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arXiv:2609.20644

Quantum Noise Limited Nonlinear Phase-Preserving Amplification of a Bosonic Mode

Abel te Riele, Tzula B. Propp

quant-phSubmitted Sep 17, 2026• Announced Sep 18, 2026• 0 citations
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Abstract

Does quantum mechanics allow for deterministic amplification schemes that simultaneously behave uniformly for all angles of bosonic phase space (i.e. phase preserving) and are nonlinear in the underlying field operators? Would such a scheme have some utility to quantum information science? In this paper we answer both questions with a resounding yes. Such amplifiers exist, but their form is highly constrained compared to the more general set of noise limited nonlinear amplifiers previously studied in the literature. This enables us to characterize the entire class of bosonic noise-limited nonlinear phase preserving amplifiers, and identify their utility: namely, the optimal amplification of Yurke-Stoler cat states and Kerr kitten states.

Comments
10 pages, 3 figures

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Does quantum mechanics allow for deterministic amplification schemes that simultaneously behave uniformly for all angles of bosonic phase space (i.e. phase preserving) and are nonlinear in the underlying field operators? Would such a scheme have some utility to quantum information science? In this paper we answer both questions with a resounding yes. Such amplifiers exist, but their form is highly constrained compared to the more general set of noise limited nonlinear amplifiers previously studied in the literature. This enables us to characterize the entire class of bosonic noise-limited nonlinear phase preserving amplifiers, and identify their utility: namely, the optimal amplification of Yurke-Stoler cat states and Kerr kitten states.
The purpose of a phase-preserving linear amplifier is to make a small signal larger, regardless of its phase, so that it can be perceived by instruments incapable of resolving the original signal, while sacrificing as little as possible in signal-to-noise ratio. Quantum mechanics limits how well this can be done: A high-gain linear amplifier must degrade the signal-to-noise ratio; the noise added by the amplifier, when 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 derive the quantum constraints on the entire distribution of added noise: We show that any phase-preserving linear amplifier is equivalent to a parametric amplifier with a physical state for the ancillary mode; the noise added to the amplified field mode is distributed according to the Wigner function of the ancilla state.
We show that detection of single photons is not subject to the fundamental limitations that accompany quantum linear amplification of bosonic mode amplitudes, even though a photodetector does amplify a few-photon input signal to a macroscopic output signal. Alternative limits are derived for nonlinear photon-number amplification schemes with optimistic implications for single-photon detection. Four commutator-preserving transformations are presented: one idealized (which is optimal) and three more realistic (less than optimal). Our description makes clear that nonlinear amplification takes place, in general, at a different frequency ω' than the frequency ω of the input photons. This can be exploited to suppress thermal noise and dark counts past what is possible with linear amplification up to a fundamental limit imposed by nonlinear amplification into a single bosonic mode.
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.
We describe a new kind of phase-preserving quantum amplifier which utilizes dissipative interactions in a parametrically coupled three-mode bosonic system. The use of dissipative interactions provides a fundamental advantage over standard cavity-based parametric amplifiers: large photon number gains are possible with quantum-limited added noise, with no limitation on the gain-bandwidth product. We show that the scheme is simple enough to be implemented both in optomechanical systems and in superconducting microwave circuits.
Quantum amplifiers are intrinsically nonlinear systems whose performance limits are set by quantum mechanics. In quantum measurement, amplifier operation is conventionally optimized in the linear regime by maximizing signal-to-noise ratio, an objective that is well-suited to parameter estimation but is typically insufficient for more general tasks such as arbitrary quantum state discrimination. Here we show that single-shot quantum state classification can benefit from operating a quantum amplifier outside the linear regime, when the measurement chain is optimized end-to-end for a task-specific cost function. We analyze a realistic superconducting readout architecture that includes state preparation, cryogenic nonlinear amplification, and room-temperature detection with finite noise. By introducing performance metrics tailored to state discrimination, we identify operating regimes in which nonlinear amplification provides a measurable advantage and clarify the trade-offs that ultimately limit classification fidelity. Building on these results, we propose a qubit readout architecture without cavity displacement that exploits nonlinear amplification to enhance single-shot state discrimination performance. Our results establish the practical value of nonlinear quantum amplifiers for quantum state discrimination and lay the foundation for a broader program to develop a general, end-to-end framework for resource-constrained optimization of nonlinear amplification in quantum information processing tasks.