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Conference on Lasers and Electro-Optics Europe & European Quantum Electronics Conference (CLEO/Europe-EQEC)

Experimental Noiseless Quantum Amplification of Coherent States of Light by Two-Photon Addition and Subtraction

Michal Neset, Jiří Fadrný, Martin Bielak, Jaromı́r Fiurášek, Miroslav Ježek, Jan Bílek

Published Jun 23, 2025• 1 citation
Publisher

Abstract

Loss suppression is a major challenge in quantum communication and quantum computing, primarily due to the limitations imposed by the no-cloning theorem. We present a noiseless quantum amplifier capable of probabilistically increasing the amplitude of coherent states without introducing additional noise to the amplified state. This is achieved through the conditional addition and subtraction of photons. Previously, experimental photon addition was restricted to a single photon. Recently, we have pushed these boundaries, demonstrating photon addition of up to three photons for the first time [1], as well as the combination of conditional addition of two photons followed by their conditional subtraction [2]. Our advanced noiseless amplifier achieves high amplification gain, fidelity, and purity, with the quadrature variances of the noiselessly amplified coherent states remaining close to the minimum uncertainty limit. Figure 1 illustrates the performance of our amplifier compared to that of an amplifier based on single-photon addition and subtraction.

DOI
10.1109/cleo/europe-eqec65582.2025.11110780

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Loss suppression is a major challenge in quantum communication and quantum computing, primarily due to the limitations imposed by the no-cloning theorem. We present a noiseless quantum amplifier capable of probabilistically increasing the amplitude of coherent states without introducing additional noise to the amplified state. This is achieved through the conditional addition and subtraction of photons. Previously, experimental photon addition was restricted to a single photon. Recently, we have pushed these boundaries, demonstrating photon addition of up to three photons for the first time [1], as well as the combination of conditional addition of two photons followed by their conditional subtraction [2]. Our advanced noiseless amplifier achieves high amplification gain, fidelity, and purity, with the quadrature variances of the noiselessly amplified coherent states remaining close to the minimum uncertainty limit. Figure 1 illustrates the performance of our amplifier compared to that of an amplifier based on single-photon addition and subtraction.
Noiseless quantum amplifiers are probabilistic quantum devices that enhance amplitude of coherent states without adding any noise, which has far reaching applications in quantum optics and quantum information processing. Here, we report on experimental implementation of an advanced noiseless quantum amplifier for coherent states of light that is based on conditional addition of two photons followed by conditional subtraction of two photons. We comprehensively characterize the noiselessly amplified coherent states via quantum state tomography and analyze the amplification gain and noise properties of the amplifier. We observe very good agreement between the experiment and theoretical predictions. Our work reveals that sequences of multiple photon additions and subtractions represent an efficient and experimentally feasible alternative to multiplexing that was originally proposed to boost the performance of noiseless quantum amplifiers. Beyond noiseless quantum amplification, our experiment represents a significant step forward towards engineering complex quantum operations on traveling light beams by coherent combinations of various sequences of multiphoton additions and subtractions.
Noiseless quantum amplifiers are probabilistic quantum devices that enhance the amplitude of coherent states without adding any noise, which has far reaching applications in quantum optics and quantum information processing. Here, we report on an experimental implementation of an advanced noiseless quantum amplifier for coherent states of light that is based on the conditional addition of two photons followed by the conditional subtraction of two photons. We comprehensively characterize the noiselessly amplified coherent states via quantum state tomography and analyze the amplification gain and noise properties of the amplifier. We observe very good agreement between the experiment and theoretical predictions. Our work reveals that sequences of multiple photon additions and subtractions represent an efficient and experimentally feasible alternative to multiplexing that was originally proposed to boost the performance of noiseless quantum amplifiers. Beyond noiseless quantum amplification, our experiment represents a significant step forward towards engineering complex quantum operations on traveling light beams by coherent combinations of various sequences of multiphoton additions and subtractions.
We suggest and investigate a scheme for non-deterministic noiseless linear amplification of coherent states using successive photon addition, (â(†))(2), where â(†) is the photon creation operator. We compare it with a previous proposal using the photon addition-then-subtraction, ââ(†), where â is the photon annihilation operator, that works as an appropriate amplifier only for weak light fields. We show that when the amplitude of a coherent state is |α| ≳ 0.91, the (â(†))(2) operation serves as a more efficient amplifier compared to the ââ(†) operation in terms of equivalent input noise. Using ââ(†) and (â(†))(2) as basic building blocks, we compare combinatorial amplifications of coherent states using (ââ(†))(2), â(†4), ââ(†)â(†2), and â(†2)ââ(†), and show that (ââ(†))(2), â(†2)ââ(†), and â(†4) exhibit strongest noiseless properties for |α| ≲ 0.51, 0.51 ≲ |α| ≲ 1.05, and |α| ≳ 1.05, respectively. We further show that the (â(†))(2) operation can be useful for amplifying superpositions of the coherent states. In contrast to previous studies, our work provides efficient schemes to implement a noiseless amplifier for light fields with medium and large amplitudes.
We propose and theoretically analyze a teleportation-based scheme for the high-fidelity noiseless quantum amplification of coherent states of light. In our approach, the probabilistic noiseless quantum amplification operation is encoded into a suitable auxiliary two-mode entangled state and then applied to the input coherent state via continuous-variable quantum teleportation. The scheme requires conditioning on the outcomes of homodyne measurements in the teleportation protocol. In contrast to high-fidelity noiseless quantum amplifiers based on combination of conditional single-photon addition and subtraction, the present scheme requires only photon subtraction in combination with auxiliary Gaussian squeezed vacuum states. We first provide a pure-state description of the protocol which allows us to to clearly explain its principles and functioning. Next we develop a more comprehensive model based on phase-space representation of quantum states, that accounts for various experimental imperfections such as excess noise in the auxiliary squeezed states or limited efficiency of the single-photon detectors that can only distinguish the presence or absence of photons. We present and analyze predictions of this phase-space model of the noiseless teleamplifier.
Large-scale quantum networking systems will inevitably require methods to overcome photon loss. While the no-cloning theorem forbids perfect and deterministic amplification of unknown quantum states, probabilistic heralded amplification schemes offer a viable path forward. Yet, for over a decade, successful multi-photon state amplification has remained out of reach, despite the fundamental importance of such states in achieving quantum advantage in optical applications. Here, we experimentally demonstrate a high-fidelity and post-selection-free amplifier for multi-photon states. We achieve heralded amplification of states with up to two photons in a single optical mode, with over a hundredfold intensity gain, and verify the coherence-preserving operation of our scheme. Our approach is scalable to higher photon numbers and enables noiseless amplification of complex multi-photon quantum states, with applications in large-scale quantum communication systems, distributed quantum metrology, and information processing.
Abstract The quantum state probabilistic amplifier is a valuable tool for significantly amplifying quantum states without introducing additional noise. However, its inherently probabilistic nature often results in a low success rate, limiting scalability and practical deployment. In this paper, we propose a loop-based amplification scheme that integrates thermal noise addition with photon subtraction. This approach notably increases the success probability P and the fidelity of the amplified quantum state. Although a trade-off exists between P and the amplification gain, our scheme achieves favorable gain across all scenarios. Furthermore, the phase variance of the output state is minimized through optimization in each case. Analytical results demonstrate that configurations with higher maximum loop iterations preserve more Gaussian characteristics in the output state compared to direct photon subtraction. Finally, we examine the performance under non-ideal conditions and suggest potential avenues for further enhancement.