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Optical communication channels are ultimately quantum-mechanical in nature, and we must therefore look beyond classical information theory to determine their communication capacity as well as to find efficient encoding and decoding schemes of the highest rates. Thermal channels, which arise from linear coupling of the field to a thermal environment, are of particular practical relevance; their classical capacity has been recently established, but their quantum capacity remains unknown. While the capacity sets the ultimate limit on reliable communication rates, it does not promise that such rates are achievable by practical means. Here we construct efficiently encodable codes for thermal channels which achieve the classical capacity and the so-called Gaussian coherent information for transmission of classical and quantum information, respectively. Our codes are based on combining polar codes with a discretization of the channel input into a finite constellation of coherent states. Encoding of classical information can be done using linear optics.
We suggest a new protocol for the information reconciliation stage of quantum key distribution based on polar codes. The suggested approach is based on the blind technique, which is proved to be useful for low-density parity-check (LDPC) codes. We sh
A secret can be an encrypted message or a private key to decrypt the ciphertext. One of the main issues in cryptography is keeping this secret safe. Entrusting secret to one person or saving it in a computer can conclude betrayal of the person or des
As with classical information, error-correcting codes enable reliable transmission of quantum information through noisy or lossy channels. In contrast to the classical theory, imperfect quantum channels exhibit a strong kind of synergy: there exist p
Polar codes are introduced for discrete memoryless broadcast channels. For $m$-user deterministic broadcast channels, polarization is applied to map uniformly random message bits from $m$ independent messages to one codeword while satisfying broadcas
Quantum error-correcting codes are used to protect qubits involved in quantum computation. This process requires logical operators, acting on protected qubits, to be translated into physical operators (circuits) acting on physical quantum states. We