arXiv subjects

Anthony J. Brady

Publications and source records attributed to Anthony J. Brady.

At least 19 recordsLinked to original sources

arXiv2026

Precision Limits of Multiparameter Markovian-Noise Metrology

Measuring stochastic signals ("noise metrology") constitutes a central task in quantum sensing and the characterization of open quantum systems. Here we establish ultimate precision bounds for multiparameter estimation of stochastic signals encoded through Markovian Lindblad dynamics, allowing for arbitrary quantum control and noiseless ancillae. Although Markovianity enforces standard-quantum-limit scaling with sensing time $T$, our bounds reveal Heisenberg-type scaling in the number of dissipative channels, $R$: when the stochastic signal exhibits high-rank correlations across the $R$ channels and the probe is entangled, the average variance (per parameter) scales no better than $Ω(1/(TR^2))$. For collective $k$-body dissipation, $R=Θ(N^k)$, signifying super-Heisenberg scaling with the system size $N$. We further show that, when the unknown parameters enter through the dissipative eigenrates, a Rapid Prepare-and-Measure (RPM) protocol that tracks many distinct quantum jumps in parallel attains these limits. In this regime, the estimation problem reduces to a multi-Poisson counting model, providing a conceptually clean route to optimal quantum noise metrology. We illustrate the breadth of the framework with applications to networked noise metrology, collective many-body dissipation, learning Pauli noise, and subdiffraction quantum imaging.

quant-ph↗

arXiv2026

Entanglement advantage in sensing power-law spatiotemporal noise correlations

Noise sensing underlies many physical applications including tests of non-classicality, thermometry, verification of correlated phases of quantum matter, and characterization of criticality. While previous works have shown that quantum resources such as entanglement and squeezing can enhance the sensitivity in estimating deterministic signals, less is known about the entanglement advantage in sensing correlated stochastic signals (noise). In this work, we compute the fundamental sensitivity limits of quantum sensors in probing spatiotemporally correlated noise. We first prove the fundamental quantum limits in sensing spatially correlated Markovian noise using entangled and unentangled sensors, respectively. Focusing on power-law spatial noise correlations, which naturally arise in condensed matter systems with long-range interactions and/or near criticality, we further derive a scalable entanglement advantage when the power-law decays slowly. Then, considering a target signal with a $1/f^{p}$-type spectrum, we demonstrate that non-Markovianity may entirely modify the nature of entanglement advantage in estimating spatial noise correlations. Our protocols can be implemented using state-of-the-art quantum sensing platforms including solid-state defects, superconducting circuits, and neutral atoms.

quant-ph↗

arXiv2026

Correlated Noise Estimation with Quantum Sensor Networks

We address the metrological problem of estimating collective stochastic properties imprinted on a network of quantum sensors. Canonical examples include center-of-mass quadrature fluctuations in a system of bosonic modes and correlated dephasing in an ensemble of qubits (e.g., spins), bosons, or fermions. We develop a theoretical framework to determine the limits of correlated (weak) noise estimation with quantum sensor networks and reveal the requirements for entanglement advantage. Notably, an advantage emerges from the synergistic interplay between quantum correlations of the sensors and ``classical'' correlations of the noises. We determine optimal entangled probe states and identify a sensing protocol -- reminiscent of a many-body echo -- that achieves the fundamental limits of measurement sensitivity for a broad class of problems, unveiling a route towards entanglement-enhanced metrology of correlated many-body phenomena.

quant-ph↗

arXiv2025

Benasque Lectures on Gaussian Bosonic Systems and Analogue Gravity

These notes are adapted from six lectures that I delivered at Analogue Gravity in Benasque 2023. They present the unified Gaussian (phase-space) framework to describe linear bosonic quantum systems, the standard tool in quantum optics and continuous-variable quantum information, emphasizing its simplicity and platform independence, with applications to semi-classical black holes and analogue gravity. Parts (I-III) develop the formalism: from harmonic dynamics and Gaussian transformations to state characterization via moments, Wigner functions, and entanglement measures. Part (IV) applies these tools to semi-classical black holes, discussing Hawking radiation and quantum superradiance in rotating black holes, and laboratory analogues in light-matter systems via toy models.

