Quantum information processing in phase space: A modular variables approach

TL;DR

This paper introduces a modular variables approach to quantum information processing in phase space, enabling more practical encoding and measurement of quantum states in infinite-dimensional systems, with experimental validation using single photons.

Contribution

It presents a novel use of modular variables to relax logical state requirements in quantum encoding, enhancing feasibility for quantum information tasks.

Findings

Protocols allow reading discrete information from logical states via modular observables.

The approach is experimentally feasible with single-photon transverse degrees of freedom.

It maintains the universality and fault tolerance of quantum operations.

Abstract

Binary quantum information can be fault tolerantly encoded in states defined in infinite dimensional Hilbert spaces. Such states define a computational basis, and permit a perfect equivalence between continuous and discrete universal operations. The drawback of this encoding is that the corresponding logical states are unphysical, meaning infinitely localized in phase space. We use the modular variables formalism to show that, in a number of protocols relevant for quantum information and for the realization of fundamental tests of quantum mechanics, it is possible to loosen the requirements on the logical subspace without jeopardizing their usefulness or their successful implementation. Such protocols involve measurements of appropriately chosen modular observables that permit the readout of the encoded discrete quantum information from the corresponding logical states. Finally, we demonstrate the experimental feasibility of our approach by applying it to the transverse degrees of freedom of single photons.