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

arXiv:1703.08686 · Scientific Reports

Entropic uncertainty relations for Markovian and non-Markovian processes under a structured bosonic reservoir

Dong Wang, Aijun Huang, Ross D. Hoehn, Fei Ming, Wen‐Yang Sun, Jiadong Shi, Ye Liu, Sabre Kais

Published Apr 13, 2017• 76 citations
arXivHTMLPDF

Abstract

The uncertainty relation is a fundamental limit in quantum mechanics and is of great importance to quantum information processing as it relates to quantum precision measurement. Due to interactions with the surrounding environment, a quantum system will unavoidably suffer from decoherence. Here, we investigate the dynamic behaviors of the entropic uncertainty relation of an atom-cavity interacting system under a bosonic reservoir during the crossover between Markovian and non-Markovian regimes. Specifically, we explore the dynamic behavior of the entropic uncertainty relation for a pair of incompatible observables under the reservoir-induced atomic decay effect both with and without quantum memory. We find that the uncertainty dramatically depends on both the atom-cavity and the cavity-reservoir interactions, as well as the correlation time, τ, of the structured reservoir. Furthermore, we verify that the uncertainty is anti-correlated with the purity of the state of the observed qubit-system. We also propose a remarkably simple and efficient way to reduce the uncertainty by utilizing quantum weak measurement reversal. Therefore our work offers a new insight into the uncertainty dynamics for multi-component measurements within an open system, and is thus important for quantum precision measurements.

DOI
10.1038/s41598-017-01094-8

Related papers

Observation of quantum-memory-assisted entropic uncertainty relation under open systems, and its steering

Pengfei Chen, Wen‐Yang Sun, Fei Ming +3 more

Abstract Quantum objects are susceptible to noise from their surrounding environments, interaction with which inevitably gives rise to quantum decoherence or dissipation effects. In this work, we examine how different types of local noise under an open system affect entropic uncertainty relations for two incompatible measurements. Explicitly, we observe the dynamics of the entropic uncertainty in the presence of quantum memory under two canonical categories of noisy environments: unital (phase flip) and nonunital (amplitude damping). Our study shows that the measurement uncertainty exhibits a non-monotonic dynamical behavior—that is, the amount of the uncertainty will first inflate, and subsequently decrease, with the growth of decoherence strengths in the two channels. In contrast, the uncertainty decreases monotonically with the growth of the purity of the initial state shared in prior. In order to reduce the measurement uncertainty in noisy environments, we put forward a remarkably effective strategy to steer the magnitude of uncertainty by means of a local non-unitary operation (i.e. weak measurement) on the qubit of interest. It turns out that this non-unitary operation can greatly reduce the entropic uncertainty, upon tuning the operation strength. Our investigations might thereby offer an insight into the dynamics and steering of entropic uncertainty in open systems.

Laser Physics Letters•Dec 12, 2017•25 citations

Dynamics of the measurement uncertainty in an open system and its controlling

Yu-Bing Yao, Dong Wang, Fei Ming +1 more

Abstract The uncertainty principle is one of the most remarkable features of quantum mechanics, originally expressed in terms of the standard deviation of two incompatible observables. Alternatively, it can be modified and written in the form of entropy to eliminate the defect in the form of standard deviation, and can also be generalized by including a memory particle that is entangled with the particle to be measured. Herein we consider a realistic scenario where the particle A to be measured is in an open environment and B as quantum memory is under an environment typically characterized by non-Markovian regimes. Specifically, it shows that the quantum memory and the non-Markovian effect can essentially inhibit the increase of uncertainty, however, the quantum memory-assisted uncertainty will finally inflate inevitably, due to that the quantum correlation of the system will be damaged gradually by the noise from the surrounding environments. To be explicit, we study the dynamic evolution of the entropic uncertainty and correlation in open system where both particles experience the noise channels. Meanwhile, we put forward some effective operation strategies to reduce the magnitude of the measurement uncertainty under the open systems. Furthermore, we explore the applications of the uncertainty relation investigated on entanglement witness and quantum channel capacity. Thus, our investigations might offer an insight into quantum measurement estimation in open systems.

Journal of Physics B Atomic Molecular and Optical Physics•Nov 13, 2019•24 citations

Unveiling the decoherence effect of noise on the entropic uncertainty relation and its control by partially collapsed operations

Min-Nan Chen, Wen‐Yang Sun, Ai-Jun Huang +3 more

Abstract In this work, we investigate the dynamics of quantum-memory-assisted entropic uncertainty relations under open systems, and how to steer the uncertainty under different types of decoherence. Specifically, we develop the dynamical behaviors of the uncertainty of interest under two typical categories of noise; bit flipping and depolarizing channels. It has been shown that the measurement uncertainty firstly increases and then decreases with the growth of the decoherence strength in bit flipping channels. In contrast, the uncertainty monotonically increases with the increase of the decoherence strength in depolarizing channels. Notably, and to a large degree, it is shown that the uncertainty depends on both the systematic quantum correlation and the minimal conditional entropy of the observed subsystem. Moreover, we present a possible physical interpretation for these distinctive behaviors of the uncertainty within such scenarios. Furthermore, we propose a simple and effective strategy to reduce the entropic uncertainty by means of a partially collapsed operation—quantum weak measurement. Therefore, our investigations might offer an insight into the dynamics of the measurment uncertainty under decoherence, and be of importance to quantum precision measurement in open systems.

