 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. 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. 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. 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.
Highlights
Quantum key distribution (QKD) uses intrinsic properties of quantum mechanics to allow for information-theoretically secure transmission of information [1–3]
The case pdist = 1 that is usually considered for quantum error correcting codes (QECCs) is only the extreme point of lowest distillation fidelity; by lowering the distillation success probability, we get access to higher fidelities
We use our methodology to carry out a detailed study on how a pure loss channel can be compensated for by using new codes and procedures for entanglement distillation
Summary
Quantum key distribution (QKD) uses intrinsic properties of quantum mechanics to allow for information-theoretically secure transmission of information [1–3]. This requires to transmit quantum systems—mostly, photons—between two parties with a sufficiently low error rate [4]. The exponential nature of channel attenuation makes it practically impossible to develop QKD systems over longer distances with direct transmission [6, 7]. Two proposals exist to deal with this issue: quantum repeaters [8–12] and trusted nodes [13–15]. The former is able to provide satisfactory security, as the repeater nodes do not have to be trusted
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