arXiv subjects

Joseph M. Lukens

Publications and source records attributed to Joseph M. Lukens.

At least 19 recordsLinked to original sources

arXiv2026

Induced random mixed states are symmetric Dirichlet mixtures

We establish an exact equivalence in distribution between $D$-dimensional random mixed states induced by partial traces over $K$-dimensional environments and the Mai-Alquier distribution, a mixture of $K$ independent Haar-random pure states weighted by a symmetric Dirichlet distribution. This identification recasts a class of expectation values for induced ensembles into calculations involving Dirichlet moments and low-order Haar averages on a single-system state space. As applications, we recover exact purity moments up to fourth order, derive the mean Hilbert--Schmidt distance between independent induced ensembles with possibly different environment dimensions, and obtain exact average determinants. These results provide a unified and constructive perspective on induced random mixed states and on the evaluation of quantities such as purity moments, overlaps, and determinants.

quant-ph↗

arXiv2026

Real-time heralded non-Gaussian teleportation resource-state generator

Quantum teleportation is a fundamental quantum communications primitive that requires an entangled resource state. In the continuous-variable regime, non-Gaussian entangled resources have been shown theoretically to improve teleportation fidelity compared to Gaussian squeezed vacuum. We experimentally demonstrate a heralded two-mode resource state for non-Gaussian teleportation capable of real-time use. We characterize this state with two-mode homodyne tomography showing it has fidelity $F=0.973\pm 0.005$ with the expected resource state. Real-time use is enabled by a photon-subtraction orchestrator system performing live coincidence detection and outputting low-jitter and low-latency heralding signals. Live collection of real-time quadrature measurements of photon-subtracted states is enabled by the development of a synchronized homodyne detection server, where the orchestrator system queries the server to collect the real-time quadrature samples corresponding to the heralded state. These results demonstrate significant advancement in enabling the use of heralded non-Gaussian states in quantum networking protocols, especially in the context of quantum repeaters, non-Gaussian quantum sensing, and measurement-based quantum computing.

quant-ph↗

arXiv2026

Quantum-Classical Coexistence Network Tomography

Quantum-classical coexistence networks (QCNs) share optical fiber between quantum and classical signals via wavelength-division multiplexing, offering a practical path to quantum communication over existing telecom infrastructure. However, co- and counter-propagating classical traffic introduce distinct depolarization noise, complicating channel characterization. We develop a tomography framework that infers per-link channel parameters of a QCN from end-to-end measurements alone. We first model each coexisting fiber by decomposing the signal evolution into photon loss, successful transmission, and three direction-dependent depolarization components. We then derive closed-form link-level estimators, and extend the approach to star-topology networks through a system of multiplicative equations across end-node pairs, together with a simple classical-signal-direction-switching protocol that resolves the remaining unknowns. On single-link experimental testbed data, we recover per-link depolarization probabilities accurately, with estimated process fidelities closely tracking the Bayesian-process-tomography baseline across multiple fiber lengths and wavelengths; residual gaps reflect the depolarization-only approximation. Absent a multi-link coexistence testbed, we validate the star-network estimators on emulated paths built from measured single-link channels. We further extend the framework in two directions: (i) a channel model that factorizes the coexisting fiber into a depolarizing-with-loss signal channel and a Raman-noise-injection channel on separate optical modes -- a completely-positive, trace-preserving tensor product -- whose link observables reduce exactly to our basic model; and (ii) a generalization to arbitrary topologies via a peeling algorithm (trees) and a least-squares estimator (meshes), validated by Monte-Carlo simulations on tree and cyclic-mesh networks.

