Quantum Cryptography Based Solely on Bell's Theorem

Abstract

Information-theoretic key agreement is impossible to achieve from scratch and must be based on some - ultimately physical - premise. In 2005, Barrett, Hardy, and Kent showed that unconditional security can be obtained in principle based on the impossibility of faster-than-light signaling; however, their protocol is inefficient and cannot tolerate any noise. While their key-distribution scheme uses quantum entanglement, its security only relies on the impossibility of superluminal signaling, rather than the correctness and completeness of quantum theory. In particular, the resulting security is device independent. Here we introduce a new protocol which is efficient in terms of both classical and quantum communication, and that can tolerate noise in the quantum channel. We prove that it offers device-independent security under the sole assumption that certain non-signaling conditions are satisfied. Our main insight is that the XOR of a number of bits that are partially secret according to the non-signaling conditions turns out to be highly secret. Note that similar statements have been well-known in classical contexts. Earlier results had indicated that amplification of such non-signaling-based privacy is impossible to achieve if the non-signaling condition only holds between events on Alice's and Bob's sides. Here, we show that the situation changes completely if such a separation is given within each of the laboratories.