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

PRX Quantum

Saturating the Maximum Success Probability Bound for Noiseless Linear Amplification Using Linear Optics

Joshua J. Guanzon, Matthew S. Winnel, Deepesh Singh, Austin P. Lund, Timothy C. Ralph

Published Jun 13, 2024• 9 citations
Publisher

Abstract

A noiseless linear amplifier (NLA) performs the highest-quality amplification allowable under the rules of quantum physics. Unfortunately, these same rules conspire against us via the no-cloning theorem, which constrains NLA operations to the domain of probabilistic processes. Nevertheless, they are useful for a wide variety of quantum protocols, with numerous proposals assuming access to an optimal NLA device that performs with the maximum possible success probability. Here we propose the first linear-optics NLA protocol that asymptotically achieves this success probability bound by modifying the Knill-Laflamme-Milburn near-deterministic teleporter into an amplifier. Published by the American Physical Society 2024

DOI
10.1103/prxquantum.5.020359

Related papers

Saturating the Maximum Success Probability Bound for Noiseless Linear Amplification Using Linear Optics

Joshua J. Guanzon, Matthew S. Winnel, Deepesh Singh +2 more

A noiseless linear amplifier (NLA) performs the highest quality amplification allowable under the rules of quantum physics. Unfortunately, these same rules conspire against us via the no-cloning theorem, which constrains NLA operations to the domain of probabilistic processes. Nevertheless, they are useful for a wide variety of quantum protocols, with numerous proposals assuming access to an optimal NLA device which performs with the maximum possible success probability. Here we propose the first linear optics NLA protocol which asymptotically achieves this success probability bound, by modifying the Knill-Laflamme-Milburn near-deterministic teleporter into an amplifier.

arXiv:2212.04274•Dec 8, 2022•0 citations

Virtual noiseless amplification

Jiří Janoušek, Helen M. Chrzanowski, Sarah Hosseini +5 more

The unavoidable addition of noise during amplification is a well known signature of quantum mechanics. It is at the heart of fundamental results such as the no-cloning theorem, quantum limited metrology, quantum key distribution and the impossibility of increasing entanglement by local operations. Nonetheless one can still avoid the unavoidable by moving to a non-deterministic protocol. This novel concept and a linear optics implementation have been proposed [1] and experimentally realised for the case of amplifying coherent states [2-4], qubits [5,6] and the concentration of phase information [7]. All these were extremely challenging experiments, with only [2] demonstrating entanglement distillation and none directly showing the EPR distillation necessary for application to CV QKD. Furthermore the success probability of these experiments was substantially worse than the theoretical considerations would imply. However as has been noted in [8,9] it is possible to virtually implement noiseless amplification (NLA) and hence entanglement distillation via post-selective measurements, achieving significant distillation with a much improved probability of success.

Conference on Lasers and Electro-Optics Europe & European Quantum Electronics Conference (CLEO/Europe-EQEC)•May 1, 2013•0 citations

Entanglement distillation rates exceeding the direct transmission bound

Farzad Ghafari, Josephine Dias, Lynden K. Shalm +4 more

Entanglement distribution is crucial for quantum communication and cryptography but is hindered by channel loss and decoherence. Noiseless linear amplification (NLA) is a probabilistic protocol that supports noiseless amplification without violating the no-cloning theorem, aiding in tasks like entanglement distillation and enhanced metrology. The probabilistic nature of NLA and other quantum repeater elements creates a significant resource overhead, which depends on the success rate of each individual probabilistic step. We experimentally demonstrate a technique to increase NLA success probability while maintaining the amplification gain and the fidelity of the amplified state with a maximally entangled state. We show that symmetrically distributing loss before and after the amplification provides an improved scaling of the success rates of NLA. Our results are a critical step towards scalable quantum repeaters and enable efficient long-distance quantum communication

arXiv:2503.21133•Mar 27, 2025•0 citations

Characterization of a measurement-based noiseless linear amplifier and its applications

