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

Laser Physics Letters

Cohering and decohering power of single-mode Gaussian noises

Soroush Haseli

Published Sep 10, 2019• 1 citation
Publisher

Abstract

Abstract Quantum coherence stems from the superposition principle of states. It shows an essential feature of quantum systems which is different from the classical phenomena. We investigate the concept of cohering and decohering power of single-mode quantum Gaussian noises. For this purpose, we use the Hellinger distance-based and Bures distance-based measure to quantify the coherence of single-mode quantum Gaussian states. We will show that both Hellinger and Bures distance-based measures are the same when quantifying the quantum coherence of pure single-mode quantum Gaussian states. In this work we will study the cohering and decohering power of single-mode attenuation and amplification noise. We will investigate the effects of the amplification parameter k and attenuation parameter on the cohering and decohering power of corresponding channels. We find that for single-mode amplification noise the cohering power is increased by increasing k , while the decohering power is decreased by increasing k . Conversely, we will see that for a single-mode attenuation channel the cohering power is decreased by increasing the attenuation parameter , while in general the decohering power is increased by increasing . We also investigate the effect of the mean photon number of the environment N on the cohering and decohering power of single-mode attenuation and amplification noises. For both of the channels the cohering power is increased, while the decohering power is decreased, by increasing N .

DOI
10.1088/1612-202x/ab3e6a

Related papers

Cohering and decohering power of Gaussian channels

Huazhen Yao, Jianwen Zhang, Yangyang Wang

In this paper, we generalized the concepts of the cohering power and decohering power to Gaussian channels for continuous-variable systems with respect to coherence measures based on the relative entropy and obtained some basic properties. In addition, the cohering power and decohering power of classical noise channels, thermal noise channels and amplifier channels are calculated.

International Journal of Quantum Information•Jun 1, 2020•0 citations

A comprehensive perspective for single-mode Gaussian coherence

S. K. Singh, Atta Ur Rahman, Mojtaba Mazaheri +1 more

Abstract In this work, we theoretically investigate single-mode Gaussian quantum coherence from a comprehensive perspective. Based on analytical expressions of the first and second moments of single-mode Gaussian states undergoing various Gaussian noisy channels, we use quantum mater equation and the method of the relative entropy to quantify the quantum coherence of any single-mode Gaussian state. We demonstrate that the displaced thermal state achieves maximum quantum coherence when using only the displaced vacuum state, which is a pure coherent state. However, for various lossy noise channels, quantum coherence shows a significant decrease. In the context of a squeezed thermal state, when controlling the squeezing parameter for a given environmental temperature, quantum coherence has been witnessed to increase. The ultimate upper bound of quantum coherence is then attained with the squeezed vacuum state. In particular, we determined the most generalized scenario of the displaced squeezed thermal state. The maximum value of quantum coherence is obtained when displacement and squeeze parameters both attain maximum value. Our study might be important in the future for the characterisation as well as the estimation of various nonclassical quantum correlations in single-mode Gaussian states.

Physica Scripta•Apr 17, 2024•12 citations

Cohering power and decohering power of Gaussian unitary operations

Yangyang Wang, Xiaofei Qi, Jinchuan Hou +1 more

Having a suitable measure to quantify the coherence of quantum states, a natural task is to evaluate the power of quantum channels for creating or destroying the coherence of input quantum states. In the present paper, by introducing the maximal coherent Gaussian states based on the relative entropy measure of coherence, we propose the (generalized) cohering power and the (generalized) decohering power of Gaussian unitary operations for continuous-variable systems. Some basic properties are obtained and the cohering power and decohering power of two special kinds of Gaussian unitary operations are calculated.

Quantum Information and Computation•Jun 1, 2019•1 citation

Quantum coherence of Gaussian states

Daniela Buono, Gaetano Nocerino, Giuseppe Petrillo +3 more

We introduce a geometric quantification of quantum coherence in single-mode Gaussian states and we investigate the behavior of distance measures as functions of different physical parameters. In the case of squeezed thermal states, we observe that re-quantization yields an effect of noise-enhanced quantum coherence for increasing thermal photon number.

arXiv:1609.00913•Sep 4, 2016•10 citations

Improving parameter estimation in Gaussian channels using quantum coherence

Jonas F. G. Santos, Carlos H. S. Vieira, Wilder R. Cardoso

Gaussian quantum channels are relevant operations in continuous variable systems. In general, given an arbitrary state, the action on it is well known, provided that the quantum channels are completely characterized. In this work, we have studied the role played by quantum coherence in the estimation of Gaussian channel parameters. For this purpose, we start by considering an initial single-mode vacuum state where coherence is generated through displaced or/and squeezing operations. Then, we consider a probe state with two resources, the average thermal number and the quantum coherence. The results are computed using the quantum Fisher information (QFI) as well as some gain functions defined in the work. We applied the estimation protocol for two paradigmatic bosonic Gaussian channels: the thermal attenuator and the thermal amplifier. Our results show that for the vacuum initial state, coherence can be exploited to obtain a high QFI. Moreover, we can state two important facts: the first being that for a small parameter region of a channel, the QFI depends on the mechanism used to generate the coherence, while the second is that the QFI depends not only on the amount of coherence but also on how it changes as a function of the parameter to be estimated. For the probe state, including also an average thermal number, the two examples show that thermal resources are not always beneficial to the QFI and that this depends on the channel structure. For the attenuator channel, the optimal probe state is only limited by the ability to implement an average thermal number and generate an amount of coherence, while for the amplifier channel, the vacuum probe state with coherence is the optimal state. Finally, we obtain a direct relation between the quantum Fisher information and the relative entropy of coherence, allowing, in principle, an experimental verification based on the measurement of the covariance matrix of the probe system.

