ar X iv : q ua nt - p h / 05 07 21 3 v 2 16 J an 2 00 6 A Method To Find Quantum Noiseless Subsystems

ar X iv : q ua nt - p h / 05 04 18 9 v 1 2 6 A pr 2 00 5 OPERATOR QUANTUM ERROR CORRECTION

We develop a mathematical foundation for operator quantum error correction. This is a new paradigm for the error correction of quantum operations that incorporates the known techniques — i.e. the standard error correction model, the method of decoherence-free subspaces, and the noiseless subsystem method — as special cases, and relies on a generalized notion of noiseless subsystems that is not ...

ar X iv : q ua nt - p h / 07 03 21 3 v 1 2 2 M ar 2 00 7 On Subsystem Codes Beating the Hamming or Singleton Bound

Subsystem codes are a generalization of noiseless subsystems, decoherence free subspaces, and quantum error-correcting codes. We prove a Singleton bound for Fqlinear subsystem codes. It follows that no subsystem code over a prime field can beat the Singleton bound. On the other hand, we show the remarkable fact that there exist impure subsystem codes beating the Hamming bound. A number of open ...

ar X iv : q ua nt - p h / 04 11 17 2 v 1 2 3 N ov 2 00 4 Information and Entropy in Quantum Theory

ar X iv : q ua nt - p h / 02 06 02 1 v 2 6 M ay 2 00 3 Entanglement and properties ∗

Various topics concerning the entanglement of composite quantum systems are considered with particular emphasis concerning the strict relations of such a problem with the one of attributing objective properties to the constituents. In particular we will focus our attention to composite quantum systems composed of identical constituents, with the purpose of dealing with subtle issues, which have...

ar X iv : q ua nt - p h / 05 04 18 9 v 2 2 8 Se p 20 05 OPERATOR QUANTUM ERROR CORRECTION

This paper is an expanded and more detailed version of the work [1] in which the Operator Quantum Error Correction protocol was introduced. This is a new scheme for the error correction of quantum operations that incorporates the known techniques — i.e. the standard error correction model, the method of decoherence-free subspaces, and the noiseless subsystem method— as special cases, and relies...