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We report the experimental generation of all four frequency-bin Bell states in a single versatile setup via successive pumping of spontaneous parametric down-conversion with single and dual spectral lines. Our scheme utilizes intensity modulation to control the pump configuration and offers turn-key generation of any desired Bell state using only off-the-shelf telecommunication equipment. We employ Bayesian inference to reconstruct the density matrices of the generated Bell states, finding fidelities ≥97% for all cases. Additionally, we demonstrate the sensitivity of the frequency-bin Bell states to common-mode and differential-mode temporal delays traversed by the photons comprising the state-presenting the potential for either enhanced resolution or nonlocal sensing enabled by our complete Bell basis synthesizer.

Accurate control of two-level systems is a longstanding problem in quantum mechanics. One such quantum system is the frequency-bin qubit: a single photon existing in superposition of two discrete frequency modes. In this Letter, we demonstrate fully arbitrary control of frequency-bin qubits in a quantum frequency processor for the first time. We numerically establish optimal settings for multiple configurations of electro-optic phase modulators and pulse shapers, experimentally confirming near-unity mode-transformation fidelity for all fundamental rotations. Performance at the single-photon level is validated through the rotation of a single frequency-bin qubit to 41 points spread over the entire Bloch sphere, as well as tracking of the state path followed by the output of a tunable frequency beam splitter, with Bayesian tomography confirming state fidelities F_{ρ}>0.98 for all cases. Such high-fidelity transformations expand the practical potential of frequency encoding in quantum communications, offering exceptional precision and low noise in general qubit manipulation.

We report the experimental realization of high-fidelity photonic quantum gates for frequency-encoded qubits and qutrits based on electro-optic modulation and Fourier-transform pulse shaping. Our frequency version of the Hadamard gate offers near-unity fidelity (0.99998±0.00003), requires only a single microwave drive tone for near-ideal performance, functions across the entire C band (1530-1570 nm), and can operate concurrently on multiple qubits spaced as tightly as four frequency modes apart, with no observable degradation in the fidelity. For qutrits, we implement a 3×3 extension of the Hadamard gate: the balanced tritter. This tritter-the first ever demonstrated for frequency modes-attains fidelity 0.9989±0.0004. These gates represent important building blocks toward scalable, high-fidelity quantum information processing based on frequency encoding.

We extend orthogonal optical coding, previously applied to multiuser classical communication networks, to entangled photons. Using a pulse shaper and sum-frequency generation for ultrafast coincidence detection, we demonstrate encoding and decoding of biphoton wave packets. Applying one code to the signal photon spreads the wave packet in time and creates a null at zero delay; filtering the idler with the matched code recovers a narrow correlation peak, whereas applying any other code leaves the wave packet spread. Our results could prove useful in the development of code-based quantum communication networks.

We demonstrate dispersion cancellation of entangled photons for arbitrary spectral orders, generalizing Franson cancellation typically considered in second order alone. Employing ultrafast coincidence detection based on sum-frequency generation in a periodically poled lithium niobate waveguide with a record-high pair conversion efficiency of 10(-5), we verify cancellation of dispersion up to fifth order. Cancellation of odd-order phase is experimentally shown to require identical signal and idler dispersion coefficients, in contrast to even-order phase, which cancels with opposite signs. These results are especially important for future work on ultrabroadband biphotons.