cs.IT↗

arXiv2026

A quantum game of telephone

Characterizing multinode quantum networks without ubiquitous local entanglement sources presents significant experimental challenges. We introduce ``quantum telephone,'' an iterative ancilla-assisted process tomography protocol that leverages intermediate detection events, effectively treating previously probed links as ancillae for subsequent links. Implemented on a deployed multinode fiber network, we observe noisy intermediate channels create fundamental parameter degeneracies that compound inference errors under sequential estimation. Counterintuitively, the inclusion of downstream near-unitary channels provides boundary constraints that, when used in tandem with global inference, can resolve ambiguity in channels earlier in the sequence. By compensating for localized information loss, this approach obviates the strict full-rank requirements of standard ancilla-assisted process tomography, even when intermediate states become completely depolarized. Overall, quantum telephone offers a hardware-efficient and information-maximizing path toward characterizing complex quantum networks with limited resources.

quant-ph↗

arXiv2026

Re-examining the Role of State Texture in Gate Identification and Fixed-Point Resource Theories

A protocol for identifying controlled-NOT (CNOT) gates versus single-qubit-only gates in universal quantum circuits using randomized input states was recently shown to be intimately connected to the quantum resource of state texture. Here we revisit this gate identification protocol and demonstrate that a more general fidelity-based formulation succeeds for nearly all laboratory bases. We then examine a broader family of quantum resource theories, where a distinct resource theory can be defined for each choice of reference pure state, establishing core resource-theoretic requirements without the computational shortcut offered by the "grand sum" employed in the original formulation of state texture. By extending from single "resourceless" states to convex sets via a convex-roof construction, we recover single-qubit measures of known resource theories such as imaginarity and coherence. Finally, we introduce a family of "fixed-point resource theories" that includes fixed-point instances of the theories of state texture, genuine coherence, purity, and athermality. For these fixed-point resource theories we show that, under free operations, the fidelity-based lower bound is weakly monotonic, while specific violations of strong monotonicity are found for the convex-roof logarithmic measure.

quant-ph↗

arXiv2026

Efficient routing and spectrum allocation in arbitrary flex-grid entanglement networks

As practical quantum networks approach large-scale deployment, the need for efficient user-to-user frequency allocation is increasing, yet current approaches only provide partial solutions to the routing and spectrum allocation problem for an arbitrary quantum network. We address this challenge for repeater-less flex-grid quantum networks based on hyperentangled photons using an efficient three-stage pipeline combining leading tools in classical networking with recent advances in numerical optimization. First, double instantiations of Yen's algorithm obtain low-loss route candidates between each pair of users and the entanglement sources. Second, the advanced process optimizer (APOPT) obtains frequency channel allocations that maximize distribution rates under fidelity constraints. Finally, the constraint programming solver using satisfiability methods (CP-SAT) assigns specific frequency bins to each link, ensuring that there is no contention between frequencies from different sources. We numerically demonstrate this approach on a representative ring network and a Manhattan incumbent local exchange carrier topology, realizing significant improvements over prior genetic algorithm approaches in speed, accuracy, and scalability. Overall, this pipeline provides an efficient heuristic workflow for optimizing broadband entanglement distribution, applicable to arbitrarily connected quantum networks integrated within the existing lightwave infrastructure.

quant-ph↗

arXiv2026

Structured Factorization Approaches for Quantum State Tomography

Since the complexity of quantum state tomography (QST) scales exponentially with system size, exploiting priors such as low-rankness, tensor-network structures, and neural-network representations is essential for scalable QST in terms of sample complexity and parameter complexity. In this paper, we introduce a unified framework, termed structured factorization, that builds on BurerMonteiro-type factorization by parametrizing the density matrix as $FF^\dagger$, where the factor $F$ is constrained to belong to a structured model class. This factorization guarantees physical validity by construction while allowing a broad range of structural priors to be incorporated directly through the choice of the factor space, ranging from the generic Cholesky decomposition to low-rank matrices, matrix product operators, and neural density operators based on multilayer perceptron and transformer architectures. Building on this structured factorization framework, we formulate QST as an optimization problem over the factor space from measurement data. We first develop a unified statistical analysis of the sample complexity of least-squares estimation for a broad class of structured quantum states. We then propose a projected gradient descent method that operates directly on the factor space and accommodates a wide range of structural parametrizations and reconstruction objectives. To further exploit the geometry of the maximum-likelihood estimation formulation and the constraints on the factors, we derive a power method that yields a step-size-free algorithm with fast convergence, recovering Covers method as a special case when the factor is unconstrained.

