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

Physical Review A

Coherent-state information concentration and purification in atomic memory

Jiří Herec, Radim Filip

Published Dec 12, 2006• 3 citations
Publisher

Abstract

We propose a feasible method of coherent-state information concentration and purification utilizing quantum memory. The method allows us to optimally concentrate and purify information carried by many noisy copies of an unknown coherent state (randomly distributed in time) to a single copy. Thus nonclassical resources and operations can be saved, if we compare information processing with many noisy copies and a single copy with concentrated and purified information.

DOI
10.1103/physreva.74.062306

Related papers

Coherent-state information concentration and purification in atomic memory

Jiří Herec, Radim Filip

We propose a feasible method of coherent-state information concentration and purification utilizing quantum memory. The method allows us to optimally concentrate and purify information carried by many noisy copies of an unknown coherent state (randomly distributed in time) to a single copy. Thus non-classical resources and operations can be saved, if we compare information processing with many noisy copies and a single copy with concentrated and purified information.

Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE•Apr 10, 2007•0 citations

Quantum amplification and purification of noisy coherent states

Xiaobin Zhao, Giulio Chiribella

Quantum-limited amplifiers increase the amplitude of quantum signals at the price of introducing additional noise. Quantum purification protocols operate in the reverse way, by reducing the noise while attenuating the signal. Here we investigate a scenario that interpolates between these two extremes. We search for the optimal physical process that generates $M$ approximate copies of a pure and amplified coherent state, starting from $N$ copies of a noisy coherent state with Gaussian modulation. We prove that the optimal deterministic processes are always Gaussian, whereas non-Gaussianity powers up probabilistic advantages in suitable parameter regimes. The optimal processes are experimentally realizable with current technology, both in the deterministic and in the probabilistic scenario. In view of this fact, we provide benchmarks that can be used to certify the experimental demonstration of the quantum-enhanced amplification and purification of coherent states.

arXiv:1701.04602•Physical Review A•Apr 4, 2017•13 citations

Universal quantum state purification under energy-preserving constraints

Xing-Chen Guo, Benchi Zhao, Xin Wang

Pure quantum states are a fundamental resource for quantum information processing, but unavoidable noise degrades their purity and limits the performance of quantum tasks. Quantum state purification attempts to restore purity by jointly processing several noisy copies of an unknown state, typically in a probabilistic way. Whether purification is possible, and how much it can achieve, depends strongly on the set of operations that are physically allowed. In this work, we study universal purification under \textit{energy-preserving operations}, which cannot exchange energy with an external environment. We identify exactly when the energy-preserving constraint forbids any universal purification advantage, and we provide concrete examples in which an advantage available to unrestricted operations disappears under energy conservation. When energy-preserving purification remains possible, we determine its optimal fidelity and success probability and construct the corresponding protocols. The framework includes unrestricted purification as a special case and extends naturally to purification assisted by an external energy resource.

quant-pharXiv:2604.15228•Apr 17, 2026•0 citations

Protocols and trade-offs of quantum state purification

Hongshun Yao, Yu-Ao Chen, Erdong Huang +3 more

Abstract Quantum state purification is crucial in quantum communication and computation, aiming to recover a purified state from multiple copies of an unknown noisy state. This work introduces a general state purification framework designed to achieve the highest fidelity with a specified probability and characterize the associated trade-offs. For i.i.d. quantum states under depolarizing noise, our framework can replicate the purification protocol proposed by Barenco et al (1997 SIAM J. Comput. 26 1541–57) and further provide exact formulas for the purification fidelity and probability with explicit trade-offs. We prove the protocols’ optimality for two copies of noisy states with any dimension and confirm its optimality for higher numbers of copies and dimensions through numerical analysis. Our methodological approach paves the way for proving the protocol’s optimality in more general scenarios and leads to optimal protocols for other noise models. Furthermore, we present a systematic implementation method via block encoding and parameterized quantum circuits, providing explicit circuits for purifying three-copy and four-copy states under depolarizing noise. Finally, we estimate the sample complexity and generalize the protocol to a recursive form, demonstrating its practicality for quantum computers with limited memory.

