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APS March Meeting Abstracts

Quantum noise limits for a class of nonlinear amplifiers

Jeffrey M. Epstein, K. Birgitta Whaley, Joshua Combes

Published Jan 1, 2019• 0 citations
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Abstract

Nonlinear amplifiers, such as the transistor, are ubiquitous in classical technology. Little is understood about the noise properties and applications of quantum nonlinear amplifiers. We introduce a class of nonlinear amplifiers that allow one to measure any normal operator with a linear detector while adding a half-quantum of vacuum fluctuations as noise at the output. When these nonlinear amplifiers are used in conjunction with noisy linear detectors, the resulting measurement in the large gain limit becomes equivalent to ideal projective measurement of the normal operator.

Related papers

Quantum limits on noise for a class of nonlinear amplifiers

Jeffrey M. Epstein, K. Birgitta Whaley, Joshua Combes

Nonlinear amplifiers such as the transistor are ubiquitous in classical technology, but their quantum analogs are not well understood. We introduce a class of nonlinear amplifiers that amplify any normal operator and add only a half quantum of vacuum noise at the output. In the large-gain limit, when used in conjunction with a noisy linear detectors, these amplifiers implement ideal measurements of the normal operator.

arXiv:2010.13851•Physical Review A•May 14, 2021•8 citations

Quantum noise in ideal operational amplifiers

Jean-Michel Courty, Francesca Grassia, Serge Reynaud

We consider a model of quantum measurement built on an ideal operational amplifier operating in the limit of infinite gain, infinite input impedance and null output impedance and with a feddback loop. We evaluate the intensity and voltage noises which have to be added to the classical amplification equations in order to fulfill the requirements of quantum mechanics. We give a description of this measurement device as a quantum network scattering quantum fluctuations from input to output ports.

•Jan 1, 1999•13 citations

Quantum noise in ideal operational amplifiers

Jean-Michel Courty, Francesca Grassia, Serge Reynaud

We consider a model of quantum measurement built on an ideal operational amplifier operating in the limit of infinite gain, infinite input impedance and null output impedance and with a feedback loop. We evaluate the intensity and voltage noises which have to be added to the classical amplification equations in order to fulfill the requirements of quantum mechanics. We give a description of this measurement device as a quantum network scattering quantum fluctuations from input to output ports.

arXiv:quant-ph/9811062•Europhysics Letters (EPL)•Apr 1, 1999•14 citations

Quantum limits on noise in linear amplifiers

Carlton M. Caves

How much noise does quantum mechanics require a linear amplifier to add to a signal it processes? An analysis of narrow-band amplifiers (single-mode input and output) yields a fundamental theorem for phase-insensitive linear amplifiers; it requires such an amplifier, in the limit of high gain, to add noise which, referred to the input, is at least as large as the half-quantum of zero-point fluctuations. For phase-sensitive linear amplifiers, which can respond differently to the two quadrature phases ("$cos\ensuremath{\omega}t$" and "$sin\ensuremath{\omega}t$"), the single-mode analysis yields an amplifier uncertainty principle---a lower limit on the product of the noises added to the two phases. A multimode treatment of linear amplifiers generalizes the single-mode analysis to amplifiers with nonzero bandwidth. The results for phase-insensitive amplifiers remain the same, but for phase-sensitive amplifiers there emerge bandwidth-dependent corrections to the single-mode results. Specifically, there is a bandwidth-dependent lower limit on the noise carried by one quadrature phase of a signal and a corresponding lower limit on the noise a high-gain linear amplifier must add to one quadrature phase. Particular attention is focused on developing a multimode description of signals with unequal noise in the two quadrature phases.

Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields•Oct 15, 1982•1,723 citations

Surpassing Quantum Noise Limits with Nonlinear Amplification

Ya-Long Ren, Rong-Teng Cao, Sheng-Li Ma +4 more

Linear quantum amplifiers are indispensable tools for quantum technologies, yet their performance is fundamentally limited by quantum noise, precluding any signal-to-noise ratio (SNR) enhancement unless supplemented by post-selection or non-classical resources. To surpass this limitation, we propose a nonlinear quantum amplification strategy that exploits the interplay between a gain-stabilized bright eigenmode of a coupled two-mode bosonic system and Kerr nonlinearity. We demonstrate that this interplay enables the signal gain to surpass the noise gain in a selected quadrature, leading to a net increase in the SNR beyond the quantum limits of conventional linear amplifiers. Our work thus establishes a novel nonlinear amplification paradigm capable of enhancing the SNR, with promising applications across quantum information processing, quantum communications, and quantum metrology.

quant-pharXiv:2603.11574•Mar 13, 2026•0 citations

Noise in phase-preserving linear amplifiers

Shashank Pandey, Jiang Zhang, Joshua Combes +1 more

The purpose of a phase-preserving linear amplifier is to make a small signal larger, so that it can be perceived by instruments incapable of resolving the original signal, while sacrificing as little as possible in signal-to-noise. Quantum mechanics limits how well this can be done: the noise added by the amplifier, referred to the input, must be at least half a quantum at the operating frequency. This well-known quantum limit only constrains the second moments of the added noise. Here we provide the quantum constraints on the entire distribution of added noise: any phasepreserving linear amplifier is equivalent to a parametric amplifier with a physical state σ for the ancillary mode; σ determines the properties of the added noise.

AIP conference proceedings•Jan 1, 2014•0 citations
Nonlinear amplifiers, such as the transistor, are ubiquitous in classical technology. Little is understood about the noise properties and applications of quantum nonlinear amplifiers. We introduce a class of nonlinear amplifiers that allow one to measure any normal operator with a linear detector while adding a half-quantum of vacuum fluctuations as noise at the output. When these nonlinear amplifiers are used in conjunction with noisy linear detectors, the resulting measurement in the large gain limit becomes equivalent to ideal projective measurement of the normal operator.
How much noise does quantum mechanics require a linear amplifier to add to a signal it processes? An analysis of narrow-band amplifiers (single-mode input and output) yields a fundamental theorem for phase-insensitive linear amplifiers; it requires such an amplifier, in the limit of high gain, to add noise which, referred to the input, is at least as large as the half-quantum of zero-point fluctuations. For phase-sensitive linear amplifiers, which can respond differently to the two quadrature phases ("$cos\ensuremath{\omega}t$" and "$sin\ensuremath{\omega}t$"), the single-mode analysis yields an amplifier uncertainty principle---a lower limit on the product of the noises added to the two phases. A multimode treatment of linear amplifiers generalizes the single-mode analysis to amplifiers with nonzero bandwidth. The results for phase-insensitive amplifiers remain the same, but for phase-sensitive amplifiers there emerge bandwidth-dependent corrections to the single-mode results. Specifically, there is a bandwidth-dependent lower limit on the noise carried by one quadrature phase of a signal and a corresponding lower limit on the noise a high-gain linear amplifier must add to one quadrature phase. Particular attention is focused on developing a multimode description of signals with unequal noise in the two quadrature phases.
Linear quantum amplifiers are indispensable tools for quantum technologies, yet their performance is fundamentally limited by quantum noise, precluding any signal-to-noise ratio (SNR) enhancement unless supplemented by post-selection or non-classical resources. To surpass this limitation, we propose a nonlinear quantum amplification strategy that exploits the interplay between a gain-stabilized bright eigenmode of a coupled two-mode bosonic system and Kerr nonlinearity. We demonstrate that this interplay enables the signal gain to surpass the noise gain in a selected quadrature, leading to a net increase in the SNR beyond the quantum limits of conventional linear amplifiers. Our work thus establishes a novel nonlinear amplification paradigm capable of enhancing the SNR, with promising applications across quantum information processing, quantum communications, and quantum metrology.
The purpose of a phase-preserving linear amplifier is to make a small signal larger, so that it can be perceived by instruments incapable of resolving the original signal, while sacrificing as little as possible in signal-to-noise. Quantum mechanics limits how well this can be done: the noise added by the amplifier, referred to the input, must be at least half a quantum at the operating frequency. This well-known quantum limit only constrains the second moments of the added noise. Here we provide the quantum constraints on the entire distribution of added noise: any phasepreserving linear amplifier is equivalent to a parametric amplifier with a physical state σ for the ancillary mode; σ determines the properties of the added noise.