arXiv subjects

Brian T. Kirby

Publications and source records attributed to Brian T. Kirby.

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

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

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↗

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

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

Reducing classical communication costs in multiplexed quantum repeaters using hardware-aware quasi-local policies

Future quantum networks will have nodes equipped with multiple quantum memories, allowing for multiplexing and entanglement distillation strategies in order to increase fidelities and reduce waiting times for end-to-end entanglement distribution. In this work, we introduce \textit{quasi-local} policies for multiplexed quantum repeater chains. In fully-local policies, nodes make decisions based only on knowledge of their own states. In our quasi-local policies, nodes have increased knowledge of the state of the repeater chain, but not necessarily full, global knowledge. Our policies exploit the observation that for most decisions the nodes have to make, they only need to have information about the connected region of the chain they belong to, and not the entire chain. In this way, we not only obtain improved performance over local policies, but we reduce the classical communication (CC) costs inherent to global-knowledge policies. Our policies also outperform the well-known and widely studied nested purification and doubling swapping policy in practically relevant parameter regimes. We also carefully examine the role of entanglement distillation. Via analytical and numerical results, we identify the parameter regimes in which distillation makes sense and is useful. In these regimes, we also address the question: "Should we distill before swapping, or vice versa?" Finally, to provide further practical guidance, we propose an experimental implementation of a multiplexing-based repeater chain, and experimentally demonstrate the key element, a high-dimensional biphoton frequency comb. We then evaluate the anticipated performance of our multiplexing-based policies in such a real-world network through simulation results for two concrete memory platforms, namely rare-earth ions and diamond vacancies.

quant-ph↗

arXiv2025

Noiseless Loss Suppression for Entanglement Distribution

Recent work by Mičuda et al. (arXiv:1206.2852v1) suggests that pairing noiseless amplification with noiseless attenuation can conditionally suppress loss terms in the direct transmission of quantum states. Here we extend this work to entangled states: first, we explore bipartite states, specifically the two-mode squeezed vacuum (TMSV) and NOON states; and second, we examine M-partite states, concentrating on W and Greenberger-Horne-Zeilinger (GHZ) states. In analogy with the original proposal, our results demonstrate that in each case under consideration, a correct combination of attenuation and amplification techniques before and after transmission through a pure loss channel can restore the initial quantum state. However, we find that for both W and NOON states, the noiseless attenuation is redundant and not required to achieve loss term suppression. This work clarifies the role of noiseless attenuation when paired with noiseless amplification for entanglement distribution and provides an operational example of how GHZ and W state entanglement differs.

quant-ph↗

arXiv2025

Enhancing Quantum State Reconstruction with Structured Classical Shadows

Quantum state tomography (QST) remains the prevailing method for benchmarking and verifying quantum devices; however, its application to large quantum systems is rendered impractical due to the exponential growth in both the required number of total state copies and classical computational resources. Recently, the classical shadow (CS) method has been introduced as a more computationally efficient alternative, capable of accurately predicting key quantum state properties. Despite its advantages, a critical question remains as to whether the CS method can be extended to perform QST with guaranteed performance. In this paper, we address this challenge by introducing a projected classical shadow (PCS) method with guaranteed performance for QST based on Haar-random projective measurements. PCS extends the standard CS method by incorporating a projection step onto the target subspace. For a general quantum state consisting of $n$ qubits, our method requires a minimum of $O(4^n)$ total state copies to achieve a bounded recovery error in the Frobenius norm between the reconstructed and true density matrices, reducing to $O(2^n r)$ for states of rank $r<2^n$ -- meeting information-theoretic optimal bounds in both cases. For matrix product operator states, we demonstrate that the PCS method can recover the ground-truth state with $O(n^2)$ total state copies, improving upon the previously established Haar-random bound of $O(n^3)$. Simulation results further validate the effectiveness of the proposed PCS method.

