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:1501.01067 · Physical Review Letters

Linear Optical Quantum Metrology with Single Photons: Exploiting Spontaneously Generated Entanglement to Beat the Shot-Noise Limit

Keith R. Motes, Jonathan P. Olson, Evan J. Rabeaux, Jonathan P. Dowling, S. Jay Olson, Peter P. Rohde

Published Apr 30, 2015• 124 citations
arXivHTMLPDF

Abstract

Quantum number-path entanglement is a resource for supersensitive quantum metrology and in particular provides for sub-shot-noise or even Heisenberg-limited sensitivity. However, such number-path entanglement has been thought to be resource intensive to create in the first place--typically requiring either very strong nonlinearities, or nondeterministic preparation schemes with feedforward, which are difficult to implement. Very recently, arising from the study of quantum random walks with multiphoton walkers, as well as the study of the computational complexity of passive linear optical interferometers fed with single-photon inputs, it has been shown that such passive linear optical devices generate a superexponentially large amount of number-path entanglement. A logical question to ask is whether this entanglement may be exploited for quantum metrology. We answer that question here in the affirmative by showing that a simple, passive, linear-optical interferometer--fed with only uncorrelated, single-photon inputs, coupled with simple, single-mode, disjoint photodetection--is capable of significantly beating the shot-noise limit. Our result implies a pathway forward to practical quantum metrology with readily available technology.

DOI
10.1103/physrevlett.114.170802

Related papers

Linear optical quantum metrology with single photons: Experimental errors, resource counting, and quantum Cramér-Rao bounds

Jonathan P. Olson, Keith R. Motes, Patrick M. Birchall +5 more

Quantum number-path entanglement is a resource for supersensitive quantum metrology and in particular provides for sub-shot-noise or even Heisenberg-limited sensitivity. However, such number-path entanglement is thought to have been resource intensive to create in the first place, typically requiring either very strong nonlinearities or nondeterministic preparation schemes with feedforward, which are difficult to implement. Recently [K. R. Motes et al., Phys. Rev. Lett. 114, 170802 (2015)], it was shown that number-path entanglement from a BosonSampling inspired interferometer can be used to beat the shot-noise limit. In this paper we compare and contrast different interferometric schemes, discuss resource counting, calculate exact quantum Cram\'er-Rao bounds, and study details of experimental errors.

arXiv:1610.07128•Physical Review A•Jul 10, 2017•31 citations

Linear Optical Quantum Metrology with Single Photons

Keith R. Motes, Jonathan P. Olson, Evan J. Rabeaux +3 more

We show that a passive, linear-optical interferometer (fed with only single-photon inputs and utilizing single-mode photodetection) is capable of beating the shotnoise limit, providing a potential pathway forward to practical quantum metrology.

Frontiers in Optics•Jan 1, 2015•0 citations

Linear optics with projective measurements for fun and profit

Pieter Kok, Hwang Lee, Colin P. Williams +1 more

The technique of projective measurements in linear optics can provide apparent, efficient nonlinear interaction between photons, which is technically problematic otherwise. We present an application of such a technique to prepare large photon-number path entanglement. Large photon-number path entanglement is an important resource for Heisenberg-limited optical interferometry, where the sensitivity of phase measurements can be improved beyond the usual shot-noise limit. A similar technique can also be applied to signal the presence of a single photon without destroying it. We further show how to build a quantum repeater for long-distance quantum communication.

Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE•May 9, 2003•0 citations

Quantum correlations in optical metrology: Heisenberg-limited phase estimation without mode entanglement

Jaspreet Sahota, Nicolás Quesada

The quantum Fisher information and quantum correlation parameters are employed to study the application of nonclassical light to the problem of parameter estimation. It is shown that the optimal measurement sensitivity of a quantum state is determined by its intermode correlations (which depends on path entanglement) and intramode correlations (which depends on the photon statistics). In light of these results, we consider the performance of quantum-enhanced optical interferometers. Furthermore, we propose a Heisenberg-limited metrology protocol involving standard elements from passive and active linear optics, for which the quantum Cram\'er-Rao bound is saturated with an intensity measurement. Interestingly, the quantum advantage for this scheme is derived solely from the nonclassical photon statistics of the probe state and does not depend on entanglement. We study the performance of this scheme in the presence of realistic losses and consequently predict a substantial enhancement over the shot-noise limit with current technological capabilities.

arXiv:1404.7110•Physical Review A•Jan 6, 2015•69 citations

Unconditional shot-noise limit violation in photonic quantum metrology (Conference Presentation)

Geoff J. Pryde, Sergei Slussarenko

Quantum metrology exploits quantum correlations to perform measurements with precision higher than can be achieved with classical approaches [1]. Photonic approaches promise transformative advances in the family of interferometric phase measurement techniques, a vital toolset used to precisely determine quantities including distance, velocity, acceleration and materials properties. Without quantum enhancement, the precision limit in optical phase sensing (i.e. the minimum uncertainty) is the shot noise limit (SNL): 1/sqrt(N) where N is the number of resources (e.g. photons) used. Entangled photons promise sensitivity surpassing the shot noise limit achievable with classical probes. The maximally phase-sensitive state is the NOON state [2], a path-entangled state of definite photon number N. Despite theoretical proposals stretching back decades [3], no measurement using such photonic (i.e. definite photon number) states has unconditionally surpassed the shot noise limit: by contrast, all such demonstrations employed postselection to discount photon loss in the source, interferometer or detectors. Here, we use the state of art single photon generation and detection technology to respectively make and measure a two-photon NOON state, and use it to perform unconditional phase sensing beyond the shot noise limit — that is, without artificially correcting for loss or any other source of imperfection [4]. We performed a two-photon NOON state polarisation interferometry measurement on a birefringent test phase. We use photons generated from a high-heralding-efficiency, high purity source of telecom-wavelength photon pairs [5], and we employ high efficiency superconducting photon detectors. Unlike previous experiments, our apparatus does not require postselection to achieve phase uncertainty below that achievable in an ideal, lossless classical interferometer. Our results show a clear violation (for a range of phases) of the stringent SNL Fisher-information bound, F_{SNL} = 2.09635, that takes into account the information in unrecorded trials arising from loss and higher order terms — making our demonstration unconditional. We also performed a direct phase sensing measurement and observed phase uncertainties more than 10 standard deviations below the SNL [4]. Our results enable quantum-enhanced phase measurements at low photon flux and open the door to the next generation of optical quantum metrology advances. References [1] V. Giovannetti, S. Lloyd, and L. Maccone, “Advances in quantum metrology,” Nat. Photon. 5, 222–229 (2011). [2] J. P. Dowling, “Quantum optical metrology–the lowdown on high-N00N states,” Contemp. Phys. 49, 125–143 (2008). [3] R. Demkowicz-Dobrzanski, M. Jarzyna, and J. Kołodynski, “Quantum limits in optical interferometry,” Prog. Opt. 60, 345–435 (2015). [4] S. Slussarenko, M. M.Weston, H. M. Chrzanowski, L. K. Shalm, V. B. Verma, S.W. Nam, and G. J. Pryde, “Unconditional violation of the shot noise limit in photonic quantum metrology,” Nat. Photon. 11, 700-703 (2017). [5] M. M. Weston, H. M. Chrzanowski, S. Wollmann, A. Boston, J. Ho, L. K. Shalm, V. B. Verma, M. S. Allman, S. W. Nam, R. B. Patel, S. Slussarenko, and G. J. Pryde, “Efficient and pure femtosecond-pulse length source of polarization-entangled photons,” Opt. Express 24, 10,869–10,879 (2016).

