arXiv subjects

Lorcan O. Conlon

Publications and source records attributed to Lorcan O. Conlon.

17 recordsLinked to original sources

arXiv2026

Deciding the Attainability of the Multiparameter Quantum Fisher Information is NP-Hard

The quantum Fisher information (QFI) sets a fundamental bound on the attainable precision when estimating multiple parameters simultaneously. Incompatibility among the individually optimal measurements can, in some cases, imply that the precision limit set by the QFI is not attainable. In certain special cases, including pure states and full-rank states, the exact conditions for when the precision limit set by the QFI can be saturated are known. However, general conditions for the attainability of the QFI with measurements on individual copies of the quantum state have long been sought. Indeed, this was recently stated as one of the five problems in quantum information theory highlighted by [P. Horodecki et al, PRX Quantum 3, 010101 (2022)]. In this work we prove that exact attainability with individual measurements is NP-hard to decide, even for a restricted set of real, constant-rank quantum models. The source problem for our proof is the NP-hard problem of deciding whether a given bipartite density matrix is separable or not. Our result shows that the longstanding difficulty in obtaining general conditions for QFI attainability reflects a fundamental computational obstruction, rather than merely a limitation of existing mathematical techniques: unless P=NP, no efficiently computable necessary-and-sufficient criterion can exist in general.

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arXiv2026

Fault-Tolerant Heisenberg-Limited Quantum Sensing

Quantum sensors hold great promise for achieving better sensitivity in the measurement of physical quantities compared to their classical counterparts. However, the conditions under which quantum advantage in sensing can be achieved are rather restrictive, and most quantum enhancements in sensing are lost in the presence of noise, errors, or a poorly calibrated system. To overcome these limitations, we are motivated to import ideas from fault-tolerant quantum computing to quantum sensing. Specifically, we consider a qubit noise model where the probability of phase-flip errors is exponentially smaller (in qubit number) compared to the probability of bit-flip errors that occur with probability $p$. For this noise structure, we demonstrate that, given a total sensing time $T$, Heisenberg scaling can be attained for times up to $T\propto 1/p^{(N+1)/2}$ for a $N$-qubit repetition code, in contrast with $T\propto 1/p$ without using a fault-tolerant sensing protocol.

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arXiv2026

$100\pmΔt$ Years of Quantum Uncertainty: From Origins to Modern Insights

Heisenberg's uncertainty principle is a cornerstone of quantum mechanics, marking a decisive departure from classical physics. Conceived almost a century ago through a thought experiment showing that measuring an electron's position inevitably disturbs its momentum, it began as a deceptively simple idea that sparked countless studies and grew into the rich research field it is today. This review traces its development into a spectrum of mathematical formulations -- known as uncertainty relations -- and explores their interconnections and wide-ranging applications. We highlight its central role in quantum metrology, where it underpins strategies for extracting information from quantum systems with ever-increasing precision, and its links to multiparameter estimation and squeezed states. This review, dedicated to the centenary of the uncertainty principle, reflects on how it has deepened our understanding of quantum theory and driven practical advances, and looks ahead to a century poised for further surprising and transformative discoveries.

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arXiv2026

Multiparameter function estimation for general Hamiltonians

Estimation of physical parameters encoded in a Hamiltonian is a central task in quantum sensing and learning. While the ultimate precision limit for estimating a single parameter coupled to a single generator is well established, the corresponding bound for estimating a function of multiple parameters-each coupled to distinct and possibly non-commuting generators-remains unknown in general. Here, we derive the ultimate quantum limit and present an estimation protocol for any function of parameters in a general Hamiltonian that attains this bound. We show that, although the task is fundamentally a multiparameter problem, our tight bound reduces to an optimized single-parameter quantum Cramér-Rao bound, even for arbitrary generator sets. Our result unifies and extends previous works, providing a general framework for optimal function estimation in quantum systems.

