There are two complementary approaches to realizing quantum information so that it is protected from a given set of error operators. Both involve encoding information by means of subsystems. Initialization-based error protection involves a quantum operation to be applied before error events occur. Operator quantum error correction, uses a recovery operation, which is to be applied after the errors. Together, the two approaches make it clear how quantum information can be stored at all stages of a process involving alternating error and quantum operations. In particular, there is always a subsystem that faithfully represents the desired quantum information. We give a definition of faithful realization of quantum information and show that it always involves subsystems. This generalizes the "subsystems principle" for quantum information advocated by Viola et al. In the presence of errors, one can make use of noiseless, (initialization) protectable, or error-correcting subsystems. We give an explicit algorithm for finding optimal noiseless subsystems by refining the strategy given in Choi and Kribs' work. Finding optimal protectable or error-correcting subsystems is in general difficult. Verifying that a subsystem is error-correcting has previously been shown to involve only linear algebra. We discuss the verification problem for protectable subsystems and reduce it to a simplified version of the problem of finding error-detecting codes.
Physical Review A (Atomic, Molecular and Optical Physics)
operator quan error corr, protectable subsystems, quan error correcting codes, quan error correction, quan subsystems
Protected Realizations of Quantum Information, Physical Review A (Atomic, Molecular and Optical Physics)
(Accessed March 2, 2024)