LOA Seminar: Nicolas Fabre (Telecom Paris): Time-frequency quantum information processing

In this talk, I will discuss the use of time and frequency degrees of freedom as continuous variables of single photons in quantum optics. Such a degree of freedom is generally discretized into modes for experimental reasons, but it is not a physical requirement. The origin of the quantumness of the time and frequency variables can be explained because of the non- commutativity of time and frequency operators – which can be defined properly when restricted to the one photon per mode subspace. As a consequence, I will show that frequency and time operators can be used to define a universal set of gates in this particular subspace. The physical implementation of the gates as well as their effect on single photon states will be discussed. The difficulty in implementing a given operation does not come from the dimensionality of the Hilbert space involved, but rather from the considered encoding. Thus, time-frequency entanglement Gaussian operations are difficult to implement deterministically. 

We will then discuss how the time-frequency as continuous variables can be used to describe naturally time or frequency parameter estimation protocols. Hong-Ou-Mandel interferometry takes advantage of the quantum nature of two-photon interference to increase the resolution of precision measurements of time delays. Here, we theoretically analyze how the precision of Hong-Ou-Mandel interferometers can be significantly improved by engineering the spectral distribution of two-photon probe states. In particular, we assess the metrological power of different classes of biphoton states with non-Gaussian time-frequency spectral distributions, considering the estimation of both time and frequency shifts. After discussing the spectral engineering of photon pairs, we will discuss the use of more general quantum states possessing a higher number of photons for estimating time shifts. We will show that the particle-number and time-frequency degree of freedom are intertwined for quantifying the ultimate precision achievable by quantum means. Increasing the number of photons of a large entangled EPR probe state actually increases the noise coming from the frequency continuous variable hence deteriorating the precision over the estimation of a time shift.