Qubit entanglement is a valuable resource for quantum information processing, where increasing its dimensionality provides a pathway towards higher capacity and increased error resilience in quantum communications, cluster computation and quantum phase measurements. Time-frequency entanglement, a continuous variable subspace, enables the high-dimensional encoding of multiple qubits per particle, bounded only by the spectral correlation bandwidth and readout timing jitter. Extending from a dimensionality of two in discrete polarization variables, here we demonstrate a hyperentangled, mode-locked, biphoton frequency comb with a time-frequency Hilbert space dimensionality of at least 648. Hong-Ou-Mandel revivals of the biphoton qubits are observed with 61 time-bin recurrences, biphoton joint spectral correlations over 19 frequency-bins, and an overall interference visibility of the high-dimensional qubits up to 98.4%. We describe the Schmidt mode decomposition analysis of the high-dimensional entanglement, in both time- and frequency-bin subspaces, not only verifying the entanglement dimensionality but also examining the time-frequency scaling. We observe a Bell violation of the high-dimensional qubits up to 18.5 standard deviations, with recurrent correlation-fringe Clauser-Horne-Shimony-Holt S-parameter up to 2.771. Our biphoton frequency comb serves as a platform for dense quantum information processing and high-dimensional quantum key distribution.
We report results of two-photon quantum holography where spatial information stored in phase holograms is retrieved by measuring quantum spatial correlations between two images formed by spatially entangled twin photons with a dimensionality of 1790 in the two-dimensional transverse space. In our experiments, the entire flux of spontaneous down converted photons illuminates the phase holograms and the photons of pairs signal-idler transmitted by the holograms are detected separately in far field on two electron-multiplying charge coupled device cameras.
Frequency-bin qudits constitute a promising tool for quantum information processing, but their high dimensionality can make for tedious characterization measurements. Here we introduce and compare compressive sensing and Bayesian mean estimation for recovering the spectral correlations of entangled photon pairs. Using a conventional compressive sensing algorithm, we reconstruct joint spectra with up to a 26-fold reduction in measurement time compared to the equivalent raster scan. Applying a custom Bayesian model to the same data, we then additionally realize reliable and consistent quantifica…
A frequency-multiplexed entangled photon pair and a high-dimensional hyperentangled photon pair are useful to realize a high-capacity quantum communication. A biphoton frequency comb (BFC) with entanglement can be used to prepare both states. We demonstrate polarization entangled BFCs with over 1400 frequency modes, which is approximately two orders of magnitude larger than those of earlier entangled BFCs, by placing a singly resonant periodically poled LiNbO3 waveguide resonator within a Sagnac loop. The BFCs are demonstrated by measuring the joint spectral intensity, cross-correlation, and a…
We investigate in a general form entanglement of biphoton qutrits and ququarts, i.e. states formed in the processes of collinear and, correspondingly, degenerate and non-degenerate Spontaneous Parametric Down-Conversion. Indistinguishability of photons and, for ququarts, joint presence of the frequency and and polarization entanglement are fully taken into account. In the case of qutrits the most general 3-parametric families of maximally entangled and non-entangled states are found, and anti-correlation of the degree of entanglement and polarization is shown to occur and to be characterized b…
Encoding quantum information in continuous variables is intrinsically faulty. Nevertheless, redundant qubits can be used for error correction, as proposed by Gottesman, Kitaev and Preskill in Phys. Rev. A \textbf{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 experimentally illustrate our results using an integrated AlGaAs photon pairs source. We show how single qubit gates can be implemented and finally propose a theoretical scheme for correcting…
Owing in large part to the advent of integrated biphoton frequency combs (BFCs), recent years have witnessed increased attention to quantum information processing in the frequency domain for its inherent high dimensionality and entanglement compatible with fiber-optic networks. Quantum state tomography (QST) of such states, however, has required complex and precise engineering of active frequency mixing operations, which are difficult to scale. To address these limitations, we propose a novel solution that employs a pulse shaper and electro-optic phase modulator (EOM) to perform random operati…
We investigate the time-frequency signatures of an on-chip biphoton frequency comb (BFC) generated from a silicon nitride microring resonator. Using a Franson interferometer, we examine the multifrequency nature of the photon pair source in a time entanglement measurement scheme; having multiple frequency modes from the BFC results in a modulation of the interference pattern. This measurement together with a Schmidt mode decomposition shows that the generated continuous variable energy-time entangled state spans multiple pair-wise modes. Additionally, we demonstrate nonlocal dispersion cancell…
Quantum entanglement is a fundamental resource for secure information processing and communications, where hyperentanglement or high-dimensional entanglement has been separately proposed towards high data capacity and error resilience. The continuous-variable nature of the energy-time entanglement makes it an ideal candidate for efficient high-dimensional coding with minimal limitations. Here we demonstrate the first simultaneous high-dimensional hyperentanglement using a biphoton frequency comb to harness the full potential in both energy and time domain. The long-postulated Hong-Ou-Mandel qu…
Phase modulation has emerged as a technique to create and manipulate high-dimensional frequency-bin entanglement. A necessary step to extending this technique to depolarized channels, such as those in a quantum networking environment, is the ability to perform phase modulation independent of photon polarization. This also necessary to harness hypertanglement in the polarization and frequency degrees of freedom for operations like Bell state discrimination. However, practical phase modulators are generally sensitive to the polarization of light and this makes them unsuited to such applications.…
We demonstrate a chip-integrated semiconductor source that combines polarization and frequency entanglement, allowing the generation of entangled biphoton states in a hybrid degree of freedom without postmanipulation. Our AlGaAs device is based on type-II spontaneous parametric down-conversion (SPDC) in a counterpropagating phase-matching scheme, in which the modal birefringence lifts the degeneracy between the two possible nonlinear interactions. This allows the direct generation of polarization-frequency entangled photons, at room temperature and telecom wavelength, and in two distinct spati…