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arXiv2026

Ultimate sensitivity of multiparameter estimation in quantum sensing with undetected photons

Quantum sensing with undetected photons is a technique where photons of one wavelength probe a sample, but information is extracted by measuring photons of another wavelength that never interacts with the sample. This has seen significant experimental advances in applications such as spectroscopy, microscopy, and bio-sensing. However, a detailed theoretical analysis using the tools of quantum metrology is currently lacking. Thus it is unclear how far away current schemes are from fundamental limits, and what the optimal measurement strategies are. We apply a multiparameter quantum estimation framework to quantify the error when estimating the unknown transmission and phase shift of a sample. The optimal measurement scheme is shown to require only a single controllable phase shift, easily implementable in existing setups. We also study how to use multipass interactions to maximise information gain. In general the optimum number of passes scales inversely with the log of the transmission of the sample. This work clarifies the metrological power of quantum sensing with undetected photons, and provides guidance for the design of experiments requiring high sensitivity.

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arXiv2026

Beating three-parameter precision trade-offs with entangling collective measurements

Quantum-mechanical incompatibility, which precludes the simultaneous precise measurement of non-commuting observables, imposes fundamental limits on the rate at which classical information can be extracted. While the potential to surpass these limits using entangling collective measurements has been explored for two parameters, the regime of three or more parameters remains largely unexplored despite its fundamental and technological importance. Here, we investigate the three-parameter trade-off relations for estimating the Bloch vector components of a qubit, comparing conventional individual measurements with entangling collective measurements. We theoretically derive and experimentally implement optimal collective measurements on two identically prepared qubits using a programmable photonic circuit. Our experimental results demonstrate a clear violation of the entanglement-free trade-off relation -- by an average of 16 standard deviations -- achieving a tomography precision beyond the reach of any individual measurement scheme. This work directly confirms that optimal collective measurements can surpass the fundamental quantum limits of individual schemes in a three-parameter setting -- thereby deepening our understanding of quantum uncertainty relations beyond the two-parameter regime and providing a clear strategy to overcome the precision trade-offs imposed by quantum incompatibility.

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arXiv2026

Precision Bounds for Characterising Quantum Measurements

Quantum measurements, alongside quantum states and processes, form a cornerstone of quantum information processing. However, unlike states and processes, their efficient characterisation remains relatively unexplored. We resolve this asymmetry by introducing a comprehensive framework for efficient detector estimation that reveals the fundamental limits to extractable parameter information and errors arising in detector analysis - the detector quantum Fisher information. Our development eliminates the need to optimise for the best probe state, while highlighting aspects of detector analysis that fundamentally differ from quantum state estimation. Through proofs, examples and experimental validation, we demonstrate the relevance and robustness of our proposal for current quantum detector technologies. By formalising a dual perspective to state estimation, our framework completes and connects the triad of efficient state, process, and detector tomography, advancing quantum information theory with broader implications for emerging technologies reliant on precisely calibrated measurements.

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arXiv2025

Enhanced continuous-variable quantum key distribution protocol via adaptive signal processing

Quantum key distribution (QKD) provides a promising approach to secure communications, with continuous-variable QKD (CV-QKD) offering compatibility with existing telecommunication infrastructure. Despite this advantage, CV-QKD is limited by challenges such as losses in terrestrial fibres and atmospheric scintillation in free-space channels. We introduce a QKD protocol that surpasses the optimal Gaussian modulated CV-QKD (GG02) protocol by utilising probabilistic filters without known physical representation. Our approach employs a Gaussian filter at Alice's station and a non-Gaussian notch-like filter at Bob's station. Alice's filter optimises modulation variance to achieve key rates near the optimal GG02 performance, while Bob's filter adapts the effective channel conditions, which can result in higher key rates than the optimal GG02 protocol. Our security analysis avoids Gaussian extremality, accurately bounding Eve's information. The protocol dynamically optimises the secret-key rate for rapidly changing channels, such as terrestrial links and satellite-to-ground communications, and can extract keys in regions deemed non-secure by parameter estimation. Implemented at software level, our protocol requires no hardware modifications and can be integrated into existing QKD systems. Experimental results show a threefold increase in key rates over the optimal GG02 protocol, while simulations for Low Earth Orbit satellite quantum communications indicate a 400-fold increase compared to the non-optimised counterpart.