Jie Zhao, Jing Yan Haw, Thomas Symul +2 more

A noiseless linear amplifier (NLA) adds no noise to the signals it processes, which works only in a probabilistic way. It can be realized approximately with either a physical implementation that truncates the working space of the NLA on a photon-number basis or a measurement-based implementation that realizes the truncation virtually by a bounded postselection filter. To examine the relationship between these two approximate NLAs, we characterize in detail the measurement-based NLA and compare it with its physical counterpart in terms of their abilities to preserve the state Gaussianity and their probability of success. The link between these amplifiers is further clarified by integrating them into a measure-and-prepare setup. We stress the equivalence between the physical and the measurement-based approaches holds only when the effective parameters, the amplification gain, the cutoff, and the amplitude of the input state, are taken into account. Finally, we construct a 1-to-infinity cloner using the two amplifiers and show that a fidelity surpassing the no-cloning limit is achievable with the measurement-based NLA.

Physical Review A•Jul 13, 2017•32 citations

Noiseless Linear Amplification with General Local Unitary Operations

Song Yang, Ningjuan Ruan, Yun Su +2 more

Noiseless linear amplification (NLA), first proposed by Ralpha et al., is a nondeterministic amplification process which gives gain to the Fock state |n〉 → g n |n〉, with g being the amplification gain. We here give a general framework for improving the NLA scheme with arbitrary general local unitary operations. We derive the improvement in the amplification gain in 0–1 photon subspace. In particular, we study if the local unitary is composed of single mode squeezing and coherent displacement operation. Finally, numerical simulations show that local unitary operation could give a further enhancement in the amplification gain as well as the success probability, making the NLA more feasible in future optic quantum communications.

Chinese Physics Letters•Jul 1, 2016•2 citations

Truly noiseless probabilistic amplification

Vedran Dunjko, Erika Andersson

Most of the schemes for ``noiseless'' amplification of coherent states, which have recently been attracting theoretical and experimental interest, share a common trait: The amplification is not truly noiseless, or perfect, for nonzero success probability. While this must hold true for all phase-independent amplification schemes, in this work we point out that truly noiseless amplification is indeed possible, provided that the states which we wish to amplify come from a finite set. Perfect amplification with unlimited average gain is then possible with finite success probability, for example, using techniques for unambiguously distinguishing between quantum states. Such realizations require only linear optics, no single-photon sources, and no photon counting. We also investigate the optimal success probability of perfect amplification of a symmetric set of coherent states. There are two regimes: low-amplitude amplification, where the target amplitude is below one, and general amplification. For the low-amplitude regime, analytic results for the optimal amplification success probabilities can be obtained. In this case a natural bound imposed by the ratio of success probabilities of optimal unambiguous discrimination of the source and amplified states can always be reached. We also show that for general amplification this bound cannot always be satisfied.

