Violation of the generalized quantum Hamming bound in quantum error correction with correlated noise

Event: 
IICQI 2010
Speaker(s): 
Talk type: 
Keynote
Abstract: 

The question of whether the quantum Hamming bound, which quantifies the minimum resources needed in order to achieve successful quantum error correction for non-degenerate codes, can be violated with degenerate codes has not been answered for more than a decade. We present a generalization of the quantum Hamming bound, which was originally formulated for the case of noise acting independently on the encoding systems, to a generic noise process. We show in particular that in the presence of correlated noise the bound is violated by employing degenerate codes.