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

arXiv:2302.01343 · Physical Review A

Measuring the quadrature coherence scale on a cloud quantum computer

Aaron Z. Goldberg, Guillaume Thekkadath, Khabat Heshami

Published Apr 14, 2023• 14 citations
arXivHTMLPDF

Abstract

Coherence underlies quantum phenomena, yet it is manifest in classical theories; delineating coherence's role is a fickle business. The quadrature coherence scale (QCS) was invented to remove such ambiguity, quantifying quantum features of any single-mode bosonic system without choosing a preferred orientation of phase space. The QCS is defined for any state, reducing to well-known quantities in appropriate limits, including Gaussian and pure states, and perhaps most importantly for a coherence measure, it is highly sensitive to decoherence. Until recently, it was unknown how to measure the QCS; we here report on an initial measurement of the QCS for squeezed light and thermal states of light. This is performed using Xanadu's machine Borealis, accessed through the cloud, which offers the configurable beam splitters and photon-number-resolving detectors essential for measuring the QCS. The data and theory match well, certifying the usefulness of interferometers and photon-counting devices in certifying quantumness.

DOI
10.1103/physreva.107.042610

Related papers

Quadrature coherence scale of linear combinations of Gaussian functions in phase space

Anaelle Hertz, Aaron Z. Goldberg, Khabat Heshami

The quadrature coherence scale (QCS) is a recently introduced measure that was shown to be an efficient witness of nonclassicality. It takes a simple form for pure and Gaussian states, but a general expression for mixed states tends to be prohibitively unwieldy. In this paper we introduce a method for computing the quadrature coherence scale of quantum states characterized by Wigner functions expressible as linear combinations of Gaussian functions. Notable examples within this framework include cat states, Gottesman-Kitaev-Preskill states, and states resulting from Gaussian transformations, measurements, and breeding protocols. In particular, we show that the quadrature coherence scale serves as a valuable tool for examining the scalability of nonclassicality in the presence of loss. Our findings lead us to put forth a conjecture suggesting that, subject to 50% loss or more, all pure states lose any QCS-certifiable nonclassicality. We also consider the quadrature coherence scale as a measure of quality of the output state of the breeding protocol.

arXiv:2402.04404•Physical Review A•Jul 1, 2024•3 citations

Quadrature Coherence Scale Driven Fast Decoherence of Bosonic Quantum Field States

Anaelle Hertz, Stephan De Bièvre

We introduce, for each state of a bosonic quantum field, its quadrature coherence scale (QCS), a measure of the range of its quadrature coherences. Under coupling to a thermal bath, the purity and QCS are shown to decrease on a timescale inversely proportional to the QCS squared. The states most fragile to decoherence are therefore those with quadrature coherences far from the diagonal. We further show a large QCS is difficult to measure since it induces small scale variations in the state's Wigner function. These two observations imply a large QCS constitutes a mark of "macroscopic coherence." Finally, we link the QCS to optical classicality: optical classical states have a small QCS and a large QCS implies strong optical nonclassicality.

arXiv:1909.05025•Physical Review Letters•Mar 5, 2020•19 citations

Thermal activation of photon catalysis in difference-intensity Mach-Zehnder interferometry with squeezed thermal light

Kirtpreet Singh, Arvind

Realistic non-Gaussian operations, which can be implemented by mixing a nonclassical Gaussian state with a Fock state at a beam splitter and then heralding on a photon-number-resolving detector, are known to improve phase estimation in a Mach-Zehnder interferometer. The existing studies have considered the single-mode squeezed vacuum for difference-intensity and parity detection, and the two-mode squeezed thermal state for parity detection alone as the initial Gaussian resources. However, a real squeezer in the lab actually produces single-mode squeezed thermal light, which has not been studied in a coherent-plus-resource interferometer. We take up this case and using the phase space Wigner picture, we obtain the heralded state produced by photon subtraction, addition and catalysis on a single-mode squeezed thermal resource, and evaluate the corresponding phase sensitivities. Single-photon catalysis, which is useless on squeezed vacuum, becomes a useful operation for any thermal occupation above $\nth\simeq0.2$, and since it heralds with a probability near one-half, it turns out to be the best success-weighted operation over the whole thermal range. In the vacuum limit our results reproduce the known hierarchy, where two-photon catalysis is the best operation. The quantum Fisher information computations confirms that thermal noise enhances the phase information encoded in the catalyzed state, demonstrating that difference-intensity detection closely approaches the ultimate precision bound across most operational regimes, and, together with a loss analysis, verifies the robustness of the effect.

