We propose various new techniques in quantum information theory, including a de Finetti style representation theorem for finite symmetric quantum states. As an application, we give a proof for the security of quantum key distribution which applies to arbitrary protocols.
We prove that the 1984 protocol of Bennett and Brassard (BB84) for quantum key distribution is secure. We first give a key distribution protocol based on entanglement purification, which can be proven secure using methods from Lo and Chau's proof of security for a similar protocol. We then show that the security of this protocol implies the security of BB84. The entanglement purification based protocol uses Calderbank-Shor-Steane codes, and properties of these codes are used to remove the use of quantum computation from the Lo-Chau protocol.   Shor and Preskill (see Phys. Rev. Lett., vol.85, p.441, 2000) have provided a simple proof of security of the standard quantum key distribution scheme by Bennett and Brassard (1984) by demonstrating a connection between key distribution and entanglement purification protocols (EPPs) with one-way communications. Here, we provide proofs of security of standard quantum key distribution schemes, Bennett and Brassard and the six-state scheme, against the most general attack, by using the techniques of two-way entanglement purification. We demonstrate clearly the advantage of classical post-processing with two-way classical communications over classical post-processing with only one-way classical communications in quantum key distribution (QKD). This is done by the explicit construction of a new protocol for (the error correction detection and privacy amplification of) Bennett and Brassard that can tolerate a bit error rate of up to 18.9 , which is higher than what any Bennett and Brassard scheme with only one-way classical communications can possibly tolerate. Moreover, we demonstrate the advantage of the six-state scheme over Bennett and Brassard by showing that the six-state scheme can strictly tolerate a higher bit error rate than Bennett and Brassard. In particular, our six-state protocol can tolerate a bit error rate of 26.4 , which is higher than the upper bound of 25 bit error rate for any secure Bennett and Brassard protocol. Consequently, our protocols may allow higher key generation rate and remain secure over longer distances than previous protocols. Our investigation suggests that two-way entanglement purification is a useful tool in the study of advantage distillation, error correction, and privacy amplification protocols. Practical application of the generalized Bells theorem in the so-called key distribution process in cryptography is reported. The proposed scheme is based on the Bohms version of the Einstein-Podolsky-Rosen gedanken experiment and Bells theorem is used to test for eavesdropping. © 1991 The American Physical Society. Ekert has described a cryptographic scheme in which Einstein-Podolsky-Rosen (EPR) pairs of particles are used to generate identical random numbers in remote places, while Bell's theorem certifies that the particles have not been measured in transit by an eavesdropper. We describe a related but simpler EPR scheme and, without invoking Bell's theorem, prove it secure against more general attacks, including substitution of a fake EPR source. Finally we show our scheme is equivalent to the original 1984 key distribution scheme of Bennett and Brassard, which uses single particles instead of EPR pairs. Quantum key distribution is widely thought to offer unconditional security in communication between two users. Unfortunately, a widely accepted proof of its security in the presence of source, device, and channel noises has been missing. This long-standing problem is solved here by showing that, given fault-tolerant quantum computers, quantum key distribution over an arbitrarily long distance of a realistic noisy channel can be made unconditionally secure. The proof is reduced from a noisy quantum scheme to a noiseless quantum scheme and then from a noiseless quantum scheme to a noiseless classical scheme, which can then be tackled by classical probability theory.