Entanglement of subspaces and error-correcting codes

Concatenating Decoherence Free Subspaces with Quantum Error Correcting Codes

An operator sum representation is derived for a decoherence-free subspace (DFS) and used to (i) show that DFSs are the class of quantum error correcting codes (QECCs) with fixed, unitary recovery operators, and (ii) find explicit representations for the Kraus operators of collective decoherence. We demonstrate how this can be used to construct a concatenated DFS-QECC code which protects against...

Constructions of good entanglement-assisted quantum error correcting codes

Entanglement-assisted quantum error correcting codes (EAQECCs) are a simple and fundamental class of codes. They allow for the construction of quantum codes from classical codes by relaxing the duality condition and using pre-shared entanglement between the sender and receiver. However, in general it is not easy to determine the number of shared pairs required to construct an EAQECC. In this pa...

Synchronizable Error-Correcting Codes

A new technique for correcting synchronization errors in the transmission of discrete-symbol information is developed. The technique can be applied to any t-additive-error-correcting Bose-Chaudhuri-Hocquenghem code, to provide protection against synchronization errors. The synchronization error is corrected at the first complete received word after the word containing the synchronization error,...

Parallel error correcting codes

Error-Correcting Codes

Transmission of information takes place over “noisy” signals. This is the case in satellite transmissions and storing data. For this reason, it is useful to encode information so that errors can be detected and corrected. For our purposes, we will assume all information to be encoded constists of words of fixed length k using symbols from a fixed alphabet, and all encoded messages are divided i...