Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Granice wspólnej precyzji i kompatybilność pomiarów w realistycznych fotonicznych czujnikach kwantowych

Jayanth Jayakumar

Published Jan 1, 2026• 0 citations
OpenAlex

Abstract

The sensitivity of a probe to a parameter characterizing a system can be described within the single-parameter estimation framework.In the simplest treatment, the parameter is estimated under ideal conditions, neglecting imperfections from system-environment interactions.More advanced analyses consider estimation in the presence of known environmental noise.Although Heisenberglimited sensitivity is lost, suitably engineered probes can still offer quantum enhancements.When the noise itself is unknown, the estimation problem becomes more complex, requiring a multiparameter approach.Fundamental precision bounds for multiparameter estimation are well established, but their practical attainability remains elusive due to the challenge of constructing measurements with good multiparameter sensitivity.For a given probe, the incompatibility of optimal observables associated with different parameters poses an additional roadblock to achieving simultaneous optimal estimation.In practice, assessing the compatibility of separable measurements is essential, since very often collective strategies that are impractical are required to saturate the bound capturing fundamental incompatibility.To this end, we consider the joint estimation of phase and phase diffusion, introducing quantifiers for information extraction and availability.We find that double homodyne measurement on states generated by the interference of N photons injected into one beamsplitter port yields the highest sensitivity.With respect to measurement compatibility, we study the joint estimation of phase and photon loss, and of phase and phase diffusion.Using the same multiphoton states, we compare double homodyne detection and photon counting against multiparameter precision benchmarks for collective and separable measurements.Among the cases considered, photon counting generally offers better performance for joint phase and loss estimation, while double homodyne still performs reasonably in some regimes for both estimation problems.

Related papers

Measurement compatibility in multiparameter quantum interferometry

Jayanth Jayakumar, Marco Barbieri, Magdalena Stobińska

The Cram\'er-Rao bound captures completely the performance of single-parameter quantum sensors. On the other hand, its extension to multiple parameters demands more caution. Different aspects need to be captured at once, including, critically, compatibility. In this article we consider compatibility in quantum interferometry for an important class of probe states, measured by double homodyne or photon counters, standard benchmarks for these applications. We include the presence of loss and phase diffusion in the estimation of a phase. Our results illustrate how different weighting of the precision on individual parameters affects their compatibility, adding to the list of considerations for quantum multiparameter estimation.

arXiv:2504.18324•Physical Review A•Sep 11, 2025•0 citations

Quantum-enhanced joint estimation of phase and phase diffusion

Jayanth Jayakumar, Monika E. Mycroft, Marco Barbieri +1 more

Abstract Accurate phase estimation in the presence of unknown phase diffusive noise is a crucial yet challenging task in noisy quantum metrology. This problem is particularly interesting due to the detrimental impact of the associated noise. Here, we investigate the joint estimation of phase and phase diffusion using generalized Holland–Burnett states, known for their experimental accessibility. These states provide performance close to the optimal state in single-parameter phase estimation, even in the presence of photon losses. We adopt a twofold approach by analyzing the joint information extraction through the double homodyne measurement and the joint information availability across all probe states. Through our analysis, we find that the highest sensitivities are obtained by using states created by directing all input photons into one port of a balanced beam splitter. Furthermore, we infer that good levels of sensitivity persist even in the presence of moderate photon losses, illustrating the remarkable resilience of our probe states under lossy conditions.

arXiv:2403.04722•New Journal of Physics•Jul 1, 2024•5 citations

Experimental Joint Estimation of Phase and Phase Diffusion via Deterministic Bell Measurements

Ben Wang, Minghao Mi, Huangqiuchen Wang +2 more

Accurate phase estimation plays a pivotal role in quantum metrology, yet its precision is significantly affected by noise, particularly phase-diffusive noise caused by phase drift. To address this challenge, the joint estimation of phase and phase diffusion has emerged as an effective approach, transforming the problem into a multi-parameter estimation task. However, the incompatibility between optimal measurements for different parameters prevents single-copy measurements from reaching the fundamental precision limits defined by the quantum Cramer-Rao bound. Meanwhile, collective measurements performed on multiple identical copies can mitigate this incompatibility and thus enhance the precision of joint parameter estimation. This work experimentally demonstrates joint phase and phase-diffusion estimation using deterministic Bell measurements on a two-qubit system. A linear optical network is employed to implement both parameter encoding and deterministic Bell measurements, achieving improved estimation precision compared to any separable measurement strategy. This work proposes a new framework for phase estimation under phase-diffusive noise and underscores the substantial advantages of collective measurements in multi-parameter quantum metrology.