gr-qc↗

arXiv2025

Physical-Layer Machine Learning with Multimode Interferometric Photon Counting

The learning of the physical world relies on sensing and data post-processing. When the signals are weak, multidimensional and correlated, the performance of learning is often bottlenecked by the quality of sensors, calling for integrating quantum sensing into the learning of such physical-layer data. An example of such a learning scenario is the stochastic quadrature displacements of electromagnetic fields, modeling optomechanical force sensing, radiofrequency photonic sensing, microwave cavity weak signal sensing, and other applications. We propose a unified protocol that combines machine learning with interferometric photon counting to reduce noise and reveal correlations. By applying variational quantum learning with multimode programmable quantum measurements, we enhance signal extraction. Our results show that multimode interferometric photon counting outperforms conventional homodyne detection proposed in prior works for tasks like principal component analysis (PCA) and cross-correlation analysis (CCA), even below vacuum noise levels. To further enhance the performance, we also integrate entanglement-enhanced modules, in the form of squeezed state distribution and anti-squeezing at detection, into the protocol. Combining multimode interferometric photon counting and multipartite entanglement, the proposed protocol provides a powerful toolbox for learning weak signals.

quant-ph↗

arXiv2025

Absolutely Maximal Entanglement in Continuous Variables

We explore absolutely maximal entanglement (AME) and k-uniformity in continuous-variable (CV) quantum systems, and show that-unlike in qudit systems-such entanglement is readily realizable in both Gaussian and non-Gaussian quantum states of multiple modes. We demonstrate that Gaussian CV cluster states are generically AME, rederiving the results of [Phys. Rev. Lett. 103, 070501 (2009)] from a generalized stabilizer formalism, and provide explicit constructions based on Cauchy, Vandermonde, totally positive, and real-block-code generator matrices. We further extend AME properties to a family of non-Gaussian states constructed from discrete Zak basis states that incorporate grid states (a.k.a., Gottesman-Kitaev-Preskill states) as non-Gaussian resources. Realizations of CV AME states enable open-destination multi-party CV teleportation, CV quantum secret sharing, CV majority-agreed key distribution, perfect-tensor networks on arbitrary geometries, and multi-unitary circuits. Our extension to non-Gaussian AME states may further provide robustness to Gaussian noise and benefits to quantum CV information processing.

quant-ph↗

arXiv2025

Incoherent Imaging with Spatially Structured Quantum Probes

Incoherent imaging, including fluorescence and absorption microscopy, is often limited by weak signals and resolution constraints -- notoriously, Rayleigh's curse. We investigate how spatially structured quantum probes, combined with quantum detection strategies like spatial mode demultiplexing and photon counting, overcome these limitations. We propose a novel imaging protocol based on twin-beam echoes that maps the generalized incoherent-imaging model -- comprising both absorption and fluorescence -- onto distinct passive imaging channels that separately encode the absorption and fluorescence signatures. This enables (i) simultaneous absorption and fluorescence imaging and (ii) direct application of well-known results from passive imaging, all featuring quantum-enhanced measurement sensitivity. Remarkably, the same protocol supports displacement-field reconstruction of multiple quadratures (e.g., oscillators' positions) and works for both conventional and subdiffraction imaging, thereby functioning as a universal quantum imaging module. We also examine the utility of Fock states in a structured spatial mode basis, which offer comparable performance in principle. Though developed for optical imaging, our framework applies broadly to quantum-optical microscopy, phononic or acoustic imaging, and mapping stochastic forces, fields, or charge distributions using an array of mechanical oscillators.