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arXiv2024

Comparison of estimation limits for quantum two-parameter estimation

Measurement estimation bounds for local quantum multiparameter estimation, which provide lower bounds on possible measurement uncertainties, have so far been formulated in two ways: by extending the classical Cramér--Rao bound (e.g., the quantum Cramér--Rao bound and the Nagaoka Cram'er--Rao bound) and by incorporating the parameter estimation framework with the uncertainty principle, as in the Lu--Wang uncertainty relation. In this work, we present a general framework that allows a direct comparison between these different types of estimation limits. Specifically, we compare the attainability of the Nagaoka Cramér--Rao bound and the Lu--Wang uncertainty relation, using analytical and numerical techniques. We show that these two limits can provide different information about the physically attainable precision. We present an example where both limits provide the same attainable precision and an example where the Lu--Wang uncertainty relation is not attainable even for pure states. We further demonstrate that the unattainability in the latter case arises because the figure of merit underpinning the Lu--Wang uncertainty relation (the difference between the quantum and classical Fisher information matrices) does not necessarily agree with the conventionally used figure of merit (mean squared error). The results offer insights into the general attainability and applicability of the Lu--Wang uncertainty relation. Furthermore, our proposed framework for comparing bounds of different types may prove useful in other settings.

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arXiv2024

Verifying the security of a continuous variable quantum communication protocol via quantum metrology

Quantum mechanics offers the possibility of unconditionally secure communication between multiple remote parties. Security proofs for such protocols typically rely on bounding the capacity of the quantum channel in use. In a similar manner, Cramér-Rao bounds in quantum metrology place limits on how much information can be extracted from a given quantum state about some unknown parameters of interest. In this work we establish a connection between these two areas. We first demonstrate a three-party sensing protocol, where the attainable precision is dependent on how many parties work together. This protocol is then mapped to a secure access protocol, where only by working together can the parties gain access to some high security asset. Finally, we map the same task to a communication protocol where we demonstrate that a higher mutual information can be achieved when the parties work collaboratively compared to any party working in isolation.

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arXiv2024

Role of the extended Hilbert space in the attainability of the Quantum Cramér-Rao bound for multiparameter estimation

The symmetric logarithmic derivative Cramér-Rao bound (SLDCRB) provides a fundamental limit to the minimum variance with which a set of unknown parameters can be estimated in an unbiased manner. It is known that the SLDCRB can be saturated provided the optimal measurements for the individual parameters commute with one another. However, when this is not the case the SLDCRB cannot be attained in general. In the experimentally relevant setting, where quantum states are measured individually, necessary and sufficient conditions for when the SLDCRB can be saturated are not known. In this setting the SLDCRB is attainable provided the SLD operators can be chosen to commute on an extended Hilbert space. However, beyond this relatively little is known about when the SLD operators can be chosen in this manner. In this paper we present explicit examples which demonstrate novel aspects of this condition. Our examples demonstrate that the SLD operators commuting on any two of the following three spaces: support space, support-kernel space and kernel space, is neither a necessary nor sufficient condition for commutativity on the extended space. We present a simple analytic example showing that the Nagaoka-Hayashi Cramér-Rao bound is not always attainable. Finally, we provide necessary and sufficient conditions for the attainability of the SLDCRB in the case when the kernel space is one-dimensional. These results provide new information on the necessary and sufficient conditions for the attainability of the SLDCRB.

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arXiv2024

Efficient Light Propagation Algorithm using Quantum Computers

Quantum algorithms can potentially overcome the boundary of computationally hard problems. One of the cornerstones in modern optics is the beam propagation algorithm, facilitating the calculation of how waves with a particular dispersion relation propagate in time and space. This algorithm solves the wave propagation equation by Fourier transformation, multiplication with a transfer function, and subsequent back transformation. This transfer function is determined from the respective dispersion relation, which can often be expanded as a polynomial. In the case of paraxial wave propagation in free space or picosecond pulse propagation, this expansion can be truncated after the quadratic term. The classical solution to the wave propagation requires $\mathcal{O}(N log N)$ computation steps, where $N$ is the number of points into which the wave function is discretized. Here, we show that the propagation can be performed as a quantum algorithm with $\mathcal{O}((log{}N)^2)$ single-controlled phase gates, indicating exponentially reduced computational complexity. We herein demonstrate this quantum beam propagation method (QBPM) and perform such propagation in both one- and two-dimensional systems for the double-slit experiment and Gaussian beam propagation. We highlight the importance of the selection of suitable observables to retain the quantum advantage in the face of the statistical nature of the quantum measurement process, which leads to sampling errors that do not exist in classical solutions.