SPIE Quantum Information Science and Technology•Oct 11, 2018•0 citations

Entanglement-enhanced quantum metrology in a noisy environment

Kunkun Wang, Xiaoping Wang, Xiang Zhan +4 more

Quantum metrology overcomes standard precision limits and plays a central role in science and technology. Practically, it is vulnerable to imperfections such as decoherence. Here we demonstrate quantum metrology for noisy channels such that entanglement with ancillary qubits enhances the quantum Fisher information for phase estimation but not otherwise. Our photonic experiment covers a range of noise for various types of channels, including for two randomly alternating channels such that assisted entanglement fails for each noisy channel individually. We simulate noisy channels by implementing space-multiplexed dual interferometers with quantum photonic inputs. We demonstrate the advantage of entanglement-assisted protocols in a phase estimation experiment run with either a single-probe or multiprobe approach. These results establish that entanglement with ancillae is a valuable approach for delivering quantum-enhanced metrology. Our approach to entanglement-assisted quantum metrology via a simple linear-optical interferometric network with easy-to-prepare photonic inputs provides a path towards practical quantum metrology.

arXiv:1707.08790•Physical Review A•Apr 19, 2018•76 citations
Quantum number-path entanglement is a resource for supersensitive quantum metrology and in particular provides for sub-shot-noise or even Heisenberg-limited sensitivity. However, such number-path entanglement has been thought to be resource intensive to create in the first place--typically requiring either very strong nonlinearities, or nondeterministic preparation schemes with feedforward, which are difficult to implement. Very recently, arising from the study of quantum random walks with multiphoton walkers, as well as the study of the computational complexity of passive linear optical interferometers fed with single-photon inputs, it has been shown that such passive linear optical devices generate a superexponentially large amount of number-path entanglement. A logical question to ask is whether this entanglement may be exploited for quantum metrology. We answer that question here in the affirmative by showing that a simple, passive, linear-optical interferometer--fed with only uncorrelated, single-photon inputs, coupled with simple, single-mode, disjoint photodetection--is capable of significantly beating the shot-noise limit. Our result implies a pathway forward to practical quantum metrology with readily available technology.
Quantum number-path entanglement is a resource for supersensitive quantum metrology and in particular provides for sub-shot-noise or even Heisenberg-limited sensitivity. However, such number-path entanglement is thought to have been resource intensive to create in the first place, typically requiring either very strong nonlinearities or nondeterministic preparation schemes with feedforward, which are difficult to implement. Recently [K. R. Motes et al., Phys. Rev. Lett. 114, 170802 (2015)], it was shown that number-path entanglement from a BosonSampling inspired interferometer can be used to beat the shot-noise limit. In this paper we compare and contrast different interferometric schemes, discuss resource counting, calculate exact quantum Cram\'er-Rao bounds, and study details of experimental errors.
The technique of projective measurements in linear optics can provide apparent, efficient nonlinear interaction between photons, which is technically problematic otherwise. We present an application of such a technique to prepare large photon-number path entanglement. Large photon-number path entanglement is an important resource for Heisenberg-limited optical interferometry, where the sensitivity of phase measurements can be improved beyond the usual shot-noise limit. A similar technique can also be applied to signal the presence of a single photon without destroying it. We further show how to build a quantum repeater for long-distance quantum communication.
The quantum Fisher information and quantum correlation parameters are employed to study the application of nonclassical light to the problem of parameter estimation. It is shown that the optimal measurement sensitivity of a quantum state is determined by its intermode correlations (which depends on path entanglement) and intramode correlations (which depends on the photon statistics). In light of these results, we consider the performance of quantum-enhanced optical interferometers. Furthermore, we propose a Heisenberg-limited metrology protocol involving standard elements from passive and active linear optics, for which the quantum Cram\'er-Rao bound is saturated with an intensity measurement. Interestingly, the quantum advantage for this scheme is derived solely from the nonclassical photon statistics of the probe state and does not depend on entanglement. We study the performance of this scheme in the presence of realistic losses and consequently predict a substantial enhancement over the shot-noise limit with current technological capabilities.
