Quantum random walks on a beam splitter array

Abstract

The general matrix representation of a beam splitter array is presented. Each beam splitter has a transmission/reflection coefficient that determines the behavior of these individual devices and, in consequence, the whole system response. The general matrix representation of each beam splitter is given as rotations of a $2n-th$ dimensional space. With these operators, the matrix that describes the entire array and, consequently, the final probability distribution of an input photon state can be calculated.

References in corpus (13)

• Quantum random walks - an introductory overview
• A Quantum Random Walk Search Algorithm
• Quantum walks of correlated particles
• Quantum Mechanical Interaction-Free Measurements
• A 2D Quantum Walk Simulation of Two-Particle Dynamics
• Implementing the quantum random walk
• Experimental Implementation of the Quantum Random-Walk Algorithm
• Quantum random walk of two photons in separable and entangled state
• Counting Statistics of Many-Particle Quantum Walks
• Ultra-long quantum walks via spin-orbit photonics
• Multi-bit quantum random number generator from a single qubit quantum walk
• Single photons in an imperfect array of beam-splitters: Interplay between percolation, backscattering and transient localization
• Interaction-Free Measurements of Optical Semitransparent Objects