Encoding quantum information in continuous variables is intrinsically faulty. Nevertheless, redundant qubits can be used for error correction, as proposed by Gottesman et al. [ Phys. Rev. A 64 012310 (2001)]. We show how to experimentally implement this encoding using time-frequency continuous degrees of freedom of photon pairs produced by spontaneous parametric down conversion. We illustrate our results using an integrated AlGaAs photon-pair source. We show how single-qubit gates can be implemented and finally propose a theoretical scheme for correcting errors in circuit-like and measurement-based architectures.

High-dimensional entangled states of light provide novel possibilities for quantum information, from fundamental tests of quantum mechanics to enhanced computation and communication protocols. In this context, the frequency degree of freedom combines the assets of robustness to propagation and easy handling with standard telecommunication components. Here, we use an integrated semiconductor chip to engineer the wavefunction and exchange statistics of frequency-entangled photon pairs directly at the generation stage, without post-manipulation. Tailoring the spatial properties of the pump beam allows generating frequency-anticorrelated, correlated and separable states, and to control the symmetry of the spectral wavefunction to induce either bosonic or fermionic behaviors. These results, obtained at room temperature and telecom wavelength, open promising perspectives for the quantum simulation of fermionic problems with photons on an integrated platform, as well as for communication and computation protocols exploiting antisymmetric high-dimensional quantum states.

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 we 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.

Hong-Ou-Mandel interferometry takes advantage of the quantum nature of two-photon interference to increase the resolution of precision measurements of time delays. Relying on few-photon probe states, this approach is applicable also in cases of extremely sensible samples and it achieves attosecond-scale (nanometer path length) resolution, which is relevant to cell biology and two-dimensional materials. 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. We find that grid states, characterized by a periodic structure of peaks in the chronocyclic Wigner function, can outperform standard biphoton states in sensing applications. The considered states can be feasibly produced with atomic photon sources, bulk nonlinear crystals and integrated photonic waveguide devices.

Despite the multitude of available methods, the characterization of ultrafast pulses remains a challenging endeavor, especially at the single-photon level. We introduce a pulse characterization scheme that maps the magnitude of its short-time Fourier transform. Contrary to many well-known solutions it does not require nonlinear effects and is therefore suitable for single-photon-level measurements. Our method is based on introducing a series of controlled time and frequency shifts, where the latter is performed via an electro-optic modulator allowing a fully-electronic experimental control. We characterized the full spectral and temporal width of a classical and single-photon-level pulse and successfully tested the applicability of the reconstruction algorithm of the spectral phase and amplitude. The method can be extended by implementing a phase-sensitive measurement and is naturally well-suited to partially-incoherent light.