Quantum mutual independence
Abstract
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. Namely, we obtain a formula for the sum of rates of qubits needed to transmit a distributed state between Alice and Bob to a decoder Charlie. We also show that mutual independence is bounded from above by the relative entropy modulo a conjecture, saying that if after removal of a single qubit the state becomes product, its initial entanglement is bounded by 1. We suspect that mutual independence is a highly singular quantity, i.e. that it is positive only on a set of measure zero; furthermore, we believe that its presence is seen on the single copy level. This appears to be born out in the classical case.
 Publication:

arXiv eprints
 Pub Date:
 February 2009
 DOI:
 10.48550/arXiv.0902.0912
 arXiv:
 arXiv:0902.0912
 Bibcode:
 2009arXiv0902.0912H
 Keywords:

 Quantum Physics