arXiv:quant-ph/9801065 · International Journal of Modern Physics B

Noise, Errors and Information in Quantum Amplification

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

Published Nov 20, 1997• 2 citations

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.

DOI: 10.1142/s0217979297001660

Related papers

Noise, errors and information in quantum amplification

D'Ariano, G M, Macchiavello, C, 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.

Jan 1, 19972 citations

Amplification under the Standard Quantum Noise Limit

Giacomo Mauro D’Ariano, Chiara Macchiavello, Matteo G. A. Paris

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.

Physical Review LettersDec 12, 19945 citations

Introduction to quantum noise, measurement, and amplification

Aashish A. Clerk, Michel Devoret, S. M. Girvin +2 more

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.

arXiv:0810.4729Reviews of Modern PhysicsApr 15, 20101,989 citations

Heralded noiseless linear amplification and quantum channels

Rémi Blandino, Marco Barbieri, Philippe Grangier +1 more

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.

arXiv:1407.6798Physical Review AJun 5, 201520 citations

Amplification uncertainty relation for probabilistic amplifiers

Ryo Namiki

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.

arXiv:1502.05031Physical Review ASep 25, 20154 citations

Quantum Noise in Linear Amplifiers

H. A. Haus, James A. Mullen

The classical definition of noise figure, based on signal-to-noise ratio, is adapted to the case when quantum noise is predominant. The noise figure is normalized to "uncertainty noise." General quantum mechanical equations for linear amplifiers are set up using the condition of linearity and the requirement that the commutator brackets of the pertinent operators are conserved in the amplification. These equations include as special cases the maser, the parametric amplifier, and the parametric up-converter. Using these equations the noise figure of a general amplifier is derived. The minimum value of this noise figure is equal to 2. The significance of the result with regard to a simultaneous phase and amplitude measurement is explored.

Physical ReviewDec 1, 1962318 citations