Quantum mutual independence

Understand

We introduce the concept of mutual independence -- correlations shared between distant parties which are independent of the environment.

• This notion is more general than the standard idea of a secret key -- it is a fully quantum and more general form of privacy.
• The states which possess mutual independence also generalize the so called private states -- those that possess private key.
• We then show that the problem of distributed compression of quantum information at distant sources can be solved in terms of mutual independence, if free entanglement between the senders and the receiver is available.