quant-ph↗

arXiv2024

On the connection between least squares, regularization, and classical shadows

Classical shadows (CS) offer a resource-efficient means to estimate quantum observables, circumventing the need for exhaustive state tomography. Here, we clarify and explore the connection between CS techniques and least squares (LS) and regularized least squares (RLS) methods commonly used in machine learning and data analysis. By formal identification of LS and RLS "shadows" completely analogous to those in CS -- namely, point estimators calculated from the empirical frequencies of single measurements -- we show that both RLS and CS can be viewed as regularizers for the underdetermined regime, replacing the pseudoinverse with invertible alternatives. Through numerical simulations, we evaluate RLS and CS from three distinct angles: the tradeoff in bias and variance, mismatch between the expected and actual measurement distributions, and the interplay between the number of measurements and number of shots per measurement. Compared to CS, RLS attains lower variance at the expense of bias, is robust to distribution mismatch, and is more sensitive to the number of shots for a fixed number of state copies -- differences that can be understood from the distinct approaches taken to regularization. Conceptually, our integration of LS, RLS, and CS under a unifying "shadow" umbrella aids in advancing the overall picture of CS techniques, while practically our results highlight the tradeoffs intrinsic to these measurement approaches, illuminating the circumstances under which either RLS or CS would be preferred, such as unverified randomness for the former or unbiased estimation for the latter.

quant-ph↗

arXiv2024

Deployed quantum link characterization via Bayesian ancilla-assisted process tomography

The development of large-scale quantum networks requires reliable quantum channels, the quality of which can be quantified by the framework of quantum process tomography. In this work, we leverage ancilla-assisted process tomography and Bayesian inference to probe a 1.6 km deployed fiber-optic link. We send one of two polarization-entangled photons from Alice in one building to Bob in another, exploiting the local qubit as an ancilla system to characterize the corresponding quantum channel. Monitoring over a 24 h period returns a steady process fidelity of 95.1(1)%, while controllable spectral filtering with passbands from 0.025-4.38 THz finds fidelities that first increase, then level off with bandwidth, suggesting both stable operation with time and minimal polarization mode dispersion. To our knowledge, these results represent the first AAPT of a deployed quantum link, revealing a valuable tool for in situ analysis of entanglement-based quantum networks.

quant-ph↗

arXiv2024

Polarization-Entanglement Dynamics in Optical Fibers: Mitigating Decay in the Non-Markovian Regime with Dynamical Decoupling

Future distributed quantum systems and networks are likely to rely, at least in part, on the existing fiber infrastructure for entanglement distribution; hence, a precise understanding of the adverse effects of imperfections in optical fibers on entanglement is essential to their operation. Here, we consider maximally entangled polarization qubits and study the decay of the entanglement caused by spatial fluctuations in the refractive index of optical fibers. We study this entanglement dynamics using the spin-boson model and numerically solve our system of equations using the hierarchical equations of motion (HEOM) formalism. We show that within the range of practically relevant system parameters, our developed model exhibits both Markovian and non-Markovian entanglement decay behavior. Further, to counter the observed entanglement decay, we propose the implementation of dynamical decoupling in optical fibers using spaced half waveplates. In particular, we numerically model the time-dependent Hamiltonians of the Carr-Purcell-Meiboom-Gill and Uhrig dynamical decoupling schemes and show a reduced rate of entanglement decay even with sparsely spaced half waveplates along the length of optical fiber. Finally, we evaluate the performance of these two schemes in multiple system configurations.

quant-ph↗

arXiv2024

Building a controlled-NOT gate between polarization and frequency

By harnessing multiple degrees of freedom (DoFs) within a single photon, controlled quantum unitaries, such as the two-qubit controlled-NOT (CNOT) gate, play a pivotal role in advancing quantum communication protocols like dense coding and entanglement distillation. In this work, we devise and realize a CNOT operation between polarization and frequency DoFs by exploiting directionally dependent electro-optic phase modulation within a fiber Sagnac loop. Alongside computational basis measurements, we validate the effectiveness of this operation through the synthesis of all four Bell states in a single photon, all with fidelities greater than 98%. This demonstration opens new avenues for manipulating hyperentanglement across these two crucial DoFs, marking a foundational step toward leveraging polarization-frequency resources in fiber networks for future quantum applications.

quant-ph↗

arXiv2024

An Exponential Reduction in Training Data Sizes for Machine Learning Derived Entanglement Witnesses

