428 performed on a single state. Only if all the questions used in a code are compatible with each other can the classical code be converted into a quantum code. Because of this constraint, attempts to date to make good LDPC-based quantum codes have failed. Brun et al. show that the compatibility requirement can be circumvented if the sender and receiver share a particular type of quantum state (called an “entangled state”) before transmission (see the figure). Entanglement is a purely quantum-mechanical phenomenon allowing, among other things, stronger correlations between a pair of distant quantum systems than would be possible were they purely classical. The prior connection between sender and receiver allows them to cancel any incompatibility in the encoding with an equal incompatibility in the decoding (a case where two wrongs do make a right), meaning that many more classical error-correcting codes, including some of the most efficient, can be converted to quantum codes. The original entangled state must be free of noise, but a successful transmission regenerates it, allowing further communication at no additional cost in entanglement.

This result is a great boon for a sender and receiver who wish to communicate on a regular basis, because they can generate entanglement once and then use it repeatedly for efficient quantum transmissions. It is less useful for a one-time connection or for storage of quantum information over time, but even there, a less efficient code could be used to generate the first collection of entanglement,