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Noise, errors and information in quantum amplification

D'Ariano, G M, Macchiavello, C, Lorenzo Maccone

Published Jan 1, 1997• 2 citations
OpenAlex

Abstract

We analyze and compare the characterization of a quantum device in terms of noise, transmitted bit-error-rate (BER) and mutual information, showing how the noise description is meaningful only for Gaussian channels. After reviewing the description of a quantum communication channel, we study the insertion of an amplifier. We focus attention on the case of direct detection, where the linear amplifier has a 3 decibels noise figure, which is usually considered an unsurpassable limit, referred to as the standard quantum limit (SQL). Both noise and BER could be reduced using an ideal amplifier, which is feasible in principle. However, just a reduction of noise beyond the SQL does not generally correspond to an improvement of the BER or of the mutual information. This is the case of a laser amplifier, where saturation can greatly reduce the noise figure, although there is no corresponding improvement of the BER. Such mechanism is illustrated on the basis of Monte Carlo simulations.

Related papers

Noise, Errors and Information in Quantum Amplification

G. M. D'ariano, C. Macchiavello, Lorenzo Maccone

We analyze and compare the characterization of a quantum device in terms of noise, transmitted bit-error-rate (BER) and mutual information, showing how the noise description is meaningful only for Gaussian channels. After reviewing the description of a quantum communication channel, we study the insertion of an amplifier. We focus attention on the case of direct detection, where the linear amplifier has a 3 decibels noise-figure, which is usually considered an unsurpassable limit, referred to as the standard quantum limit (SQL). Both noise and BER could be reduced using an ideal amplifier, which is feasible in principle. However, just a reduction of noise beyond the SQL does not generally correspond to an improvement of the BER or of the mutual information. This is the case of a laser amplifier, where saturation can greatly reduce the noise-figure, although there is no corresponding improvement of the BER. Such mechanism is illustrated on the basis of Monte Carlo simulations.

arXiv:quant-ph/9801065•International Journal of Modern Physics B•Nov 20, 1997•2 citations

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Amplification uncertainty relation for probabilistic amplifiers

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Traditionally, quantum amplification limit refers to the property of inevitable noise addition on canonical variables when the field amplitude of an unknown state is linearly transformed through a quantum channel. Recent theoretical studies have determined amplification limits for cases of probabilistic quantum channels or general quantum operations by specifying a set of input states or a state ensemble. However, it remains open how much excess noise on canonical variables is unavoidable and whether there exists a fundamental trade-off relation between the canonical pair in a general amplification process. In this paper we present an uncertainty-product form of amplification limits for general quantum operations by assuming an input ensemble of Gaussian-distributed coherent states. It can be derived as a straightforward consequence of canonical uncertainty relations and retrieves basic properties of the traditional amplification limit. In addition, our amplification limit turns out to give a physical limitation on probabilistic reduction of an Einstein-Podolsky-Rosen uncertainty. In this regard, we find a condition that probabilistic amplifiers can be regarded as local filtering operations to distill entanglement. This condition establishes a clear benchmark to verify an advantage of non-Gaussian operations beyond Gaussian operations with a feasible input set of coherent states and standard homodyne measurements.

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A Space Shift Keying-Based Optimization Scheme for Secure Communication in IIoT

Han Zhu, Zhentao Huang, Chan–Tong Lam +3 more

Security and privacy are vital challenges in Industrial Internet of Things (IIoT) systems due to the inherent broadcast property of industrial wireless communication. Therefore, how to improve the security of smart devices in IIoT systems has attracted widespread attention. In this article, a novel security optimization scheme for space shift keying (SSK)-based IIoT systems is proposed by applying secrecy enhancing techniques in the physical layer. Specifically, two methods are adopted in the proposed optimization scheme. First, the sender transmits artificial noise (AN) to interfere with the eavesdropper, while the legitimate receiver can eliminate AN. Second, the sender can select optimal antennas based on the proposed minmax criteria to transmit AN and information, which further promotes the security of industrial wireless communication. The optimal antenna selection pattern increases the difference of the average mutual information between the legitimate receiver and the eavesdropper. In addition, the proposed minmax antenna selection approach only requires the channel state information of the legitimate receiver, which satisfies the application scenario of unknown eavesdropper attacks in IIoT. Finally, we adopt a deep learning-based maximum likelihood (ML) detection algorithm to detect the optimal antenna index and analyze the bit error rate (BER) and secrecy rate (SR) of the proposed optimization scheme. Simulation results show that the proposed scheme can achieve similar SR improvements and superior BER performance compared with the state-of-the-art scheme, namely the signal-leakage-to-noise ratio (SLNR) scheme. The BER performance of the proposed scheme achieves a maximum of 100 times superior to that of the SLNR scheme when the signal-to-noise ratio (SNR) is 27 dB. Moreover, the proposed scheme outperforms the traditional antenna selection scheme (random selection) in terms of BER and SR.

