Quantum information with modular variables

TL;DR

This paper presents a new method using modular variables to encode and process quantum information in continuous variable systems, enabling adaptation of finite-dimensional protocols to infinite-dimensional quantum states.

Contribution

It introduces a formalism based on modular variables and non-Gaussian operators for quantum information processing in continuous variable systems.

Findings

Develops a general recipe for adapting quantum protocols to infinite-dimensional systems.

Describes implementation of single and two-qubit gates using this formalism.

Discusses potential realization in quantum optical setups.

Abstract

We introduce a novel strategy, based on the use of modular variables, to encode and deterministically process quantum information using states described by continuous variables. Our formalism leads to a general recipe to adapt existing quantum information protocols, originally formulated for finite dimensional quantum systems, to infinite dimensional systems described by continuous variables. This is achieved by using non unitary and non-gaussian operators, obtained from the superposition of gaussian gates, together with adaptative manipulations in qubit systems defined in infinite dimensional Hilbert spaces. We describe in details the realization of single and two qubit gates and briefly discuss their implementation in a quantum optical set-up.