  One of the remarkable features of quantum mechanics is the ability to ensure
secrecy. Private states embody this effect, as they are precisely those
multipartite quantum states from which two parties can produce a shared secret
that cannot in any circumstance be correlated to an external system. Naturally,
these play an important role in quantum key distribution (QKD) and quantum
information theory. However, a general distillation method has heretofore been
missing. Inspired by Koashi's complementary control scenario (arXiv:0704.3661v1
[quant-ph]), we give a new definition of private states in terms of one party's
potential knowledge of two complementary measurements made on the other and use
this to construct a general method of private state distillation using quantum
error-correcting codes. The procedure achieves the same key rate as recent,
more information-theoretic approaches while demonstrating the physical
principles underlying privacy of the key. Additionally, the same approach can
be used to establish the hashing inequality for entanglement distillation, as
well as the direct quantum coding theorem.