quant-ph↗

arXiv2025

Optimally learning functions in interacting quantum sensor networks

Estimating extensive combinations of local parameters in distributed quantum systems is a central problem in quantum sensing, with applications ranging from magnetometry to timekeeping. While optimal strategies are known for sensing non-interacting Hamiltonians in quantum sensor networks, fundamental limits in the presence of uncontrolled interactions remain unclear. Here, we establish optimal bounds and protocols for estimating a linear combination of local parameters of Hamiltonians with arbitrary, unknown interactions. In the process, we more generally establish bounds for learning any linear combination of Hamiltonian coefficients for arbitrary, commuting terms. Our results unify and extend existing bounds for non-interacting qubits and multimode interferometers, providing a general framework for distributed sensing and Hamiltonian learning in realistic many-body systems.

quant-ph↗

arXiv2025

Advances in Bosonic Quantum Error Correction with Gottesman-Kitaev-Preskill Codes: Theory, Engineering and Applications

Encoding quantum information into a set of harmonic oscillators is considered a hardware efficient approach to mitigate noise for reliable quantum information processing. Various codes have been proposed to encode a qubit into an oscillator -- including cat codes, binomial codes and Gottesman-Kitaev-Preskill (GKP) codes -- and are among the first to reach a break-even point for quantum error correction. Though GKP codes are widely recognized for their promise in quantum computation, they also facilitate near-optimal quantum communication rates in bosonic channels and offer the ability to safeguard arbitrary quantum states of oscillators. This review focuses on the basic working mechanism, performance characterization, and the many applications of GKP codes -- emphasizing recent experimental progress in superconducting circuit architectures and theoretical advancements in multimode GKP qubit codes and oscillators-to-oscillators (O2O) codes. We begin with a preliminary continuous-variable formalism needed for bosonic codes. We then proceed to the quantum engineering involved to physically realize GKP states. We take a deep dive into GKP stabilization and preparation in superconducting architectures and examine proposals for realizing GKP states in the optical domain (along with a concise review of GKP realization in trapped-ion platforms). Finally, we present multimode GKP qubits and GKP-O2O codes, examine code performance and discuss applications of GKP codes in quantum information processing tasks such as computing, communication, and sensing.

quant-ph↗

arXiv2024

Exponential entanglement advantage in sensing correlated noise

In this work, we propose a new form of exponential quantum advantage in the context of sensing correlated noise. Specifically, we focus on the problem of estimating parameters associated with Lindblad dephasing dynamics, and show that entanglement can lead to an exponential enhancement in the sensitivity (as quantified via quantum Fisher information of the sensor state) for estimating a small parameter characterizing the deviation of system Lindbladians from a class of maximally correlated dephasing dynamics. This result stands in stark contrast with previously studied scenarios of sensing uncorrelated dephasing noise, where one can prove that entanglement does not lead to an advantage in the signal-to-noise ratio. Our work thus opens a novel pathway towards achieving entanglement-based sensing advantage, which may find applications in characterizing decoherence dynamics of near-term quantum devices. Further, our approach provides a potential quantum-enhanced probe of many-body correlated phases by measuring noise generated by a sensing target. We also discuss realization of our protocol using near-term quantum hardware.

quant-ph↗

arXiv2024

Entanglement from rotating black holes in thermal baths

We extend previous efforts to quantify the entanglement generated in Hawking's evaporation process by including rotation and thermal environments (e.g. the cosmic microwave background). Both extensions are needed to describe real black holes in our universe. Leveraging techniques from Gaussian quantum information, we find that the black hole's ergoregion is an active source of quantum entanglement and that thermal environments drastically degrade entanglement generation. Our predictions are suitable to be tested in the lab using analogue platforms and also provide tools to assess the fate of quantum information for black holes in more generic settings.