quant-ph↗

arXiv2026

High-Dimensional Quantum Photonics: Roadmap

The field of high-dimensional quantum photonics involves the use of multimode photonic degrees-of-freedom such as the spatial, temporal, or spectral structure of light to encode multi-level quantum states. Recent years have seen rapid progress in the development of methods to generate, manipulate, and distribute such quantum states of light and their use in a range of quantum technology applications that offer practical advantages over conventional qubit-based approaches. High-dimensional quantum states of light encoded in photonic time-bins, frequency-bins, transverse-spatial modes, waveguide paths, and temporal modes have enabled noise-robust fundamental tests of quantum mechanics, error-resilient and high-capacity quantum communication protocols, andas well as efficient approaches for quantum information processing, to name just a few examples. However, research in this field has progressed fairly independently, with little exchange across different photonic degrees-of-freedom or between experiment and theory and no comprehensive comparison between degrees-of-freedom. This roadmap aims to bridge this gap by surveying progress in each area and identifying shared challenges and opportunities that cut across two or more photonic degrees-of-freedoms. We review early work and state-of-the-art experimental techniques under development for high-dimensional quantum states encoded in single and entangled photons, as well as theoretical tools for their measurement and certification. We outline the main outstanding challenges for theory and each experimental degree-of-freedom, identifying promising future directions of research that may enable these to be overcome. We end by discussing interconnections and shared challenges centered around their distribution, measurement, and manipulation, with a view towards their integration into next-generation quantum technology platforms and applications.

quant-ph↗

arXiv2026

High-resolution tunable frequency beamsplitter enabled by an integrated silicon pulse shaper

We demonstrate high-fidelity, tunable, and ultrafine-resolution on-chip frequency beamsplitters using a quantum frequency processor based on an integrated pulse shaper with six spectral channels. Near-ideal Hadamard gate performance is achieved, with fidelity F > 0.9995 and modified success probability P > 0.9621 maintained across frequency spacings from 2-5 GHz and down to as few as four spectral pulse shaper channels. The system's support of frequency spacings as narrow as 2 GHz significantly surpasses prior bulk demonstrations and enables arbitrary splitting ratios via spectral phase or modulation index control. These results establish a scalable and resource-efficient platform for integrated frequency-bin quantum photonics, opening new directions in quantum information processing, including densely parallel single-qubit operations and multidimensional gate implementations.

quant-ph↗

arXiv2026

Photonic Links for Spin-Based Quantum Sensors

A growing variety of optically accessible spin qubits have emerged in recent years as key components for quantum sensors, qubits, and quantum memories. However, the scalability of conventional spin-based quantum architectures remains limited by direct microwave delivery, which introduces thermal noise, electromagnetic cross-talk, and design constraints for cryogenic, high-field, and distributed systems. In this work, we present a unified framework for RF-over-fiber (RFoF) control of optically accessible spins through RFoF optically detected magnetic resonance (ODMR) spectroscopy of nitrogen-vacancy (NV) centers in diamond. The RFoF platform relies on an electro-optically modulated telecom-band laser that transmits microwave signals over fiber and a high-speed photodiode that recovers the RF waveform to drive NV center spin transitions. We obtain an RFoF efficiency of 1.81\% at 2.90~GHz, corresponding to $P_{\mathrm{RF,out}}=-0.7$~dBm. The RFoF architecture provides a path toward low-noise, thermally isolated, and cryo-compatible ODMR systems bridging conventional spin-based quantum sensing protocols with emerging distributed quantum technologies.

quant-ph↗

arXiv2026

A paradigm for universal quantum information processing with integrated acousto-optic frequency beamsplitters

