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1. High-dimensional time-frequency entanglement in a singly-filtered biphoton frequency comb

   https://doi.org/10.1038/s42005-023-01370-2  

   Cheng, Xiang; Chang, Kai-Chi; Sarihan, Murat Can; Mueller, Andrew; Spiropulu, Maria; Shaw, Matthew D; Korzh, Boris; Faraon, Andrei; Wong, Franco_N C; Shapiro, Jeffrey H; et al (December 2023, Communications Physics)

   Abstract High-dimensional quantum entanglement is a cornerstone for advanced technology enabling large-scale noise-tolerant quantum systems, fault-tolerant quantum computing, and distributed quantum networks. The recently developed biphoton frequency comb (BFC) provides a powerful platform for high-dimensional quantum information processing in its spectral and temporal quantum modes. Here we propose and generate a singly-filtered high-dimensional BFC via spontaneous parametric down-conversion by spectrally shaping only the signal photons with a Fabry-Pérot cavity. High-dimensional energy-time entanglement is verified through Franson-interference recurrences and temporal correlation with low-jitter detectors. Frequency- and temporal- entanglement of our singly-filtered BFC is then quantified by Schmidt mode decomposition. Subsequently, we distribute the high-dimensional singly-filtered BFC state over a 10 km fiber link with a post-distribution time-bin dimension lower bounded to be at least 168. Our demonstrations of high-dimensional entanglement and entanglement distribution show the singly-filtered quantum frequency comb’s capability for high-efficiency quantum information processing and high-capacity quantum networks. 

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2. 648 Hilbert-space dimensionality in a biphoton frequency comb: entanglement of formation and Schmidt mode decomposition

   https://doi.org/10.1038/s41534-021-00388-0  

   Chang, Kai-Chi; Cheng, Xiang; Sarihan, Murat Can; Vinod, Abhinav Kumar; Lee, Yoo Seung; Zhong, Tian; Gong, Yan-Xiao; Xie, Zhenda; Shapiro, Jeffrey H.; Wong, Franco N.; et al (December 2021, npj Quantum Information)

   null (Ed.)

   Abstract Qudit entanglement is an indispensable resource for quantum information processing since increasing dimensionality provides a pathway to higher capacity and increased noise resilience in quantum communications, and cluster-state quantum computations. In continuous-variable time–frequency entanglement, encoding multiple qubits per photon is only limited by the frequency correlation bandwidth and detection timing jitter. Here, we focus on the discrete-variable time–frequency entanglement in a biphoton frequency comb (BFC), generating by filtering the signal and idler outputs with a fiber Fabry–Pérot cavity with 45.32 GHz free-spectral range (FSR) and 1.56 GHz full-width-at-half-maximum (FWHM) from a continuous-wave (cw)-pumped type-II spontaneous parametric downconverter (SPDC). We generate a BFC whose time-binned/frequency-binned Hilbert space dimensionality is at least 324, based on the assumption of a pure state. Such BFC’s dimensionality doubles up to 648, after combining with its post-selected polarization entanglement, indicating a potential 6.28 bits/photon classical-information capacity. The BFC exhibits recurring Hong–Ou–Mandel (HOM) dips over 61 time bins with a maximum visibility of 98.4% without correction for accidental coincidences. In a post-selected measurement, it violates the Clauser–Horne–Shimony–Holt (CHSH) inequality for polarization entanglement by up to 18.5 standard deviations with an S -parameter of up to 2.771. It has Franson interference recurrences in 16 time bins with a maximum visibility of 96.1% without correction for accidental coincidences. From the zeroth- to the third-order Franson interference, we infer an entanglement of formation ( E of ) up to 1.89 ± 0.03 ebits—where 2 ebits is the maximal entanglement for a 4 × 4 dimensional biphoton—as a lower bound on the 61 time-bin BFC’s high-dimensional entanglement. To further characterize time-binned/frequency-binned BFCs we obtain Schmidt mode decompositions of BFCs generated using cavities with 45.32, 15.15, and 5.03 GHz FSRs. These decompositions confirm the time–frequency scaling from Fourier-transform duality. Moreover, we present the theory of conjugate Franson interferometry—because it is characterized by the state’s joint-temporal intensity (JTI)—which can further help to distinguish between pure-state BFC and mixed state entangled frequency pairs, although the experimental implementation is challenging and not yet available. In summary, our BFC serves as a platform for high-dimensional quantum information processing and high-dimensional quantum key distribution (QKD). 

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3. Generation and characterization of ultrabroadband polarization–frequency hyperentangled photons

   https://doi.org/10.1364/OL.503127  

   Lu, Hsuan-Hao; Alshowkan, Muneer; Myilswamy, Karthik V.; Weiner, Andrew M.; Lukens, Joseph M.; Peters, Nicholas A. (January 2023, Optics Letters)

   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. 

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

   https://doi.org/10.1038/s41467-022-31639-z  

   Lu, Hsuan-Hao; Myilswamy, Karthik V.; Bennink, Ryan S.; Seshadri, Suparna; Alshaykh, Mohammed S.; Liu, Junqiu; Kippenberg, Tobias J.; Leaird, Daniel E.; Weiner, Andrew M.; Lukens, Joseph M. (December 2022, Nature Communications)

   Abstract 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 Si 3 N 4 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. 

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5. An accurate treatment of scattering and diffusion in piecewise power-law models for cosmic ray and radiation/neutrino transport

   https://doi.org/10.1093/mnras/stac3283  

   Hopkins, Philip F (December 2022, Monthly Notices of the Royal Astronomical Society)

   ABSTRACT A popular numerical method to model the dynamics of a ‘full spectrum’ of cosmic rays (CRs), also applicable to radiation/neutrino hydrodynamics, is to discretize the spectrum at each location/cell as a piecewise power law in ‘bins’ of momentum (or frequency) space. This gives rise to a pair of conserved quantities (e.g. CR number and energy) that are exchanged between cells or bins, which in turn give the update to the normalization and slope of the spectrum in each bin. While these methods can be evolved exactly in momentum-space (e.g. considering injection, absorption, continuous losses/gains), numerical challenges arise dealing with spatial fluxes, if the scattering rates depend on momentum. This has often been treated either by neglecting variation of those rates ‘within the bin,’ or sacrificing conservation – introducing significant errors. Here, we derive a rigorous treatment of these terms, and show that the variation within the bin can be accounted for accurately with a simple set of scalar correction coefficients that can be written entirely in terms of other, explicitly evolved ‘bin-integrated’ quantities. This eliminates the relevant errors without added computational cost, has no effect on the numerical stability of the method, and retains manifest conservation. We derive correction terms both for methods that explicitly integrate flux variables (e.g. two-moment or M1-like) methods, as well as single-moment (advection-diffusion, FLD-like) methods, and approximate corrections valid in various limits. 

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