Quantum Information Processing by Weaving Quantum Talbot Carpets

Abstract

Single photon interference due to passage through a periodic grating is considered in a novel proposal for processing D-dimensional quantum systems (quDits) encoded in the spatial degrees of freedom of light. We show that free space propagation naturally implements basic single quDit gates by means of the Talbot effect: an intricate time-space carpet of light in the near field diffraction regime. Adding a diagonal phase gate, we show that a complete set of single quDit gates can be implemented. We then introduce a spatially-dependent beam splitter that allows implementation of controlled operations between two quDits. A new form of universal quantum information processing can then be implemented with linear optics and ancilla photons. Though we consider photons, our scheme should be directly applicable to a number of other physical systems. Interpretation of the Talbot effect as a quantum logic operation provides a beautiful and interesting way to visualize quantum computation through wave propagation and interference.

11 pages, 8 figures

References in corpus (8)

• Beating the channel capacity limit for linear photonic superdense coding
• Experimentally testable state-independent quantum contextuality
• Complete experimental toolbox for alignment-free quantum communication
• Imaging high-dimensional spatial entanglement with a camera
• Magic state distillation in all prime dimensions using quantum Reed-Muller codes
• Continuous variable quantum computation with spatial degrees of freedom of photons
• Enhancing the Violation of the Einstein-Podolsky-Rosen Local Realism by Quantum Hyper-entanglement
• Factorization of numbers with Gauss sums: I. Mathematical background