Entanglement can Completely Defeat Quantum Noise

We describe two quantum channels that individually cannot send any classical information without some chance of decoding error. But together a single use of each channel can send quantum information perfectly reliably. This proves that the zero-error classical capacity exhibits superactivation, the extreme form of the superadditivity phenomenon in which entangled inputs allow communication over zero-capacity channels. But our result is stronger still, as it even allows zero-error quantum communication when the two channels are combined. Thus our result shows a new remarkable way in which entanglement across two systems can be used to resist noise, in this case perfectly. We also show a new form of superactivation by entanglement shared between sender and receiver.

Figure 1

The set of zeros of a set of simultaneous polynomial equations either (a) comprises the entire space, or (b) has measure 0. To show that it is measure 0, it therefore suffices to find a single point outside of the set (b).