Quantum metrology exploits quantum correlations to perform measurements with precision higher than can be achieved with classical approaches [1]. Photonic approaches promise transformative advances in the family of interferometric phase measurement techniques, a vital toolset used to precisely determine quantities including distance, velocity, acceleration and materials properties. Without quantum enhancement, the precision limit in optical phase sensing (i.e. the minimum uncertainty) is the shot noise limit (SNL): 1/sqrt(N) where N is the number of resources (e.g. photons) used. Entangled photons promise sensitivity surpassing the shot noise limit achievable with classical probes. The maximally phase-sensitive state is the NOON state [2], a path-entangled state of definite photon number N. Despite theoretical proposals stretching back decades [3], no measurement using such photonic (i.e. definite photon number) states has unconditionally surpassed the shot noise limit: by contrast, all such demonstrations employed postselection to discount photon loss in the source, interferometer or detectors. Here, we use the state of art single photon generation and detection technology to respectively make and measure a two-photon NOON state, and use it to perform unconditional phase sensing beyond the shot noise limit — that is, without artificially correcting for loss or any other source of imperfection [4]. We performed a two-photon NOON state polarisation interferometry measurement on a birefringent test phase. We use photons generated from a high-heralding-efficiency, high purity source of telecom-wavelength photon pairs [5], and we employ high efficiency superconducting photon detectors. Unlike previous experiments, our apparatus does not require postselection to achieve phase uncertainty below that achievable in an ideal, lossless classical interferometer. Our results show a clear violation (for a range of phases) of the stringent SNL Fisher-information bound, F_{SNL} = 2.09635, that takes into account the information in unrecorded trials arising from loss and higher order terms — making our demonstration unconditional. We also performed a direct phase sensing measurement and observed phase uncertainties more than 10 standard deviations below the SNL [4]. Our results enable quantum-enhanced phase measurements at low photon flux and open the door to the next generation of optical quantum metrology advances. References [1] V. Giovannetti, S. Lloyd, and L. Maccone, “Advances in quantum metrology,” Nat. Photon. 5, 222–229 (2011). [2] J. P. Dowling, “Quantum optical metrology–the lowdown on high-N00N states,” Contemp. Phys. 49, 125–143 (2008). [3] R. Demkowicz-Dobrzanski, M. Jarzyna, and J. Kołodynski, “Quantum limits in optical interferometry,” Prog. Opt. 60, 345–435 (2015). [4] S. Slussarenko, M. M.Weston, H. M. Chrzanowski, L. K. Shalm, V. B. Verma, S.W. Nam, and G. J. Pryde, “Unconditional violation of the shot noise limit in photonic quantum metrology,” Nat. Photon. 11, 700-703 (2017). [5] M. M. Weston, H. M. Chrzanowski, S. Wollmann, A. Boston, J. Ho, L. K. Shalm, V. B. Verma, M. S. Allman, S. W. Nam, R. B. Patel, S. Slussarenko, and G. J. Pryde, “Efficient and pure femtosecond-pulse length source of polarization-entangled photons,” Opt. Express 24, 10,869–10,879 (2016).
Quantum metrology overcomes standard precision limits and plays a central role in science and technology. Practically, it is vulnerable to imperfections such as decoherence. Here we demonstrate quantum metrology for noisy channels such that entanglement with ancillary qubits enhances the quantum Fisher information for phase estimation but not otherwise. Our photonic experiment covers a range of noise for various types of channels, including for two randomly alternating channels such that assisted entanglement fails for each noisy channel individually. We simulate noisy channels by implementing space-multiplexed dual interferometers with quantum photonic inputs. We demonstrate the advantage of entanglement-assisted protocols in a phase estimation experiment run with either a single-probe or multiprobe approach. These results establish that entanglement with ancillae is a valuable approach for delivering quantum-enhanced metrology. Our approach to entanglement-assisted quantum metrology via a simple linear-optical interferometric network with easy-to-prepare photonic inputs provides a path towards practical quantum metrology.