Quantum cryptography with a predetermined key, using continuous variable Einstein-Podolsky-Rosen correlations

Correlations of the type discussed by EPR in their original 1935 paradox for continuous variables exist for the quadrature phase amplitudes of two spatially separated fields. These correlations were experimentally reported in 1992. We propose to use such EPR beams in quantum cryptography, to transmit with high efficiency messages in such a way that the receiver and sender may later determine whether eavesdropping has occurred. The merit of the new proposal is in the possibility of transmitting a reasonably secure yet predetermined key. This would allow relay of a cryptographic key over long distances in the presence of lossy channels. Intriguing is the possibility of using quantum mechanics to transmit signals in a way that any eavesdropping can be detected by the receiver and sender. This new field of quantum cryptography [1,2] has attracted much attention. In the pioneering proposal of Bennett and Brassard [1] the sender (Alice) transmits to the receiver (Bob) photon pulses in one of two orthogonal polarisations (labeled 0 and 1), where the orientation (basis) of polarisation randomly shifts between 0 and 45. The 0, 1 choice of polarisation represents the bit value. Bob randomly selects a basis (0 or 45) for a polarisation measurement, and records the resulting bit value. Alice and Bob later compare notes, through a public channel, on the sequence of orientations (0 or 45) chosen. The bit sequence where Bob selected the same orientation as Alice forms a key, to be used later to encrypt messages. While classically an eavesdropper could measure with perfect accuracy components of polarisation along both directions, quantum mechanics forbids this by way of the uncertainty principle. As a consequence the eavesdropper cannot always regenerate the original state transmitted by Alice. The resulting discrepancy between the results recorded by Alice and Bob gives warning to the interference by the eavesdropper. No discrepancy implies a secure key. Other proposals , such as that suggested by Ekert, propose to use a sequence of two spatially separated photons with correlated polarisation, and whose joint polarisation measurements are predicted by quantum mechanics to show a violation of a Bell inequality . Such fields have no local hidden variable interpretation. Any measurement, and subsequent state regeneration to mask interference, by an eavesdropper along one of these two channels