arXiv:1811.08670•Physical Review A•Oct 18, 2012•16 citations
A noiseless linear amplifier (NLA) performs the highest-quality amplification allowable under the rules of quantum physics. Unfortunately, these same rules conspire against us via the no-cloning theorem, which constrains NLA operations to the domain of probabilistic processes. Nevertheless, they are useful for a wide variety of quantum protocols, with numerous proposals assuming access to an optimal NLA device that performs with the maximum possible success probability. Here we propose the first linear-optics NLA protocol that asymptotically achieves this success probability bound by modifying the Knill-Laflamme-Milburn near-deterministic teleporter into an amplifier. Published by the American Physical Society 2024
A noiseless linear amplifier (NLA) performs the highest quality amplification allowable under the rules of quantum physics. Unfortunately, these same rules conspire against us via the no-cloning theorem, which constrains NLA operations to the domain of probabilistic processes. Nevertheless, they are useful for a wide variety of quantum protocols, with numerous proposals assuming access to an optimal NLA device which performs with the maximum possible success probability. Here we propose the first linear optics NLA protocol which asymptotically achieves this success probability bound, by modifying the Knill-Laflamme-Milburn near-deterministic teleporter into an amplifier.
The unavoidable addition of noise during amplification is a well known signature of quantum mechanics. It is at the heart of fundamental results such as the no-cloning theorem, quantum limited metrology, quantum key distribution and the impossibility of increasing entanglement by local operations. Nonetheless one can still avoid the unavoidable by moving to a non-deterministic protocol. This novel concept and a linear optics implementation have been proposed [1] and experimentally realised for the case of amplifying coherent states [2-4], qubits [5,6] and the concentration of phase information [7]. All these were extremely challenging experiments, with only [2] demonstrating entanglement distillation and none directly showing the EPR distillation necessary for application to CV QKD. Furthermore the success probability of these experiments was substantially worse than the theoretical considerations would imply. However as has been noted in [8,9] it is possible to virtually implement noiseless amplification (NLA) and hence entanglement distillation via post-selective measurements, achieving significant distillation with a much improved probability of success.
Entanglement distribution is crucial for quantum communication and cryptography but is hindered by channel loss and decoherence. Noiseless linear amplification (NLA) is a probabilistic protocol that supports noiseless amplification without violating the no-cloning theorem, aiding in tasks like entanglement distillation and enhanced metrology. The probabilistic nature of NLA and other quantum repeater elements creates a significant resource overhead, which depends on the success rate of each individual probabilistic step. We experimentally demonstrate a technique to increase NLA success probability while maintaining the amplification gain and the fidelity of the amplified state with a maximally entangled state. We show that symmetrically distributing loss before and after the amplification provides an improved scaling of the success rates of NLA. Our results are a critical step towards scalable quantum repeaters and enable efficient long-distance quantum communication
A noiseless linear amplifier (NLA) adds no noise to the signals it processes, which works only in a probabilistic way. It can be realized approximately with either a physical implementation that truncates the working space of the NLA on a photon-number basis or a measurement-based implementation that realizes the truncation virtually by a bounded postselection filter. To examine the relationship between these two approximate NLAs, we characterize in detail the measurement-based NLA and compare it with its physical counterpart in terms of their abilities to preserve the state Gaussianity and their probability of success. The link between these amplifiers is further clarified by integrating them into a measure-and-prepare setup. We stress the equivalence between the physical and the measurement-based approaches holds only when the effective parameters, the amplification gain, the cutoff, and the amplitude of the input state, are taken into account. Finally, we construct a 1-to-infinity cloner using the two amplifiers and show that a fidelity surpassing the no-cloning limit is achievable with the measurement-based NLA.
Noiseless linear amplification (NLA), first proposed by Ralpha et al., is a nondeterministic amplification process which gives gain to the Fock state |n〉 → g n |n〉, with g being the amplification gain. We here give a general framework for improving the NLA scheme with arbitrary general local unitary operations. We derive the improvement in the amplification gain in 0–1 photon subspace. In particular, we study if the local unitary is composed of single mode squeezing and coherent displacement operation. Finally, numerical simulations show that local unitary operation could give a further enhancement in the amplification gain as well as the success probability, making the NLA more feasible in future optic quantum communications.
Most of the schemes for ``noiseless'' amplification of coherent states, which have recently been attracting theoretical and experimental interest, share a common trait: The amplification is not truly noiseless, or perfect, for nonzero success probability. While this must hold true for all phase-independent amplification schemes, in this work we point out that truly noiseless amplification is indeed possible, provided that the states which we wish to amplify come from a finite set. Perfect amplification with unlimited average gain is then possible with finite success probability, for example, using techniques for unambiguously distinguishing between quantum states. Such realizations require only linear optics, no single-photon sources, and no photon counting. We also investigate the optimal success probability of perfect amplification of a symmetric set of coherent states. There are two regimes: low-amplitude amplification, where the target amplitude is below one, and general amplification. For the low-amplitude regime, analytic results for the optimal amplification success probabilities can be obtained. In this case a natural bound imposed by the ratio of success probabilities of optimal unambiguous discrimination of the source and amplified states can always be reached. We also show that for general amplification this bound cannot always be satisfied.