IEEE Systems Journal•Sep 18, 2023•17 citations
We analyze and compare the characterization of a quantum device in terms of noise, transmitted bit-error-rate (BER) and mutual information, showing how the noise description is meaningful only for Gaussian channels. After reviewing the description of a quantum communication channel, we study the insertion of an amplifier. We focus attention on the case of direct detection, where the linear amplifier has a 3 decibels noise figure, which is usually considered an unsurpassable limit, referred to as the standard quantum limit (SQL). Both noise and BER could be reduced using an ideal amplifier, which is feasible in principle. However, just a reduction of noise beyond the SQL does not generally correspond to an improvement of the BER or of the mutual information. This is the case of a laser amplifier, where saturation can greatly reduce the noise figure, although there is no corresponding improvement of the BER. Such mechanism is illustrated on the basis of Monte Carlo simulations.
We analyze and compare the characterization of a quantum device in terms of noise, transmitted bit-error-rate (BER) and mutual information, showing how the noise description is meaningful only for Gaussian channels. After reviewing the description of a quantum communication channel, we study the insertion of an amplifier. We focus attention on the case of direct detection, where the linear amplifier has a 3 decibels noise-figure, which is usually considered an unsurpassable limit, referred to as the standard quantum limit (SQL). Both noise and BER could be reduced using an ideal amplifier, which is feasible in principle. However, just a reduction of noise beyond the SQL does not generally correspond to an improvement of the BER or of the mutual information. This is the case of a laser amplifier, where saturation can greatly reduce the noise-figure, although there is no corresponding improvement of the BER. Such mechanism is illustrated on the basis of Monte Carlo simulations.
We show that a saturable amplifier can beat the "3 dB" quantum noise figure of linear amplifiers, approaching the ideal "0 dB" Heisenberg limit. Noise suppression is due to nonlinear saturation effects which cut off the high-intensity tail of the photon distribution. A Monte Carlo simulation of an actual semiconductor laser amplifier leads to a minimum noise figure of 0.51 dB, with a still sizable gain of 10.8 dB. The best performance corresponds to an output signal photon number which equals 0.7 times the saturation number.
The topic of quantum noise has become extremely timely due to the rise of quantum information physics and the resulting interchange of ideas between the condensed matter and atomic, molecular, optical--quantum optics communities. This review gives a pedagogical introduction to the physics of quantum noise and its connections to quantum measurement and quantum amplification. After introducing quantum noise spectra and methods for their detection, the basics of weak continuous measurements are described. Particular attention is given to the treatment of the standard quantum limit on linear amplifiers and position detectors within a general linear-response framework. This approach is shown how it relates to the standard Haus-Caves quantum limit for a bosonic amplifier known in quantum optics and its application to the case of electrical circuits is illustrated, including mesoscopic detectors and resonant cavity detectors.
The employ of a heralded noiseless linear amplifier has been proven as a useful tool for mitigating imperfections in quantum channels. Its analysis is usually conducted within specific frameworks, for which the set of input states for a given protocol is fixed. Here we obtain a more general description by showing that a noisy and lossy Gaussian channel followed by a heralded noiseless linear amplifier has a general description in terms of effective channels. This has the advantage of offering a simpler mathematical description, best suited for mixed states, both Gaussian and non-Gaussian. We investigate the main properties of this effective system, and illustrate its potential by applying it to loss compensation and reduction of phase uncertainty.
Traditionally, quantum amplification limit refers to the property of inevitable noise addition on canonical variables when the field amplitude of an unknown state is linearly transformed through a quantum channel. Recent theoretical studies have determined amplification limits for cases of probabilistic quantum channels or general quantum operations by specifying a set of input states or a state ensemble. However, it remains open how much excess noise on canonical variables is unavoidable and whether there exists a fundamental trade-off relation between the canonical pair in a general amplification process. In this paper we present an uncertainty-product form of amplification limits for general quantum operations by assuming an input ensemble of Gaussian-distributed coherent states. It can be derived as a straightforward consequence of canonical uncertainty relations and retrieves basic properties of the traditional amplification limit. In addition, our amplification limit turns out to give a physical limitation on probabilistic reduction of an Einstein-Podolsky-Rosen uncertainty. In this regard, we find a condition that probabilistic amplifiers can be regarded as local filtering operations to distill entanglement. This condition establishes a clear benchmark to verify an advantage of non-Gaussian operations beyond Gaussian operations with a feasible input set of coherent states and standard homodyne measurements.
Security and privacy are vital challenges in Industrial Internet of Things (IIoT) systems due to the inherent broadcast property of industrial wireless communication. Therefore, how to improve the security of smart devices in IIoT systems has attracted widespread attention. In this article, a novel security optimization scheme for space shift keying (SSK)-based IIoT systems is proposed by applying secrecy enhancing techniques in the physical layer. Specifically, two methods are adopted in the proposed optimization scheme. First, the sender transmits artificial noise (AN) to interfere with the eavesdropper, while the legitimate receiver can eliminate AN. Second, the sender can select optimal antennas based on the proposed minmax criteria to transmit AN and information, which further promotes the security of industrial wireless communication. The optimal antenna selection pattern increases the difference of the average mutual information between the legitimate receiver and the eavesdropper. In addition, the proposed minmax antenna selection approach only requires the channel state information of the legitimate receiver, which satisfies the application scenario of unknown eavesdropper attacks in IIoT. Finally, we adopt a deep learning-based maximum likelihood (ML) detection algorithm to detect the optimal antenna index and analyze the bit error rate (BER) and secrecy rate (SR) of the proposed optimization scheme. Simulation results show that the proposed scheme can achieve similar SR improvements and superior BER performance compared with the state-of-the-art scheme, namely the signal-leakage-to-noise ratio (SLNR) scheme. The BER performance of the proposed scheme achieves a maximum of 100 times superior to that of the SLNR scheme when the signal-to-noise ratio (SNR) is 27 dB. Moreover, the proposed scheme outperforms the traditional antenna selection scheme (random selection) in terms of BER and SR.