quant-pharXiv:2512.22558•Advanced Science•Dec 30, 2025•0 citations

Entangling measurements for multiparameter estimation with two qubits

Emanuele Roccia, Ilaria Gianani, Luca Mancino +4 more

Abstract Careful tailoring the quantum state of probes offers the capability of investigating matter at unprecedented precisions. Rarely, however, the interaction with the sample is fully encompassed by a single parameter, and the information contained in the probe needs to be partitioned on multiple parameters. There exist, then, practical bounds on the ultimate joint-estimation precision set by the unavailability of a single optimal measurement for all parameters. Here, we discuss how these considerations are modified for two-level quantum probes — qubits — by the use of two copies and entangling measurements. We find that the joint estimation of phase and phase diffusion benefits from such collective measurement, while for multiple phases no enhancement can be observed. We demonstrate this in a proof-of-principle photonics setup.

arXiv:1704.03327•Quantum Science and Technology•Oct 9, 2017•59 citations

Compatibility in multiparameter quantum metrology

Sammy Ragy, Marcin Jarzyna, Rafał Demkowicz-Dobrzański

Simultaneous estimation of multiple parameters in quantum metrological models is complicated by factors relating to the (i) existence of a single probe state allowing for optimal sensitivity for all parameters of interest, (ii) existence of a single measurement optimally extracting information from the probe state on all the parameters, and (iii) statistical independence of the estimated parameters. We consider the situation when these concerns present no obstacle, and for every estimated parameter the variance obtained in the multiparameter scheme is equal to that of an optimal scheme for that parameter alone, assuming all other parameters are perfectly known. We call such models compatible. In establishing a rigorous theoretical framework for investigating compatibility, we clarify some ambiguities and inconsistencies present in the literature and discuss several examples to highlight interesting features of unitary and nonunitary parameter estimation, as well as deriving new bounds for physical problems of interest, such as the simultaneous estimation of phase and local dephasing.

arXiv:1608.02634•Physical Review A•Nov 10, 2016•304 citations

Multiparameter Estimation with Two-Qubit Probes in Noisy Channels

Lorcán O. Conlon, Ping Koy Lam, Syed M. Assad

This work compares the performance of single- and two-qubit probes for estimating several phase rotations simultaneously under the action of different noisy channels. We compute the quantum limits for this simultaneous estimation using collective and individual measurements by evaluating the Holevo and Nagaoka-Hayashi Cramér-Rao bounds, respectively. Several quantum noise channels are considered, namely the decohering channel, the amplitude damping channel, and the phase damping channel. For each channel, we find the optimal single- and two-qubit probes. Where possible we demonstrate an explicit measurement strategy that saturates the appropriate bound and we investigate how closely the Holevo bound can be approached through collective measurements on multiple copies of the same probe. We find that under the action of the considered channels, two-qubit probes show enhanced parameter estimation capabilities over single-qubit probes for almost all non-identity channels, i.e., the achievable precision with a single-qubit probe degrades faster with increasing exposure to the noisy environment than that of the two-qubit probe. However, in sufficiently noisy channels, we show that it is possible for single-qubit probes to outperform maximally entangled two-qubit probes. This work shows that, in order to reach the ultimate precision limits allowed by quantum mechanics, entanglement is required in both the state preparation and state measurement stages. It is hoped the tutorial-esque nature of this paper will make it easily accessible.

