Two-mode squeezing over deployed fiber coexisting with conventional communications.

Squeezed light is a crucial resource for continuous-variable (CV) quantum information science. Distributed multi-mode squeezing is critical for enabling CV quantum networks and distributed quantum sensing. To date, multi-mode squeezing measured by homodyne detection has been limited to single-room experiments without coexisting classical signals, i.e., on "dark" fiber. Here, after distribution through separate fiber spools (5 km), -0.9 ± 0.1-dB coexistent two-mode squeezing is measured. Moreover, after distribution through separate deployed campus fibers (about 250 m and 1.2 km), -0.5 ± 0.1-dB coexistent two-mode squeezing is measured. Prior to distribution, the squeezed modes are each frequency multiplexed with several classical signals-including the local oscillator and conventional network signals-demonstrating that the squeezed modes do not need dedicated dark fiber. After distribution, joint two-mode squeezing is measured and recorded for post-processing using triggered homodyne detection in separate locations. This demonstration enables future applications in quantum networks and quantum sensing that rely on distributed multi-mode squeezing.

Generation and characterization of ultrabroadband polarization-frequency hyperentangled photons.

We generate ultrabroadband photon pairs entangled in both polarization and frequency bins through an all-waveguided Sagnac source covering the entire optical C- and L-bands (1530-1625 nm). We perform comprehensive characterization of high-fidelity states in multiple dense wavelength-division multiplexed channels, achieving full tomography of effective four-qubit systems. Additionally, leveraging the inherent high dimensionality of frequency encoding and our electro-optic measurement approach, we demonstrate the scalability of our system to higher dimensions, reconstructing states in a 36-dimensional Hilbert space consisting of two polarization qubits and two frequency-bin qutrits. Our findings hold potential significance for quantum networking, particularly dense coding and entanglement distillation in wavelength-multiplexed quantum networks.

High-dimensional discrete Fourier transform gates with a quantum frequency processor.

The discrete Fourier transform (DFT) is of fundamental interest in photonic quantum information, yet the ability to scale it to high dimensions depends heavily on the physical encoding, with practical recipes lacking in emerging platforms such as frequency bins. In this article, we show that d-point frequency-bin DFTs can be realized with a fixed three-component quantum frequency processor (QFP), simply by adding to the electro-optic modulation signals one radio-frequency harmonic per each incremental increase in d. We verify gate fidelity F W>0.9997 and success probability P W>0.965 up to d = 10 in numerical simulations, and experimentally implement the solution for d = 3, utilizing measurements with parallel DFTs to quantify entanglement and perform tomography of multiple two-photon frequency-bin states. Our results furnish new opportunities for high-dimensional frequency-bin protocols in quantum communications and networking.

Broadband polarization-entangled source for C+L-band flex-grid quantum networks.

The rising demand for transmission capacity in optical networks has motivated steady interest in expansion beyond the standard C-band (1530-1565 nm) into the adjacent L-band (1565-1625 nm) for an approximate doubling of capacity in a single stroke. However, in the context of quantum networking, the L-band has yet to be fully leveraged with the suite of advanced tools for characterization and management available from classical lightwave communications. In this work, we demonstrate an ultrabroadband two-photon source integrating both C- and L-band wavelength-selective switches for complete control of spectral routing and allocation across 7.5 THz in a single setup. Polarization state tomography of all 150 pairs of 25-GHz-wide channels reveals an average fidelity of 0.98 and total distillable entanglement greater than 181 kebits/s. This source is explicitly designed for flex-grid optical networks and can facilitate optimal utilization of entanglement resources across the full C+L-band.

Complete Frequency-Bin Bell Basis Synthesizer.

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.

Agile frequency transformations for dense wavelength-multiplexed communications.

The broad bandwidth and spectral efficiency of photonics has facilitated unparalleled speeds in long-distance lightwave communication. Yet efficient routing and control of photonic information without optical-to-electrical conversion remains an ongoing research challenge. Here, we demonstrate a practical approach for dynamically transforming the carrier frequencies of dense wavelength-division-multiplexed data. Combining phase modulators and pulse shapers into an all-optical frequency processor, we realize both cyclic channel hopping and 1-to-N broadcasting of input data streams for systems with N = 2 and N = 3 users. Our method involves no optical-to-electrical conversion and enables low-noise, reconfigurable routing of fiber-optic signals with in principle arbitrary wavelength operations in a single platform, offering new potential for low-latency all-optical networking.

