Quantum cryptography with trinary quantum systems

We try to create the cryptographic scheme of producing two identical keys using, for the first time, entangled trinary quantum systems for quantum key distribution. The advantage of trinary quantum systems over the normally used binary quantum systems is an increased coding density and a higher security margin. The trinary quantum systems are encoded into the orbital angular momentum of photons, namely Laguerre -Gaussian modes with azimuthally index 1 +1, 0 and -1, respectively. The orbital angular momentum is controlled with phase holograms. In an Ekert-type protocol the violation of a three-dimensional Bell inequality verifies the security of the generated keys. A key is obtained with a trinary quantum system error rate of approximately 10%.