Frequency-bin encoding offers tremendous potential in quantum photonic information processing, in which a single waveguide can support hundreds of lightpaths in a naturally phase-stable fashion. This stability, however, comes at a cost: arbitrary unitary operations can be realized by cascaded electro-optic phase modulators and pulse shapers, but require nontrivial numerical optimization for design and have thus far been limited to discrete tabletop components. In this article, we propose, formalize, and computationally evaluate a new paradigm for universal frequency-bin quantum information processing using acousto-optic scattering processes between distinct transverse modes. We show that controllable phase matching in intermodal processes enables 2$\times$2 frequency beamsplitters and transverse-mode-dependent phase shifters, which together comprise cascadable FRequency-transverse-mODe Operations (FRODOs) that can synthesize any unitary via analytical decomposition procedures. Modeling the performance of both random gates and discrete Fourier transforms, we demonstrate the feasibility of high-fidelity quantum operations with existing integrated photonics technology, highlighting prospects of parallelizable operations achieving 100\% bandwidth utilization. Our approach is realizable with CMOS technology, opening the door to scalable on-chip quantum information processing in the frequency domain.

quant-ph↗

arXiv2025

Comparing Homodyne and Heterodyne Tomography of Quantum States of Light

Non-Gaussian quantum states are critical resources in photonic quantum information processing, rendering their generation and characterization of increasing importance in quantum optics. In this work, we theoretically and numerically analyze the relative efficiency of homodyne versus heterodyne measurements for reconstructing non-Gaussian states, a major outstanding question in continuous-variable tomography. Combining a Fisher information-based formalism with simulated experiments, we find homodyne tomography to outperform heterodyne measurements for all non-Gaussian states tested, although the separation between the two modalities proves significantly narrower than suggested by the asymptotic Cramer-Rao lower bound. Our results should find use for optimizing measurement strategies in practical continuous-variable quantum systems.

quant-ph↗

arXiv2025

Beyond critical coupling: optimal design considerations for spontaneous four-wave mixing in microring resonators

We present a self-contained analytical model for biphoton generation in microring resonators. Encompassing both all-pass and add-drop geometries, identical and distinct pump and biphoton coupling coefficients, and continuous-wave and pulsed pumping, our interaction-picture-based approach reveals time-frequency biphoton correlations while also predicting absolute generation rates. Under continuous-wave excitation, we find critical coupling of both the pump and biphoton to maximize the rate of single photons extracted from the microring, whereas critical coupling of the pump but overcoupling of the biphoton maximize the two-photon rate. Under pulsed pumping, overcoupling of both pump and biphoton (to different degrees) maximizes photon extraction probabilities, albeit under a tradeoff with spectral factorability that we quantify via parameter scans over a range of coupler pairings. As a whole, our formalism should prove valuable for the practical design of integrated photon sources, merging a flexible and intuitive biphoton-centric depiction with quantitative predictions closely tied to experimental parameters.

quant-ph↗

arXiv2025

In situ quantum verification of polarization-stabilized optical channels

The active stabilization of polarization channels is a task of growing importance as quantum networks move to deployed demonstrations over existing fiber infrastructure. However, the uniquely strict requirements for high-fidelity qubit transmission complicate the extent to which classical solutions may apply to future quantum networks, particularly in terms of recognizing noise sources present in low-flux, nonunitary channels. Here we introduce a novel in situ benchmarking approach that augments a classical polarization tracking system, limited to unitary correction, with simultaneously transmitted quantum light for ancilla-assisted process tomography of the full quantum map. Implemented in a local-area quantum network, our method uses the reconstructed map both to validate the classical compensation and to expose noise sources it fails to capture. A sliding measurement window that continuously updates the estimated quantum process further increases sensitivity to rapid channel fluctuations. Our results should unlock new opportunities for in situ channel characterization in quantum-classical coexistence networks.

