6 Subsystem Codes
Subsystem codes were recently introduced in an effort to unify quantum
error-correcting codes, decoherence free subspaces, and noiseless subsystems. A
subsystem code 
is a subspace of a finite-dimensional Hilbert space that
is decomposed into a tensor product of two vector spaces 
and 
, respectively
called the subsystem 
and the co-subsystem 
. The main idea is that the
information is encoded in the subsystem 
and that all errors affecting the
co-subsystem 
are ignored.
Clifford codes are the most natural way to construct subsystem codes
such that 
is a stabilizer code, the dimensions of 
and 
can be
controlled, and the set of detectable errors can be determined.
One of our key results is that any additive classical error-correcting codes yields a subsystem code, no self-orthogonality is needed!
- A. Klappenecker and P.K. Sarvepalli. Clifford code construction of
operator quantum error correcting codes. quant-ph/0604161, April
2006
@Unpublished{pre0604,
author = {Klappenecker, A. and Sarvepalli, P.K.},
title = {Clifford code construction of operator quantum error correcting codes},
note = {quant-ph/0604161},
month = {April},
year = 2006
}