gr-qc↗

arXiv2024

Safeguarding Oscillators and Qudits with Distributed Two-Mode Squeezing

Recent advancements in multi-mode Gottesman-Kitaev-Preskill (GKP) codes have shown great promise in enhancing the protection of both discrete and analog quantum information. This broadened range of protection brings opportunities beyond quantum computing to benefit quantum sensing by safeguarding squeezing -- the essential resource in many quantum metrology protocols. However, the potential for quantum sensing to benefit quantum error correction has been less explored. In this work, we provide a unique example where techniques from quantum sensing can be applied to improve multi-mode GKP codes. Inspired by distributed quantum sensing, we propose the distributed two-mode squeezing (dtms) GKP codes that offer benefits in error correction with minimal active encoding operations. Indeed, the proposed codes rely on a single (active) two-mode squeezing element and an array of beamsplitters that effectively distributes continuous-variable correlations to many GKP ancillae, similar to continuous-variable distributed quantum sensing. Despite this simple construction, the code distance achievable with dtms-GKP qubit codes is comparable to previous results obtained through brute-force numerical search [PRX Quantum 4, 040334 (2023)]. Moreover, these codes enable analog noise suppression beyond that of the best-known two-mode codes [Phys. Rev. Lett. 125, 080503 (2020)] without requiring an additional squeezer. We also provide a simple two-stage decoder for the proposed codes, which appears near-optimal for the case of two modes and permits analytical evaluation.

quant-ph↗

arXiv2024

Quantum-enhanced dark matter detection with in-cavity control: mitigating the Rayleigh curse

The nature of dark matter is a fundamental puzzle in modern physics. A major approach of searching for dark matter relies on detecting feeble noise in microwave cavities. However, the quantum advantages of common quantum resources such as squeezing are intrinsically limited by the Rayleigh curse -- a constant loss places a sensitivity upper bound on these quantum resources. In this paper, we propose an in-situ protocol to mitigate such Rayleigh limit. The protocol consists of three steps: in-cavity quantum state preparation, axion accumulation with tunable time duration, and measurement. For the quantum source, we focus on the single-mode squeezed state (SMSS), and the entanglement-assisted case using signal-ancilla pairs in two-mode squeezed state (TMSS), where the ancilla does not interact with the axion. From quantum Fisher information rate evaluation, we derive the requirement of cavity quality factor, thermal noise level and squeezing gain for quantum advantage. When the squeezing gain becomes larger, the optimal axion accumulation time decreases to reduce loss and mitigate the Rayleigh curse -- the quantum advantage keeps increasing with the squeezing gain. Overall, we find that TMSS is more sensitive in the low temperature limit. In the case of SMSS, as large gain is required for advantage over vacuum, homodyne is sufficient to achieve optimality. For TMSS, anti-squeezing and photon counting is necessary to be optimal. Thanks to the recent advance in magnetic-field-resilient in-cavity squeezing and rapidly coupling out for photon counting, the proposed protocol is compatible with axion detection scenario.

quant-ph↗

arXiv2024

Entanglement from superradiance and rotating quantum fluids of light

The amplification of radiation by superradiance is a universal phenomenon observed in numerous physical systems. We demonstrate that superradiant scattering generates entanglement for different input states, including coherent states, thereby establishing the inherently quantum nature of this phenomenon. To put these concepts to the test, we propose a novel approach to create horizonless ergoregions, which are nonetheless dynamically stable thanks to the dissipative dynamics of a polaritonic fluid of light. We numerically simulate the system to demonstrate the creation of a stable ergoregion. Subsequently, we investigate rotational superradiance within this system, with a primary focus on entanglement generation and the possibilities for its enhancement using current techniques. Our methods permit the investigation of quantum emission by rotational superradiance in state-of-the-art experiments, in which the input state can be controlled at will.

