Event-by-event Simulation of Quantum Cryptography Protocols∗

Cryptography is an artifice of exchanging information between two parties such that an unauthorized person cannot retrieve this information. To this end, the sender usually employs some key to encrypt the information to be transmitted, and the receiver applies a decryption algorithm to recover the original information. If the cryptographic system is secure, an eavesdropper can decipher the encrypted message if and only if the eavesdropper knows the key. Thus, the central problem of cryptography is to establish a powerful key. We may imagine that the more bits the key contains and the more complicated the key is, the more secure the process is. But, in practice, if the key is generated and transmitted in a conventional, electronic way, it may be possible to intercept the key. Then, the eavesdropper can make a copy of the exchanged information without changing it, such that the sender or receiver did not notice that the information has been intercepted. Quantum cryptography uses microscopic objects such as individual photons as information carriers. One of the characteristic features of such microscopic systems is that a measurement may change the information that the microscopic system carries. Therefore, if an eavesdropper attempts to make a measurement to determine a bit of the key, there is no guarantee that the information carried by the microscopic system is left unchanged. If the quantum cryptography protocol is designed properly, the presence of the eavesdropper is revealed by an increase of the error rate in the bits that are being transmitted from sender to receiver. Although there is no doubt that quantum theory is very successful in describing a vast number of experimental results, it is well-known that quantum theory has nothing to say about individual events that are being recorded in experiments. Yet, quantum cryptography uses individual events to transmit information, its security being guaranteed by axioms. Since the inception of quantum theory, the major fundamental problem of incorporating in quantum theory the fact that we observe events only is often referred to as the quantum measure-