Physical Underpinnings of Privacy

TL;DR

This paper explores the physical foundations of quantum privacy, introducing a new method for private state distillation based on quantum error correction, which aligns with recent information-theoretic results and clarifies the underlying physical principles.

Contribution

It provides a novel physical perspective on private state distillation and introduces a general, error-correcting code-based method that achieves optimal key rates.

Findings

Achieves the same key rate as recent information-theoretic approaches.

Establishes the hashing inequality for entanglement distillation.

Demonstrates the direct quantum coding theorem using the new approach.

Abstract

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.