The fifth lesson concluded the study of quantum cloning. We began by describing cloning experiments using parametric conversion of coded quibits in photon polarization, the principle of which had been given in the previous lesson. These experiments enabled us to demonstrate directly the effect of amplification of a field mode by stimulated emission, and to obtain cloning fidelity in good agreement with theory. These experiments are extremely delicate, however, as they require great care in the optical alignment and temporal tuning of the modes. Above all, they rely on "post-selection" processes that retain only a tiny fraction of events.
We then turned to the analysis of cloning as a cryptographic attack method . The interception by an eavesdropper (Eve) of a bit key exchanged by two partners (Alice and Bob) would be possible if perfect cloning existed. All Eve would have to do is clone the qubits sent by Alice, keep one copy and let the other reach Bob, then wait for the exchange of information between Alice and Bob to deduce the key. The impossibility of perfect cloning limits the effectiveness of this strategy, but allows Eve to acquire partial information about the key. By obtaining this information, she disturbs the qubits received by Bob, providing him with clues to her interception. The limit imposed by quantum theory on the fidelity of cloning makes it possible to define the limit to the rate of noise acceptable on a quantum communication channel for the exchange of a cryptographic key that we want to be safe from espionage.
We concluded our study of cloning by making the link between cloning and the transmission of superluminal information. As mentioned above, perfect cloning would make instantaneous communication of information possible in an EPR-type experiment, which would be contrary to the principle of relativity. Taking up an argument by Nicolas Gisin, we show that the fidelity F = 5/6 of optimal cloning corresponds to the upper bound, beyond which superluminal communication would become possible. In other words, the fidelity of optimal cloning is a necessary condition to ensure peaceful coexistence between the principles of relativity and those of non-relativistic quantum physics. This coexistence is not in itself self-evident. The fact that the properties of entanglement, based on a physics in which the speed of light plays no fundamental role, are compatible with the principle of relativistic causality is remarkable.