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arXiv2023

Discriminating mixed qubit states with collective measurements

It is a central fact in quantum mechanics that non-orthogonal states cannot be distinguished perfectly. This property ensures the security of quantum key distribution. It is therefore an important task in quantum communication to design and implement strategies to optimally distinguish quantum states. In general, when we have access to multiple copies of quantum states the optimal measurement will be a collective measurement. However, to date, collective measurements have not been used to enhance quantum state discrimination. One of the main reasons for this is the fact that, in the usual state discrimination setting with equal prior probabilities, at least three copies of a quantum state are required to be measured collectively to outperform separable measurements. This is very challenging experimentally. In this work, by considering unequal prior probabilities, we propose and experimentally demonstrate a protocol for distinguishing two copies of single qubit states using collective measurements which achieves a lower probability of error than can be achieved by any non-entangling measurement. We implement our measurements on an IBM Q System One device, a superconducting quantum processor. Additionally, we implemented collective measurements on three and four copies of the unknown state and found they performed poorly.

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arXiv2023

Optimal Single Qubit Tomography: Realization of Locally Optimal Measurements on a Quantum Computer

Quantum bits, or qubits, are the fundamental building blocks of present quantum computers. Hence, it is important to be able to characterize the state of a qubit as accurately as possible. By evaluating the qubit characterization problem from the viewpoint of quantum metrology, we are able to find optimal measurements under the assumption of good prior knowledge. We implement these measurements on a superconducting quantum computer. Our experiment produces sufficiently low error to allow the saturation of the theoretical limits, given by the Nagaoka--Hayashi bound. We also present simulations of adaptive measurement schemes utilizing the proposed method. The results of the simulations show the robustness of the method in characterizing arbitrary qubit states with different amounts of prior knowledge.

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arXiv2023

Testing the postulates of quantum mechanics with coherent states of light and homodyne detection

Quantum mechanics has withstood every experimental test thus far. However, it relies on ad-hoc postulates which require experimental verification. Over the past decade there has been a great deal of research testing these postulates, with numerous tests of Born's rule for determining probabilities and the complex nature of the Hilbert space being carried out. Although these tests are yet to reveal any significant deviation from textbook quantum theory, it remains important to conduct such tests in different configurations and using different quantum states. Here we perform the first such test using coherent states of light in a three-arm interferometer combined with homodyne detection. Our proposed configuration requires additional assumptions, but allows us to use quantum states which exist in a larger Hilbert space compared to previous tests. For testing Born's rule, we find that the third order interference is bounded to be $κ$ = 0.002 $\pm$ 0.004 and for testing whether quantum mechanics is complex or not we find a Peres parameter of F = 1.0000 $\pm$ 0.0003 (F = 1 corresponds to the expected complex quantum mechanics). We also use our experiment to test Glauber's theory of optical coherence.

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arXiv2023

Approaching optimal entangling collective measurements on quantum computing platforms

Entanglement is a fundamental feature of quantum mechanics and holds great promise for enhancing metrology and communications. Much of the focus of quantum metrology so far has been on generating highly entangled quantum states that offer better sensitivity, per resource, than what can be achieved classically. However, to reach the ultimate limits in multi-parameter quantum metrology and quantum information processing tasks, collective measurements, which generate entanglement between multiple copies of the quantum state, are necessary. Here, we experimentally demonstrate theoretically optimal single- and two-copy collective measurements for simultaneously estimating two non-commuting qubit rotations. This allows us to implement quantum-enhanced sensing, for which the metrological gain persists for high levels of decoherence, and to draw fundamental insights about the interpretation of the uncertainty principle. We implement our optimal measurements on superconducting, trapped-ion and photonic systems, providing an indication of how future quantum-enhanced sensing networks may look.

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arXiv2021

Optimal probes for continuous variable quantum illumination

Quantum illumination is the task of determining the presence of an object in a noisy environment. We determine the optimal continuous variable states for quantum illumination in the limit of zero object reflectivity. We prove that the optimal single mode state is a coherent state, while the optimal two mode state is the two-mode squeezed-vacuum state. We find that these probes are not optimal at non-zero reflectivity, but remain near optimal. This demonstrates the viability of the continuous variable platform for an experimentally accessible, near optimal quantum illumination implementation.

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