  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.