Photonic time-frequency entanglement is a promising resource for quantum information processing technologies. We investigate swapping of continuous-variable entanglement in the time-frequency degree of freedom using three-wave mixing in the low-gain regime with the aim of producing heralded biphoton states with high purity and low multi-pair probability. Heralding is achieved by combining one photon from each of two biphoton sources via sum-frequency generation to create a herald photon. We present a realistic model with pulsed pumps, investigate the effects of resolving the frequency of the h…
Nonclassical photon sources of high brightness are key components of quantum communication technologies. We here demonstrate the generation of narrowband, nonclassical photon pairs by employing spontaneous four-wave mixing in an optically-dense ensemble of cold atoms within a hollow-core fiber. The brightness of our source approaches the limit of achievable generated spectral brightness at which successive photon pairs start to overlap in time. For a generated spectral brightness per pump power of up to $2\times 10^{9} \ \textrm{pairs/(s MHz mW)}$ we observe nonclassical correlations at pump p…
We demonstrate a two-photon interference experiment for phase coherent biphoton frequency combs (BFCs), created through spectral amplitude filtering of biphotons with a continuous broadband spectrum. By using an electro-optic phase modulator, we project the BFC lines into sidebands that overlap in frequency. The resulting high-visibility interference patterns provide an approach to verify frequency-bin entanglement even with slow single-photon detectors; we show interference patterns with visibilities that surpass the classical threshold for qubit and qutrit states. Additionally, we show that …
Recent theoretical investigations on tomographic entanglement indicators have showcased the advantages of the tomographic approach in the context of continuous-variable (CV), spin and hybrid quantum systems. Direct estimation of entanglement using experimental data from the IBM quantum computing platform and NMR experiments have also been carried out in earlier work. A similar investigation in the context of CV systems is necessary to fully assess the utility of our tomographic approach. In this paper, we highlight the advantages of our approach in the context of experiments reported in the li…
The Bell basis, a set of maximally entangled biphoton state, is a critical prerequisite towards quantum information processing, and many quantum applications have highlighted the requirement for the manipulation of high-dimensional Bell basis. While the Bell states can be created by using ingenious single-photon quantum gates, its implementation complexity in higher dimensions is significantly increased. Here we present an elaborate approach to show that the adaptive pump modulation enable the efficient preparation of Bell basis in arbitrary-dimensional Hilbert space. A complete set of four-di…
We show that, when the integration time of the single photon detectors is longer than the correlation time of the biphoton, the attainable spatial resolution in ghost imaging with entangled signal idler pairs generated in type II spontaneous parametric down conversion is limited by the angular spread of single-frequency-signal idler pairs. If, however, the detector integration time is shorter than the biphoton correlation time, the transverse k-vectors of different spectral components combine coherently in the image, improving the spatial resolution.
Cavity-enhanced single photon sources exhibit mode-locked biphoton states with comb-like correlation functions. Our ultrabright source additionally emits either single photon pairs or two-photon NOON states, dividing the output into an even and an odd comb respectively. With even-comb photons we demonstrate revivals of the typical non-classical Hong-Ou-Mandel interference up to the 84th dip, corresponding to a path length difference exceeding 100 m. With odd-comb photons we observe single photon interference fringes modulated over twice the displacement range of the Hong-Ou-Mandel interference…
Quantum walks in atomic systems, owing to their continuous nature, are especially well-suited for the simulation of many-body physics and can potentially offer an exponential speedup in solving certain black box problems. Photonics offers an alternate route to simulating such nonclassical behavior in a more robust platform. However, in photonic implementations to date, an increase to the depth of a continuous quantum walk requires modifying the footprint of the system. Here we report continuous walks of a two-photon quantum frequency comb with entanglement across multiple dimensions. The coupl…
High-dimensional quantum states are promising resources for quantum communication and processing. In this context the frequency degree of freedom of light combines the advantages of robustness and easy handling with standard classical telecommunication components. In this work we propose a method to generate and control the symmetry of broadband biphoton frequency states, based on the interplay of cavity effects and relative temporal delay between the two photons of each pair. We demonstrate it using an integrated AlGaAs semiconductor platform producing quantum frequency combs, working at room…
We demonstrate a novel scheme to generate frequency-entangled qudits with dimension number higher than 10 and to distribute them over optical fibers of 15 km in total length. This scheme combines the technique of spectral engineering of biphotons generated by spontaneous parametric down-conversion and the technique of spectrally resolved Hong-Ou-Mandel interference. We characterized the comb-like spectral correlation structures of the qudits by time of arrival measurement and correlated spectral intensity measurement. The generation and distribution of the distinct entangled frequency modes ma…
We predict that all-optically reconfigurable generation of photon pairs with tailored spatial entanglement can be realized via spontaneous parametric down-conversion in integrated nonlinear coupled waveguides. The required elements of the output quantum wavefunction are directly mapped from the amplitudes and phases of the classical laser pump inputs in each waveguide. This is achieved through special nonuniform domain poling, which locally inverts the sign of quadratic nonlinear susceptibility and accordingly shapes the interference of biphoton quantum states generated along the waveguides. W…
An efficient simulator for quantum systems is one of the original goals for the efforts to develop a quantum computer [1]. In recent years, synthetic dimension in photonics [2] have emerged as a potentially powerful approach for simulation that is free from the constraint of geometric dimensionality. Here we demonstrate a quantum-correlated synthetic crystal, based upon a coherently-controlled broadband quantum frequency comb produced in a chip-scale dynamically modulated lithium niobate microresonator. The time-frequency entanglement inherent with the comb modes significantly extends the dime…