quant-pharXiv:2610.22004•Oct 16, 2026•0 citations

In situ characterization of a photon-subtraction device via heralding counts and homodyne detection

Priyanka Sharma, Matteo G. A. Paris, Stefano Olivares

Photon subtraction is one of the most important techniques for generating non-Gaussian optical states and constitutes a key resource for quantum information processing and quantum metrology. The practical performance of a photon-subtraction device is primarily determined by the transmissivity of the beam splitter and the quantum efficiency of the heralding detector. Accurate knowledge of these parameters is therefore essential for assessing the quality of the generated non-classical states. In this work, we propose an experimentally feasible in situ scheme for the simultaneous estimation of these two parameters using only the measurement data produced during the operation of the device. Our protocol combines the click statistics of an on/off heralding detector with homodyne measurements performed on the transmitted mode of the beam splitter when fed by a displaced squeezed state. Within the framework of classical multi-parameter estimation theory, we derive the corresponding Fisher information matrix and investigate both joint and sequential estimation strategies. For simultaneous measurement of parameters, we evaluate the sloppiness of the underlying statistical model and analyze its dependence on the measured quadrature, probe photon number, squeezing fraction, beam splitter transmissivity, and detector efficiency. Our analysis proves that an appropriate choice of the homodyne quadrature substantially reduces parameter degeneracy and enables efficient simultaneous estimation. Furthermore, we show that the joint estimation strategy consistently provides a lower estimation bound than the sequential estimation approach over a broad range of experimentally relevant parameters.

quant-pharXiv:2609.10100•Sep 10, 2026•0 citations

Spin coherence scale: Operator-ordering sensitivity beyond the Heisenberg-Weyl group

Aaron Z. Goldberg, Andre J. Rodrigues, Y. Batuhan Yilmaz +2 more

We introduce the spin coherence scale as a measure of quantum coherence for spin systems, generalizing the quadrature coherence scale (QCS) previously defined for quadrature observables. This SU($2$)-invariant measure quantifies the off-diagonal coherences of a quantum state in angular momentum bases, weighted by the classical distinguishability of the superposed states. It serves as a witness of nonclassicality, provides both upper and lower bounds on the Hilbert-Schmidt distance to the set of classical (spin coherent) states, and bounds the Wigner negativity of a spin state. We demonstrate that many hallmark properties of the QCS carry over to the spin setting, including its links to noise susceptibility of a state and moments of quasiprobability distributions and its experimental realizability with a two-copy scheme. The spin coherence scale has direct implications for quantum metrology in the guise of rotation sensing. We also generalize the framework to SU($n$) systems, identifying the unique SU($n$)-invariant depolarization channel and outlining a broad, Lie-algebraic approach to defining and characterizing the properties of coherence scale beyond harmonic oscillators.

arXiv:2510.09747•Physical Review A•Apr 30, 2026•0 citations

Coherence and incoherence in quadrature basis

Laura Ares, Alfredo Luis

How to manage coherence as a continuous variable quantum resource is still an open question. We face this situation from the very definition of incoherent states in quadrature basis. We apply several measures of coherence for some physical states of light relative to a quadrature basis. We examine the action on the coherence of several transformations such as beam splittings and squeezing.

