Time-frequency as quantum continuous variables

TL;DR

This paper introduces a second quantization framework for frequency-based continuous variables quantum computation using single photons, defining new operators and gates that enable quantum information processing similar to polarization-based methods.

Contribution

It develops a novel second quantization approach to frequency and time variables, establishing their use as universal quantum computation tools within the single photon subspace.

Findings

Frequency and time operators satisfy canonical commutation relations.

Universal quantum gates can be constructed using these operators.

Frequency and time variables can implement quantum protocols akin to polarization.

Abstract

We present a second quantization description of frequency-based continuous variables quantum computation in the subspace of single photons. For this, we define frequency and time operators using the free field Hamiltonian and its Fourier transform, and show that these observables, when restricted to the one photon per mode subspace, reproduce the canonical position-momentum commutation relations. As a consequence, frequency and time operators can be used to define a universal set of gates in this particular subspace. We discuss the physical implementation of these gates as well as their effect on single photon states, and show that frequency and time variables can also be used to implement continuous variables quantum information protocols, in the same way than polarization is currently used as a two-dimensional quantum variable.