Quantum codes and macroscopic superpositions
Julio R. Gea-Banacloche · Physical Review A · 2000
It is shown that encoding the state of a quantum computer (or other quantum information-processing device) for error correction has the effect of making its operating states macroscopically indistinguishable; all the more, the more ``stable'' the code is, that is, the more errors it can correct in each pass. It is also shown that for nondegenerate codes the expectation values of macroscopic observables in such encoded states are identical to those that would be obtained for a totally mixed state of maximum entropy, where again the degree of indistinguishability increases with the number of errors corrected by the code. The results can be used to estimate the decoherence rates for systems of qubits under certain forms of interaction with the environment: it is found that when the qubits are encoded all coherent superpositions decay, to lowest order, at the same rate, which scales more slowly with the number of physical qubits than the decoherence rate for macroscopic coherent superpositions (``Schr\"odinger cats'') of the bare qubits.