We propose a support vector machine (SVM) based approach for generating an entanglement witness that requires exponentially less training data than previously proposed methods. SVMs generate hyperplanes represented by a weighted sum of expectation values of local observables whose coefficients are optimized to sum to a positive number for all separable states and a negative number for as many entangled states as possible near a specific target state. Previous SVM-based approaches for entanglement witness generation used large amounts of randomly generated separable states to perform training, a task with considerable computational overhead. Here, we propose a method for orienting the witness hyperplane using only the significantly smaller set of states consisting of the eigenstates of the generalized Pauli matrices and a set of entangled states near the target entangled states. With the orientation of the witness hyperplane set by the SVM, we tune the plane's placement using a differential program that ensures perfect classification accuracy on a limited test set as well as maximal noise tolerance. For $N$ qubits, the SVM portion of this approach requires only $O(6^N)$ training states, whereas an existing method needs $O(2^{4^N})$. We use this method to construct witnesses of 4 and 5 qubit GHZ states with coefficients agreeing with stabilizer formalism witnesses to within 6.5 percent and 1 percent, respectively. We also use the same training states to generate novel 4 and 5 qubit W state witnesses. Finally, we computationally verify these witnesses on small test sets and propose methods for further verification.

quant-ph↗

arXiv2023

Photonic crystal cavity IQ modulators in thin-film lithium niobate for coherent communications

Thin-Film Lithium Niobate (TFLN) is an emerging integrated photonic platform showing great promise due to its large second-order nonlinearity at microwave and optical frequencies, cryogenic compatibility, large piezoelectric response, and low optical loss at visible and near-infrared wavelengths. These properties enabled Mach-Zehnder interferometer-based devices to demonstrate amplitude- and in-phase/quadrature (IQ) modulation at voltage levels compatible with complementary metal-oxide-semiconductor (CMOS) electronics. Maintaining low-voltage operation requires centimeter-scale device lengths, making it challenging to realize the large-scale circuits required by ever-increasing bandwidth demands in data communications. Reduced device sizes reaching the 10 um scale are possible with photonic crystal (PhC) cavities. So far, their operation has been limited to modulation of amplitudes and required circulators or lacked cascadability. Here, we demonstrate a compact IQ modulator using two PhC cavities operating as phase shifters in a Fabry-Perot-enhanced Michelson interferometer configuration. It supports cascadable amplitude and phase modulation at GHz bandwidths with CMOS-compatible voltages. While the bandwidth limitation of resonant devices is often considered detrimental, their compactness enables dense co-integration with CMOS electronics where clock-rate-level operation (few GHz) removes power-hungry electrical time-multiplexing. Recent demonstrations of chip-scale transceivers with dense-wavelength division multiplied transceivers could be monolithically implemented and driven toward ultimate information densities using TFLN electro-optic frequency combs and our PhC IQ modulators.

physics.optics↗

arXiv2023

Complete characterization of quantum correlations by randomized measurements

The fact that quantum mechanics predicts stronger correlations than classical physics is an essential cornerstone of quantum information processing. Indeed, these quantum correlations are a valuable resource for various tasks, such as quantum key distribution or quantum teleportation, but characterizing these correlations in an experimental setting is a formidable task, especially in scenarios where no shared reference frames are available. By definition, quantum correlations are reference-frame independent, i.e., invariant under local transformations; this physically motivated invariance implies, however, a dedicated mathematical structure and, therefore, constitutes a roadblock for an efficient analysis of these correlations in experiments. Here we provide a method to directly measure any locally invariant property of quantum states using locally randomized measurements, and we present a detailed toolbox to analyze these correlations for two quantum bits. We implement these methods experimentally using pairs of entangled photons, characterizing their usefulness for quantum teleportation and their potential to display quantum nonlocality in its simplest form. Our results can be applied to various quantum computing platforms, allowing simple analysis of correlations between arbitrary distant qubits in the architecture.

quant-ph↗

arXiv2023

Entanglement distillation based on polarization and frequency hyperentanglement

Entanglement distillation has many applications in quantum information processing and is an important tool for improving the quality and efficiency of quantum communication, cryptography, computing, and simulation. We propose an entanglement distillation scheme using only one pair of polarization-frequency hyperentangled photons, which can be equivalently viewed as containing two pairs of entangled logical qubits: a pair of polarization-entangled qubits and a pair of frequency-entangled qubits. To perform the required CNOT operation between the two qubits we consider the use of a polarization-dependent frequency converter. Compared to past methods of entanglement distillation that relied on polarization and spatial-mode/energy-time degree of freedom, the utilization of frequency-encoded qubits offers an advantage in that it is immune to bit-flip errors when the channel is linear. After distillation, the fidelity of polarization entanglement can be significantly improved by sacrificing the frequency degree of freedom. Through simulation, we show that high fidelity gains, large yield, and high distillation rate can be achieved. Our distillation scheme is simple to implement with current technologies, compatible with existing telecommunication fiber networks, and is a promising approach for achieving efficient quantum communication.

quant-ph↗