ua nt - p h / 99 07 07 3 v 1 2 2 Ju l 1 99 9 Continuous Variable Quantum Cryptography

We propose a quantum cryptographic scheme in which small phase and amplitude modulations of CW light beams carry the key information. The presence of EPR type correlations provides the quantum protection. Quantum cryptographic schemes use fundamental properties of quantum mechanics to ensure the protection of random number keys [1,2]. In particular the act of measurement in quantum mechanics inevitably disturbs the system. Further more, for single quanta such as a photon, simultaneous measurements of non-commuting variables are forbidden. By randomly encoding the information between non-commuting observables of a stream of single photons any eavesdropper (Eve) is forced to guess which observable to measure for each photon. On average, half the time Eve will guess wrong, revealing her self through the back action of the measurement to the sender (Alice) and receiver (Bob). There are some disadvantages in working with single photons, particularly in free-space where scattered light levels can be high. Also it is of fundamental interest to quantum information research to investigate links between discrete variable, single photon phenomena and continuous variable , multi-photon effects. This motivates a consideration of quantum cryptography using multi-photon light modes. In particular we consider encoding key information as small signals carried on the amplitude and and phase quadrature amplitudes of the beam. These are the analogues of position and momentum for a light mode and hence are continuous, conjugate variables. Although simultaneous measurements of these non-commuting observables can be made in various ways, for example splitting the beam on a 50:50 beamsplitter and then making homodyne measurements on each beam, the information that can be obtained is strictly limited by the generalized uncertainty principle for simultaneous measurements [3,4]. If an ideal measurement of one quadrature amplitude produces a result with a signal to noise of (1) then a simultaneous measurement of both quadratures cannot give a signal to noise result in excess of 1