arXiv:2307.13936•Entropy•Jul 26, 2023•6 citations
The sensitivity of a probe to a parameter characterizing a system can be described within the single-parameter estimation framework.In the simplest treatment, the parameter is estimated under ideal conditions, neglecting imperfections from system-environment interactions.More advanced analyses consider estimation in the presence of known environmental noise.Although Heisenberglimited sensitivity is lost, suitably engineered probes can still offer quantum enhancements.When the noise itself is unknown, the estimation problem becomes more complex, requiring a multiparameter approach.Fundamental precision bounds for multiparameter estimation are well established, but their practical attainability remains elusive due to the challenge of constructing measurements with good multiparameter sensitivity.For a given probe, the incompatibility of optimal observables associated with different parameters poses an additional roadblock to achieving simultaneous optimal estimation.In practice, assessing the compatibility of separable measurements is essential, since very often collective strategies that are impractical are required to saturate the bound capturing fundamental incompatibility.To this end, we consider the joint estimation of phase and phase diffusion, introducing quantifiers for information extraction and availability.We find that double homodyne measurement on states generated by the interference of N photons injected into one beamsplitter port yields the highest sensitivity.With respect to measurement compatibility, we study the joint estimation of phase and photon loss, and of phase and phase diffusion.Using the same multiphoton states, we compare double homodyne detection and photon counting against multiparameter precision benchmarks for collective and separable measurements.Among the cases considered, photon counting generally offers better performance for joint phase and loss estimation, while double homodyne still performs reasonably in some regimes for both estimation problems.
The Cram\'er-Rao bound captures completely the performance of single-parameter quantum sensors. On the other hand, its extension to multiple parameters demands more caution. Different aspects need to be captured at once, including, critically, compatibility. In this article we consider compatibility in quantum interferometry for an important class of probe states, measured by double homodyne or photon counters, standard benchmarks for these applications. We include the presence of loss and phase diffusion in the estimation of a phase. Our results illustrate how different weighting of the precision on individual parameters affects their compatibility, adding to the list of considerations for quantum multiparameter estimation.
Abstract Accurate phase estimation in the presence of unknown phase diffusive noise is a crucial yet challenging task in noisy quantum metrology. This problem is particularly interesting due to the detrimental impact of the associated noise. Here, we investigate the joint estimation of phase and phase diffusion using generalized Holland–Burnett states, known for their experimental accessibility. These states provide performance close to the optimal state in single-parameter phase estimation, even in the presence of photon losses. We adopt a twofold approach by analyzing the joint information extraction through the double homodyne measurement and the joint information availability across all probe states. Through our analysis, we find that the highest sensitivities are obtained by using states created by directing all input photons into one port of a balanced beam splitter. Furthermore, we infer that good levels of sensitivity persist even in the presence of moderate photon losses, illustrating the remarkable resilience of our probe states under lossy conditions.
Accurate phase estimation plays a pivotal role in quantum metrology, yet its precision is significantly affected by noise, particularly phase-diffusive noise caused by phase drift. To address this challenge, the joint estimation of phase and phase diffusion has emerged as an effective approach, transforming the problem into a multi-parameter estimation task. However, the incompatibility between optimal measurements for different parameters prevents single-copy measurements from reaching the fundamental precision limits defined by the quantum Cramer-Rao bound. Meanwhile, collective measurements performed on multiple identical copies can mitigate this incompatibility and thus enhance the precision of joint parameter estimation. This work experimentally demonstrates joint phase and phase-diffusion estimation using deterministic Bell measurements on a two-qubit system. A linear optical network is employed to implement both parameter encoding and deterministic Bell measurements, achieving improved estimation precision compared to any separable measurement strategy. This work proposes a new framework for phase estimation under phase-diffusive noise and underscores the substantial advantages of collective measurements in multi-parameter quantum metrology.
Abstract Careful tailoring the quantum state of probes offers the capability of investigating matter at unprecedented precisions. Rarely, however, the interaction with the sample is fully encompassed by a single parameter, and the information contained in the probe needs to be partitioned on multiple parameters. There exist, then, practical bounds on the ultimate joint-estimation precision set by the unavailability of a single optimal measurement for all parameters. Here, we discuss how these considerations are modified for two-level quantum probes — qubits — by the use of two copies and entangling measurements. We find that the joint estimation of phase and phase diffusion benefits from such collective measurement, while for multiple phases no enhancement can be observed. We demonstrate this in a proof-of-principle photonics setup.
Simultaneous estimation of multiple parameters in quantum metrological models is complicated by factors relating to the (i) existence of a single probe state allowing for optimal sensitivity for all parameters of interest, (ii) existence of a single measurement optimally extracting information from the probe state on all the parameters, and (iii) statistical independence of the estimated parameters. We consider the situation when these concerns present no obstacle, and for every estimated parameter the variance obtained in the multiparameter scheme is equal to that of an optimal scheme for that parameter alone, assuming all other parameters are perfectly known. We call such models compatible. In establishing a rigorous theoretical framework for investigating compatibility, we clarify some ambiguities and inconsistencies present in the literature and discuss several examples to highlight interesting features of unitary and nonunitary parameter estimation, as well as deriving new bounds for physical problems of interest, such as the simultaneous estimation of phase and local dephasing.
This work compares the performance of single- and two-qubit probes for estimating several phase rotations simultaneously under the action of different noisy channels. We compute the quantum limits for this simultaneous estimation using collective and individual measurements by evaluating the Holevo and Nagaoka-Hayashi Cramér-Rao bounds, respectively. Several quantum noise channels are considered, namely the decohering channel, the amplitude damping channel, and the phase damping channel. For each channel, we find the optimal single- and two-qubit probes. Where possible we demonstrate an explicit measurement strategy that saturates the appropriate bound and we investigate how closely the Holevo bound can be approached through collective measurements on multiple copies of the same probe. We find that under the action of the considered channels, two-qubit probes show enhanced parameter estimation capabilities over single-qubit probes for almost all non-identity channels, i.e., the achievable precision with a single-qubit probe degrades faster with increasing exposure to the noisy environment than that of the two-qubit probe. However, in sufficiently noisy channels, we show that it is possible for single-qubit probes to outperform maximally entangled two-qubit probes. This work shows that, in order to reach the ultimate precision limits allowed by quantum mechanics, entanglement is required in both the state preparation and state measurement stages. It is hoped the tutorial-esque nature of this paper will make it easily accessible.