quant-ph↗

arXiv2025

Developing a practical model for noise in entangled photon detection

We develop a comprehensive model for the effective two-photon density matrix produced by a parametric source of entangled photon pairs under a variety of detector configurations commonly seen in a laboratory setting: two and four photon number-resolving (PNR) and threshold detectors. We derive the probability of obtaining a single coincidence assuming Poisson-distributed photon pairs, non-unit detection efficiency, and dark counts; obtain the effective density matrix; and use this quantity to compute the fidelity of the generated quantum state. The 4 PNR case admits an analytic result valid for any combination of parameters, while all other cases leverage low-efficiency approximations to arrive at closed-form expressions. Interestingly, our model reveals appreciable fidelity improvements from four detectors as opposed to two yet minimal advantages for PNR over threshold detectors in the regimes explored. Overall, our work provides a valuable tool for the quantitative design of two-photon experiments under realistic nonidealities.

quant-ph↗

arXiv2025

Scalable Bayesian Monte Carlo: fast uncertainty estimation beyond deep ensembles

This work introduces a new method designed for Bayesian deep learning called scalable Bayesian Monte Carlo (SBMC). The method is comprised of a model and an algorithm. The model interpolates between a point estimator and the posterior. The algorithm is a parallel implementation of sequential Monte Carlo sampler (SMC$_\parallel$) or Markov chain Monte Carlo (MCMC$_\parallel$). We collectively refer to these consistent (asymptotically unbiased) algorithms as Bayesian Monte Carlo (BMC), and any such algorithm can be used in our SBMC method. The utility of the method is demonstrated on practical examples: MNIST, CIFAR, IMDb. A systematic numerical study reveals that for the same wall-clock time as state-of-the-art (SOTA) methods like deep ensembles (DE), SBMC achieves comparable or better accuracy and substantially improved uncertainty quantification (UQ)--in particular, epistemic UQ. This is demonstrated on the downstream task of estimating the confidence in predictions, which can be used for reliability assessment or abstention decisions.

stat.ML↗

arXiv2025

Comparison of parallel SMC and MCMC for Bayesian deep learning

This work systematically compares parallel implementations of consistent (asymptotically unbiased) Bayesian deep learning algorithms: sequential Monte Carlo sampler (SMC$_\parallel$) or Markov chain Monte Carlo (MCMC$_\parallel$). We provide a proof of convergence for SMC$_\parallel$ showing that it theoretically achieves the same level of convergence as a single monolithic SMC sampler, while the reduced communication lowers wall-clock time. It is well-known that the first samples from MCMC need to be discarded to eliminate initialization bias, and that the number of discarded samples must grow like the logarithm of the number of parallel chains to control that bias for MCMC$_\parallel$. A systematic empirical numerical study on MNIST, CIFAR, and IMDb, reveals that parallel implementations of both methods perform comparably to non-parallel implementations in terms of performance and total cost, and also comparably to each other. However, both methods still require a large wall-clock time, and suffer from catastrophic non-convergence if they aren't run for long enough.

stat.ML↗

arXiv2025

Hybrid classical-quantum communication networks

Over the past several decades, the proliferation of global classical communication networks has transformed various facets of human society. Concurrently, quantum networking has emerged as a dynamic field of research, driven by its potential applications in distributed quantum computing, quantum sensor networks, and secure communications. This prompts a fundamental question: rather than constructing quantum networks from scratch, can we harness the widely available classical fiber-optic infrastructure to establish hybrid quantum-classical networks? This paper aims to provide a comprehensive review of ongoing research endeavors aimed at integrating quantum communication protocols, such as quantum key distribution, into existing lightwave networks. This approach offers the substantial advantage of reducing implementation costs by allowing classical and quantum communication protocols to share optical fibers, communication hardware, and other network control resources, arguably the most pragmatic solution in the near term. In the long run, classical communication will also reap the rewards of innovative quantum communication technologies, such as quantum memories and repeaters. Accordingly, our vision for the future of the Internet is that of heterogeneous communication networks thoughtfully designed for the seamless support of both classical and quantum communications.

quant-ph↗