arXiv:2409.09675•Physical Review A•May 2, 2025•11 citations

Cohering and decohering power of quantum channels

Azam Mani, Vahid Karimipour

We introduce the concepts of cohering and decohering power of quantum channels. Using the axiomatic definition of the coherence measure, we show that the optimization required for calculations of these measures can be restricted to pure input states and hence greatly simplified. We then use two examples of this measure, one based on the skew information and the other based on the ${l}_{1}$ norm; we find the cohering and decohering measures of a number of one-, two-, and $n$-qubit channels. Contrary to the view at first glance, it is seen that quantum channels can have cohering power. It is also shown that a specific property of a qubit unitary map is that it has equal cohering and decohering power in any basis. Finally, we derive simple relations between cohering and decohering powers of unitary qubit gates and their tensor products, results which have physically interesting implications.

arXiv:1506.02304•Physical Review A•Sep 29, 2015•155 citations
Abstract Quantum coherence stems from the superposition principle of states. It shows an essential feature of quantum systems which is different from the classical phenomena. We investigate the concept of cohering and decohering power of single-mode quantum Gaussian noises. For this purpose, we use the Hellinger distance-based and Bures distance-based measure to quantify the coherence of single-mode quantum Gaussian states. We will show that both Hellinger and Bures distance-based measures are the same when quantifying the quantum coherence of pure single-mode quantum Gaussian states. In this work we will study the cohering and decohering power of single-mode attenuation and amplification noise. We will investigate the effects of the amplification parameter k and attenuation parameter on the cohering and decohering power of corresponding channels. We find that for single-mode amplification noise the cohering power is increased by increasing k , while the decohering power is decreased by increasing k . Conversely, we will see that for a single-mode attenuation channel the cohering power is decreased by increasing the attenuation parameter , while in general the decohering power is increased by increasing . We also investigate the effect of the mean photon number of the environment N on the cohering and decohering power of single-mode attenuation and amplification noises. For both of the channels the cohering power is increased, while the decohering power is decreased, by increasing N .
Abstract In this work, we theoretically investigate single-mode Gaussian quantum coherence from a comprehensive perspective. Based on analytical expressions of the first and second moments of single-mode Gaussian states undergoing various Gaussian noisy channels, we use quantum mater equation and the method of the relative entropy to quantify the quantum coherence of any single-mode Gaussian state. We demonstrate that the displaced thermal state achieves maximum quantum coherence when using only the displaced vacuum state, which is a pure coherent state. However, for various lossy noise channels, quantum coherence shows a significant decrease. In the context of a squeezed thermal state, when controlling the squeezing parameter for a given environmental temperature, quantum coherence has been witnessed to increase. The ultimate upper bound of quantum coherence is then attained with the squeezed vacuum state. In particular, we determined the most generalized scenario of the displaced squeezed thermal state. The maximum value of quantum coherence is obtained when displacement and squeeze parameters both attain maximum value. Our study might be important in the future for the characterisation as well as the estimation of various nonclassical quantum correlations in single-mode Gaussian states.
Having a suitable measure to quantify the coherence of quantum states, a natural task is to evaluate the power of quantum channels for creating or destroying the coherence of input quantum states. In the present paper, by introducing the maximal coherent Gaussian states based on the relative entropy measure of coherence, we propose the (generalized) cohering power and the (generalized) decohering power of Gaussian unitary operations for continuous-variable systems. Some basic properties are obtained and the cohering power and decohering power of two special kinds of Gaussian unitary operations are calculated.
Gaussian quantum channels are relevant operations in continuous variable systems. In general, given an arbitrary state, the action on it is well known, provided that the quantum channels are completely characterized. In this work, we have studied the role played by quantum coherence in the estimation of Gaussian channel parameters. For this purpose, we start by considering an initial single-mode vacuum state where coherence is generated through displaced or/and squeezing operations. Then, we consider a probe state with two resources, the average thermal number and the quantum coherence. The results are computed using the quantum Fisher information (QFI) as well as some gain functions defined in the work. We applied the estimation protocol for two paradigmatic bosonic Gaussian channels: the thermal attenuator and the thermal amplifier. Our results show that for the vacuum initial state, coherence can be exploited to obtain a high QFI. Moreover, we can state two important facts: the first being that for a small parameter region of a channel, the QFI depends on the mechanism used to generate the coherence, while the second is that the QFI depends not only on the amount of coherence but also on how it changes as a function of the parameter to be estimated. For the probe state, including also an average thermal number, the two examples show that thermal resources are not always beneficial to the QFI and that this depends on the channel structure. For the attenuator channel, the optimal probe state is only limited by the ability to implement an average thermal number and generate an amount of coherence, while for the amplifier channel, the vacuum probe state with coherence is the optimal state. Finally, we obtain a direct relation between the quantum Fisher information and the relative entropy of coherence, allowing, in principle, an experimental verification based on the measurement of the covariance matrix of the probe system.
We introduce the concepts of cohering and decohering power of quantum channels. Using the axiomatic definition of the coherence measure, we show that the optimization required for calculations of these measures can be restricted to pure input states and hence greatly simplified. We then use two examples of this measure, one based on the skew information and the other based on the l1{l}_{1}l1​ norm; we find the cohering and decohering measures of a number of one-, two-, and nnn-qubit channels. Contrary to the view at first glance, it is seen that quantum channels can have cohering power. It is also shown that a specific property of a qubit unitary map is that it has equal cohering and decohering power in any basis. Finally, we derive simple relations between cohering and decohering powers of unitary qubit gates and their tensor products, results which have physically interesting implications.