arXiv:2404.01138•Quantum Science and Technology•Apr 28, 2025•8 citations

Probabilistic purification of noisy coherent states

Petr Marek, Radim Filip

(pp609-623) A basic feasible probabilistic purification of unknown noisy coherent states, outgoing from different state preparations with unknown mean number of thermal photons, is proposed. The scheme is based only on a linear-optical network with an avalanche photo-diode or heterodyne (homodyne) detection used to post-select a successful processing. The suggested probabilistic method can produce an output state with a lower noise than both quantum deterministic and classical probabilistic purification method. The purification applied in the state preparation can increase classical capacity of communication and security of quantum key distribution.

arXiv:0706.1932•Quantum Information and Computation•Sep 1, 2007•5 citations

Experimental purification of coherent states

Ulrik L. Andersen, Radim Filip, Jaromı́r Fiurášek +2 more

We propose a scheme for optimal Gaussian purification of coherent states from several imperfect copies. The proposal is experimentally demonstrated for the case of two copies of a coherent state sent through independent noisy channels. Our purification protocol relies on only linear optics and an ancilla vacuum state, rendering this approach an interesting alternative to the more complex protocols of entanglement distillation and quantum error correction.

arXiv:quant-ph/0508178•Physical Review A•Dec 1, 2005•30 citations
We propose a feasible method of coherent-state information concentration and purification utilizing quantum memory. The method allows us to optimally concentrate and purify information carried by many noisy copies of an unknown coherent state (randomly distributed in time) to a single copy. Thus nonclassical resources and operations can be saved, if we compare information processing with many noisy copies and a single copy with concentrated and purified information.
Quantum-limited amplifiers increase the amplitude of quantum signals at the price of introducing additional noise. Quantum purification protocols operate in the reverse way, by reducing the noise while attenuating the signal. Here we investigate a scenario that interpolates between these two extremes. We search for the optimal physical process that generates MMM approximate copies of a pure and amplified coherent state, starting from NNN copies of a noisy coherent state with Gaussian modulation. We prove that the optimal deterministic processes are always Gaussian, whereas non-Gaussianity powers up probabilistic advantages in suitable parameter regimes. The optimal processes are experimentally realizable with current technology, both in the deterministic and in the probabilistic scenario. In view of this fact, we provide benchmarks that can be used to certify the experimental demonstration of the quantum-enhanced amplification and purification of coherent states.
Pure quantum states are a fundamental resource for quantum information processing, but unavoidable noise degrades their purity and limits the performance of quantum tasks. Quantum state purification attempts to restore purity by jointly processing several noisy copies of an unknown state, typically in a probabilistic way. Whether purification is possible, and how much it can achieve, depends strongly on the set of operations that are physically allowed. In this work, we study universal purification under \textit{energy-preserving operations}, which cannot exchange energy with an external environment. We identify exactly when the energy-preserving constraint forbids any universal purification advantage, and we provide concrete examples in which an advantage available to unrestricted operations disappears under energy conservation. When energy-preserving purification remains possible, we determine its optimal fidelity and success probability and construct the corresponding protocols. The framework includes unrestricted purification as a special case and extends naturally to purification assisted by an external energy resource.
Abstract Quantum state purification is crucial in quantum communication and computation, aiming to recover a purified state from multiple copies of an unknown noisy state. This work introduces a general state purification framework designed to achieve the highest fidelity with a specified probability and characterize the associated trade-offs. For i.i.d. quantum states under depolarizing noise, our framework can replicate the purification protocol proposed by Barenco et al (1997 SIAM J. Comput. 26 1541–57) and further provide exact formulas for the purification fidelity and probability with explicit trade-offs. We prove the protocols’ optimality for two copies of noisy states with any dimension and confirm its optimality for higher numbers of copies and dimensions through numerical analysis. Our methodological approach paves the way for proving the protocol’s optimality in more general scenarios and leads to optimal protocols for other noise models. Furthermore, we present a systematic implementation method via block encoding and parameterized quantum circuits, providing explicit circuits for purifying three-copy and four-copy states under depolarizing noise. Finally, we estimate the sample complexity and generalize the protocol to a recursive form, demonstrating its practicality for quantum computers with limited memory.
(pp609-623) A basic feasible probabilistic purification of unknown noisy coherent states, outgoing from different state preparations with unknown mean number of thermal photons, is proposed. The scheme is based only on a linear-optical network with an avalanche photo-diode or heterodyne (homodyne) detection used to post-select a successful processing. The suggested probabilistic method can produce an output state with a lower noise than both quantum deterministic and classical probabilistic purification method. The purification applied in the state preparation can increase classical capacity of communication and security of quantum key distribution.