gr-qc↗

arXiv2023

Optimal encoding of oscillators into more oscillators

Bosonic encoding of quantum information into harmonic oscillators is a hardware efficient approach to battle noise. In this regard, oscillator-to-oscillator codes not only provide an additional opportunity in bosonic encoding, but also extend the applicability of error correction to continuous-variable states ubiquitous in quantum sensing and communication. In this work, we derive the optimal oscillator-to-oscillator codes among the general family of Gottesman-Kitaev-Preskill (GKP)-stablizer codes for homogeneous noise. We prove that an arbitrary GKP-stabilizer code can be reduced to a generalized GKP two-mode-squeezing (TMS) code. The optimal encoding to minimize the geometric mean error can be constructed from GKP-TMS codes with an optimized GKP lattice and TMS gains. For single-mode data and ancilla, this optimal code design problem can be efficiently solved, and we further provide numerical evidence that a hexagonal GKP lattice is optimal and strictly better than the previously adopted square lattice. For the multimode case, general GKP lattice optimization is challenging. In the two-mode data and ancilla case, we identify the D4 lattice -- a 4-dimensional dense-packing lattice -- to be superior to a product of lower dimensional lattices. As a by-product, the code reduction allows us to prove a universal no-threshold-theorem for arbitrary oscillators-to-oscillators codes based on Gaussian encoding, even when the ancilla are not GKP states.

quant-ph↗

arXiv2023

A numerical study of measurement-induced phase transitions in the Sachdev-Ye-Kitaev model

Continuous monitoring of an otherwise closed quantum system has been found to lead to a measurement-induced phase transition (MIPT) characterized by abrupt changes in the entanglement or purity of the many-body quantum state. For an entanglement MIPT, entangling dynamics compete with measurement dynamics, pushing the system either to a phase with extensive entanglement or to a phase with low-level entanglement. For purification MIPTs, projective measurements effectively cool and localize the system, inducing a transition from a mixed state to an uncorrelated pure state. In this work, we numerically simulate monitored dynamics in the all-to-all Sachdev-Ye-Kitaev (SYK) model for finite N. We witness both entanglement and purification MIPTs in the steady-state. It is often said that there is an equivalence between entanglement and purification MIPTs, however we provide numerical evidence to the contrary, implying that entanglement and purification MIPTs are indeed two distinct phenomena. The reason for such a distinction is quite simple: entanglement can revive after a completely projective measurement -- if measurements do not occur too often in time -- but impurity cannot.

quant-ph↗

arXiv2022

Entanglement-enhanced optomechanical sensor array for dark matter searches

The nature of dark matter is one of the most important open questions in modern physics. The search for dark matter is challenging since, besides gravitational interaction, it feebly interacts with ordinary matter. Mechanical sensors are one of the leading candidates for dark matter searches in the low frequency region. Here, we propose entanglement-enhanced optomechanical sensing systems to assist the search for DM with mechanical sensing devices. To assess the performance of our setup, we adopt the integrated sensitivity, which is particularly suitable for broadband sensing as it precisely quantifies the bandwidth-sensitivity tradeoff of the system. We then show that, by coherently operating the optomechanical sensor array and utilizing continuous-variable multi-partite entanglement between the optical fields, the array of sensors has a scaling advantage over independent sensors (i.e., $\sqrt{M}\rightarrow M$, where $M$ is the number of sensors) as well as a performance boost due to entanglement. Such an advantage is robust to imhomogeneities of the mechanical sensors and is achievable with off-the-shelf experimental components.

quant-ph↗

arXiv2022

Robustness of entanglement in Hawking radiation for optical systems immersed in thermal baths

Entanglement is the quantum signature of Hawking's particle pair-creation from causal horizons, for gravitational and analog systems alike. Ambient thermal fluctuations, ubiquitous in realistic situations, strongly affects the entanglement generated in the Hawking process, completely extinguishing it when the ambient temperature is comparable to the Hawking temperature. In this work, we show that optical analog systems have a built-in robustness to thermal fluctuations which are at rest in the laboratory. In such systems, horizons move relative to the laboratory frame at velocities close to the speed of light. We find that a subtle interplay between this relative velocity and dispersion protects the Hawking-generated entanglement -- allowing ambient temperatures several orders of magnitude larger than the Hawking temperature without significantly affecting entanglement.

gr-qc↗