Quantum information processing with continuous variables

Quantum information theory is built on creating, manipulating and reading qubits yet some of the dramatic experimental successes, such as unconditional quantum teleportation, quantum cryptography with coherent states, and threshold quantum secret sharing, have been achieved for continuous variables. I will explain continuous variable quantum information processing, discuss its realizations as quantum optics experiments, expose the weaknesses, extol the strengths, and consider its future. The field of continuous variable quantum information processing is exciting on several levels. The mathematics is elegant, and the quantum optics experiments can be understood in terms of Hamiltonians that obey the symplectic algebra. The experiments make use of sophisticated, yet well-developed, technology such as the ability to squeeze the vacuum fluctuations of light, perform balanced homodyne detection, and prepare highly coherent states of light. Decoherence is often negligible in these settings. These advantages make continuous variable quantum information processing the best avenue for first proofs-of-concept. The field faces formidable challenges, including encoding quantum information into continous variables allowing for robust error correction, achieving nonlinear transformations outside the symplectic transformations that allow universal unitary transformations of the field without significant decoherence, and security proofs for quantum cryptography. These challenges are not insurmountable; rather they add to the excitement of the field, which I will discuss.