Detrimental Decoherence
  We propose and discuss two conjectures on the nature of information leaks (decoherence) for quantum computers. These conjectures, if (or when) they hold, are damaging for quantum error-correction as required by fault-tolerant quantum computation.   The first conjecture asserts that information leaks for a pair of substantially entangled qubits are themselves substantially positively correlated.   The second conjecture asserts that in a noisy quantum computer with highly entangled qubits there will be a strong effect of error synchronization.   We present more general conjectures for arbitrary noisy quantum systems. 
Gil Kalai