arXiv:2307.08333•Jul 17, 2023•0 citations
Coherence underlies quantum phenomena, yet it is manifest in classical theories; delineating coherence's role is a fickle business. The quadrature coherence scale (QCS) was invented to remove such ambiguity, quantifying quantum features of any single-mode bosonic system without choosing a preferred orientation of phase space. The QCS is defined for any state, reducing to well-known quantities in appropriate limits, including Gaussian and pure states, and perhaps most importantly for a coherence measure, it is highly sensitive to decoherence. Until recently, it was unknown how to measure the QCS; we here report on an initial measurement of the QCS for squeezed light and thermal states of light. This is performed using Xanadu's machine Borealis, accessed through the cloud, which offers the configurable beam splitters and photon-number-resolving detectors essential for measuring the QCS. The data and theory match well, certifying the usefulness of interferometers and photon-counting devices in certifying quantumness.
The quadrature coherence scale (QCS) is a recently introduced measure that was shown to be an efficient witness of nonclassicality. It takes a simple form for pure and Gaussian states, but a general expression for mixed states tends to be prohibitively unwieldy. In this paper we introduce a method for computing the quadrature coherence scale of quantum states characterized by Wigner functions expressible as linear combinations of Gaussian functions. Notable examples within this framework include cat states, Gottesman-Kitaev-Preskill states, and states resulting from Gaussian transformations, measurements, and breeding protocols. In particular, we show that the quadrature coherence scale serves as a valuable tool for examining the scalability of nonclassicality in the presence of loss. Our findings lead us to put forth a conjecture suggesting that, subject to 50% loss or more, all pure states lose any QCS-certifiable nonclassicality. We also consider the quadrature coherence scale as a measure of quality of the output state of the breeding protocol.
We introduce, for each state of a bosonic quantum field, its quadrature coherence scale (QCS), a measure of the range of its quadrature coherences. Under coupling to a thermal bath, the purity and QCS are shown to decrease on a timescale inversely proportional to the QCS squared. The states most fragile to decoherence are therefore those with quadrature coherences far from the diagonal. We further show a large QCS is difficult to measure since it induces small scale variations in the state's Wigner function. These two observations imply a large QCS constitutes a mark of "macroscopic coherence." Finally, we link the QCS to optical classicality: optical classical states have a small QCS and a large QCS implies strong optical nonclassicality.
Realistic non-Gaussian operations, which can be implemented by mixing a nonclassical Gaussian state with a Fock state at a beam splitter and then heralding on a photon-number-resolving detector, are known to improve phase estimation in a Mach-Zehnder interferometer. The existing studies have considered the single-mode squeezed vacuum for difference-intensity and parity detection, and the two-mode squeezed thermal state for parity detection alone as the initial Gaussian resources. However, a real squeezer in the lab actually produces single-mode squeezed thermal light, which has not been studied in a coherent-plus-resource interferometer. We take up this case and using the phase space Wigner picture, we obtain the heralded state produced by photon subtraction, addition and catalysis on a single-mode squeezed thermal resource, and evaluate the corresponding phase sensitivities. Single-photon catalysis, which is useless on squeezed vacuum, becomes a useful operation for any thermal occupation above $\nth\simeq0.2$, and since it heralds with a probability near one-half, it turns out to be the best success-weighted operation over the whole thermal range. In the vacuum limit our results reproduce the known hierarchy, where two-photon catalysis is the best operation. The quantum Fisher information computations confirms that thermal noise enhances the phase information encoded in the catalyzed state, demonstrating that difference-intensity detection closely approaches the ultimate precision bound across most operational regimes, and, together with a loss analysis, verifies the robustness of the effect.
Photon subtraction is one of the most important techniques for generating non-Gaussian optical states and constitutes a key resource for quantum information processing and quantum metrology. The practical performance of a photon-subtraction device is primarily determined by the transmissivity of the beam splitter and the quantum efficiency of the heralding detector. Accurate knowledge of these parameters is therefore essential for assessing the quality of the generated non-classical states. In this work, we propose an experimentally feasible in situ scheme for the simultaneous estimation of these two parameters using only the measurement data produced during the operation of the device. Our protocol combines the click statistics of an on/off heralding detector with homodyne measurements performed on the transmitted mode of the beam splitter when fed by a displaced squeezed state. Within the framework of classical multi-parameter estimation theory, we derive the corresponding Fisher information matrix and investigate both joint and sequential estimation strategies. For simultaneous measurement of parameters, we evaluate the sloppiness of the underlying statistical model and analyze its dependence on the measured quadrature, probe photon number, squeezing fraction, beam splitter transmissivity, and detector efficiency. Our analysis proves that an appropriate choice of the homodyne quadrature substantially reduces parameter degeneracy and enables efficient simultaneous estimation. Furthermore, we show that the joint estimation strategy consistently provides a lower estimation bound than the sequential estimation approach over a broad range of experimentally relevant parameters.
We introduce the spin coherence scale as a measure of quantum coherence for spin systems, generalizing the quadrature coherence scale (QCS) previously defined for quadrature observables. This SU(222)-invariant measure quantifies the off-diagonal coherences of a quantum state in angular momentum bases, weighted by the classical distinguishability of the superposed states. It serves as a witness of nonclassicality, provides both upper and lower bounds on the Hilbert-Schmidt distance to the set of classical (spin coherent) states, and bounds the Wigner negativity of a spin state. We demonstrate that many hallmark properties of the QCS carry over to the spin setting, including its links to noise susceptibility of a state and moments of quasiprobability distributions and its experimental realizability with a two-copy scheme. The spin coherence scale has direct implications for quantum metrology in the guise of rotation sensing. We also generalize the framework to SU(nnn) systems, identifying the unique SU(nnn)-invariant depolarization channel and outlining a broad, Lie-algebraic approach to defining and characterizing the properties of coherence scale beyond harmonic oscillators.