Fully Arbitrary Control of Frequency-Bin Qubits.

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.

Quantum frequency combs and Hong-Ou-Mandel interferometry: the role of spectral phase coherence.

The Hong-Ou-Mandel interferometer is a versatile tool for analyzing the joint properties of photon pairs, relying on a truly quantum interference effect between two-photon probability amplitudes. While the theory behind this form of two-photon interferometry is well established, the development of advanced photon sources and exotic two-photon states has highlighted the importance of quantifying precisely what information can and cannot be inferred from features in a Hong-Ou-Mandel interference trace. Here we examine Hong-Ou-Mandel interference with regard to a particular class of states, so-called quantum frequency combs, and place special emphasis on the role spectral phase plays in these measurements. We find that this form of two-photon interferometry is insensitive to the relative phase between different comb line pairs. This is true even when different comb line pairs are mutually coherent at the input of a Hong-Ou-Mandel interferometer and the fringe patterns display sharp temporal features. Consequently, Hong-Ou-Mandel interference cannot speak to the presence of high-dimensional frequency-bin entanglement in two-photon quantum frequency combs.

Arbitrary shaping of biphoton correlations using near-field frequency-to-time mapping.

Frequency-to-time mapping (FTM) is a technique used to mirror the spectral shape of an optical waveform in the time domain. The regular approach, based on the far-field condition, requires large amounts of dispersion for successful mapping. However, when the far-field condition is insurmountable for achieving a desired temporal profile, another technique, termed near-field FTM, can be employed to assist with the mapping. For the first time, we demonstrate a shaper-assisted near-field FTM using entangled photon pairs. By pre-modifying the two-photon spectral amplitude and phase before propagating the photon pairs through dispersion, we can achieve arbitrary temporal correlations in the near-field region.

Frequency-domain Hong-Ou-Mandel interference with linear optics.

The Hong-Ou-Mandel (HOM) interference is one of the most fundamental quantum-mechanical effects that reveal a nonclassical behavior of single photons. Two identical photons that are incident on the input ports of an unbiased beam splitter always exit the beam splitter together from the same output port, an effect referred to as photon bunching. In this Letter, we utilize a single electro-optic phase modulator as a probabilistic frequency beam splitter, which we exploit to observe HOM interference between two photons that are in different spectral modes, yet are identical in other characteristics. Our approach enables linear optical quantum information processing protocols using the frequency degree of freedom in photons such as quantum computing techniques with linear optics.

Electro-Optic Frequency Beam Splitters and Tritters for High-Fidelity Photonic Quantum Information Processing.

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.

Dispersion-corrected frequency-resolved optical gating.

The phase retrieval algorithm of a frequency-resolved optical gating (FROG) is generalized to handle traces seriously distorted by group delay dispersion and non-uniform phase-matching spectra arising from the nonlinear crystal. In our proof-of-concept experiments, 15 mm thick aperiodically poled lithium niobate was employed in FROG, and successfully reconstructed chirped signal pulses were actually stretched by >5 times inside the crystal. This method is particularly promising in the measurement of weak few-cycle pulses produced by supercontinuum generation in fibers.

Bayesian tomography of high-dimensional on-chip biphoton frequency combs with randomized measurements.

Owing in large part to the advent of integrated biphoton frequency combs, 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 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 solution that employs a pulse shaper and electro-optic phase modulator to perform random operations instead of mixing in a prescribed manner. We successfully verify the entanglement and reconstruct the full density matrix of biphoton frequency combs generated from an on-chip Si3N4 microring resonator in up to an 8 × 8-dimensional two-qudit Hilbert space, the highest dimension to date for frequency bins. More generally, our employed Bayesian statistical model can be tailored to a variety of quantum systems with restricted measurement capabilities, forming an opportunistic tomographic framework that utilizes all available data in an optimal way.