Linear-optical dynamics of one-dimensional anyons

TL;DR

This paper explores the dynamics of one-dimensional anyons under linear optical Hamiltonians, revealing how their exchange phase influences quantum behaviors and enabling universal quantum computation with novel entangled states.

Contribution

It introduces a framework for studying anyonic linear optics, demonstrating their potential for quantum gates and state generation, and establishing their computational universality.

Findings

Anyonic exchange phase affects bunching behaviors.

Aharonov-Bohm effect enables entangling gates.

Anyonic mirror can generate cat states.

Abstract

We study the dynamics of bosonic and fermionic anyons defined on a one-dimensional lattice, under the effect of Hamiltonians quadratic in creation and annihilation operators, commonly referred to as linear optics. These anyonic models are obtained from deformations of the standard bosonic or fermionic commutation relations via the introduction of a non-trivial exchange phase between different lattice sites. We study the effects of the anyonic exchange phase on the usual bosonic and fermionic bunching behaviors. We show how to exploit the inherent Aharonov-Bohm effect exhibited by these particles to build a deterministic, entangling two-qubit gate and prove quantum computational universality in these systems. We define coherent states for bosonic anyons and study their behavior under two-mode linear-optical devices. In particular we prove that, for a specific value of the exchange factor, an anyonic mirror can generate cat states, an important resource in quantum information processing with continuous variables.