Physical underpinnings of privacy
Joseph M. Renes, Jean-Christian Boileau · Physical Review A · 2008
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 under any circumstances be correlated with 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 [M. Koashi, e-print arXiv:0704.3661 (2007)], 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.