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:quant-ph/0312169 · Journal of Optics B Quantum and Semiclassical Optics

From linear optical quantum computing to Heisenberg-limited interferometry

Hwang Lee, Pieter Kok, Colin P. Williams, Jonathan P Dowling

Published Jul 28, 2004• 7 citations
arXivHTMLPDF

Abstract

The working principles of linear optical quantum computing are based on photodetection, namely, projective measurements. The use of photodetection can provide efficient nonlinear interactions between photons at the single-photon level, which is technically problematic otherwise. We report an application of such a technique to prepare quantum correlations as an important resource for Heisenberg-limited optical interferometry, where the sensitivity of phase measurements can be improved beyond the usual shot-noise limit. Furthermore, using such nonlinearities, optical quantum nondemolition measurements can now be carried out at the single-photon level.

DOI
10.1088/1464-4266/6/8/026

Related papers

From Linear Optical Quantum Computing to Heisenberg-Limited Interferometry

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

Abstract. The working principles of linear optical quantum computing are based on photodetection, namely, projective measurements. The use of photodetection can provide efficient nonlinear interactions between photons at the single-photon level, which is technically problematic otherwise. We report an application of such a technique to prepare quantum correlations as an important resource for Heisenberglimited optical interferometry, where the sensitivity of phase measurements can be improved beyond the usual shot-noise limit. Furthermore, using such nonlinearities, optical quantum nondemolition measurements can now be carried out at the singlephoton level. § To whom correspondence should be addressed (jonathan.p.dowling@jpl.nasa.gov) From Linear Optical Quantum Computing... 2 1. Effective nonlinearities by projective measurements Looking back, scalable quantum computation with linear optics was considered to be impossible due to the lack of efficient two-qubit logic gates, despite the ease of implementation of one-qubit gates. Two-qubit gates necessarily need a nonlinear interaction between the two photons, and the efficiency of this nonlinear interaction is

Civil War Book Review•Jan 1, 2003•6 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

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 +3 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 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.

arXiv:1501.01067•Physical Review Letters•Apr 30, 2015•124 citations

Linear Optical Quantum Information Processing, Imaging, and Sensing

Nickolas M. VanMeter, Zhanghan Wu, Hugo V. Cable +8 more

We investigate linear optical approaches to quantum information processing, clarifying how linear optics and projective measurements can be used to create designer optical nonlinearities at the few photon level. We apply the lessons learned to develop optimized schemes for generating entangled photonic states for quantum imaging, with super-resolution below the Rayleigh limit, and for quantum sensing, with super-sensitivity below the shot-noise limit.

International Conference on Quantum Information•Jan 1, 2007•0 citations

Achieving Heisenberg-Scaling Precision with Projective Measurement on Single Photons

Geng Chen, Lijian Zhang, Wen-Hao Zhang +11 more

It has been suggested that both quantum superpositions and nonlinear interactions are important resources for quantum metrology. However, to date the different roles that these two resources play in the precision enhancement are not well understood. Here, we experimentally demonstrate a Heisenberg-scaling metrology to measure the parameter governing the nonlinear coupling between two different optical modes. The intense mode with n (more than 10^{6} in our work) photons manifests its effect through the nonlinear interaction strength which is proportional to its average photon number. The superposition state of the weak mode, which contains only a single photon, is responsible for both the linear Hamiltonian and the scaling of the measurement precision. By properly preparing the initial state of single photon and making projective photon-counting measurements, the extracted classical Fisher information (FI) can saturate the quantum FI embedded in the combined state after coupling, which is ∼n^{2} and leads to a practical precision ≃1.2/n. Free from the utilization of entanglement, our work paves a way to realize Heisenberg-scaling precision when only a linear Hamiltonian is involved.

arXiv:1808.02683•Physical Review Letters•Aug 8, 2018•39 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
The working principles of linear optical quantum computing are based on photodetection, namely, projective measurements. The use of photodetection can provide efficient nonlinear interactions between photons at the single-photon level, which is technically problematic otherwise. We report an application of such a technique to prepare quantum correlations as an important resource for Heisenberg-limited optical interferometry, where the sensitivity of phase measurements can be improved beyond the usual shot-noise limit. Furthermore, using such nonlinearities, optical quantum nondemolition measurements can now be carried out at the single-photon level.
Abstract. The working principles of linear optical quantum computing are based on photodetection, namely, projective measurements. The use of photodetection can provide efficient nonlinear interactions between photons at the single-photon level, which is technically problematic otherwise. We report an application of such a technique to prepare quantum correlations as an important resource for Heisenberglimited optical interferometry, where the sensitivity of phase measurements can be improved beyond the usual shot-noise limit. Furthermore, using such nonlinearities, optical quantum nondemolition measurements can now be carried out at the singlephoton level. § To whom correspondence should be addressed (jonathan.p.dowling@jpl.nasa.gov) From Linear Optical Quantum Computing... 2 1. Effective nonlinearities by projective measurements Looking back, scalable quantum computation with linear optics was considered to be impossible due to the lack of efficient two-qubit logic gates, despite the ease of implementation of one-qubit gates. Two-qubit gates necessarily need a nonlinear interaction between the two photons, and the efficiency of this nonlinear interaction is
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.
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.
It has been suggested that both quantum superpositions and nonlinear interactions are important resources for quantum metrology. However, to date the different roles that these two resources play in the precision enhancement are not well understood. Here, we experimentally demonstrate a Heisenberg-scaling metrology to measure the parameter governing the nonlinear coupling between two different optical modes. The intense mode with n (more than 10^{6} in our work) photons manifests its effect through the nonlinear interaction strength which is proportional to its average photon number. The superposition state of the weak mode, which contains only a single photon, is responsible for both the linear Hamiltonian and the scaling of the measurement precision. By properly preparing the initial state of single photon and making projective photon-counting measurements, the extracted classical Fisher information (FI) can saturate the quantum FI embedded in the combined state after coupling, which is ∼n^{2} and leads to a practical precision ≃1.2/n. Free from the utilization of entanglement, our work paves a way to realize Heisenberg-scaling precision when only a linear Hamiltonian is involved.
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.