Laser Physics Letters•Dec 12, 2017•28 citations

Impact of reservoir squeezing on quantum-memory-assisted entropic uncertainty relations

Hamad Ali, Abdul Basit, Fuli Li

The entropic uncertainty principle imposes a limit on how precisely two incompatible observables can be measured, which can be reduced when quantum memory is involved. We theoretically investigate the dynamics of the quantum-memory-assisted entropic uncertainty relation when either quantum memory alone or both the measured particle and the quantum memory interact with a squeezed-vacuum bath through energy-preserving interactions. We show that in both scenarios, the squeezing phase of the reservoir decreases the entropic uncertainty (EU), whereas the squeezing strength increases the EU. In addition, we find that EU can be significantly reduced when both the measured particle and quantum memory are subjected to a common squeezed-vacuum bath. Furthermore, we explore the key factors controlling the behavior of EU by exploring the competition between quantum discord and minimal missing information. Moreover, we examine the tightness of the entropic uncertainty bound (EUB) in both system-environment setups and observe that the EUB is less tight when both the measured particle and quantum memory are coupled to a common squeezed-vacuum bath.

Physical Review A•Mar 17, 2025•7 citations

Measurement uncertainty and dense coding in a two-qubit system: Combined effects of bosonic reservoir and dipole–dipole interaction

Saeed Haddadi, Ming‐Liang Hu, Youssef Khedif +3 more

The uncertainty principle imposes a limitation on the measurement accuracy of two incompatible observables and has potential applications in quantum information science. We explore the bipartite entropic uncertainty relation and dense coding for two qubits coupled via dipole–dipole interaction and subject to a bosonic reservoir. It is shown that there exists a trade-off between the uncertainty bound and the dense coding capacity which results in their opposite dynamical behaviors. Moreover, the behaviors of the measurement uncertainty and the dense coding capacity rely crucially on the initial system–reservoir correlation, the strength of the dipole–dipole interaction, and the degree of non-Markovianity, and one can reduce the measurement uncertainty and enhance the dense coding capacity by tuning these parameters to appropriate values.

Results in Physics•Dec 3, 2021•36 citations

Interplay between nonequilibrium and non-Markovianity in controlling the entropic uncertainty bound

Abdul Basit, Hamad Ali, Gao Xianlong +3 more

The entropic uncertainty relation imposes a limit on the accuracy of measurement outcomes of two conjugate observables, which can be reduced in the presence of quantum memory. We theoretically study the dynamical behaviors of the quantum-memory-assisted entropic uncertainty relation for a bipartite system under local nonequilibrium dephasing environments and a common nonequilibrium dephasing environment. Particularly, we study the influence of the competition between nonequilibrium and non-Markovianity in controlling the entropic uncertainty bound (EUB) in weak- and strong-coupling regimes. We find that the nonequilibrium nature renders a promising protocol to efficiently harness the EUB in both regimes without requiring any operations on the main system. Further, we reveal that the EUB can be significantly reduced in a common bath case compared to the case of local baths. Moreover, we elucidate the primary factor responsible for governing the dynamical behaviors of EUB by examining the interplay between quantum discord and the minimal missing information about the particle to be measured. In addition, we investigate the state preparation and measurement choice (SPMC) condition in both environmental setups with weak- and strong-coupling regimes. Remarkably, we show that the SPMC condition does not hold in the common environment scenario.

Physical Review A•Jul 9, 2024•7 citations
The uncertainty relation is a fundamental limit in quantum mechanics and is of great importance to quantum information processing as it relates to quantum precision measurement. Due to interactions with the surrounding environment, a quantum system will unavoidably suffer from decoherence. Here, we investigate the dynamic behaviors of the entropic uncertainty relation of an atom-cavity interacting system under a bosonic reservoir during the crossover between Markovian and non-Markovian regimes. Specifically, we explore the dynamic behavior of the entropic uncertainty relation for a pair of incompatible observables under the reservoir-induced atomic decay effect both with and without quantum memory. We find that the uncertainty dramatically depends on both the atom-cavity and the cavity-reservoir interactions, as well as the correlation time, τ, of the structured reservoir. Furthermore, we verify that the uncertainty is anti-correlated with the purity of the state of the observed qubit-system. We also propose a remarkably simple and efficient way to reduce the uncertainty by utilizing quantum weak measurement reversal. Therefore our work offers a new insight into the uncertainty dynamics for multi-component measurements within an open system, and is thus important for quantum precision measurements.
Abstract Quantum objects are susceptible to noise from their surrounding environments, interaction with which inevitably gives rise to quantum decoherence or dissipation effects. In this work, we examine how different types of local noise under an open system affect entropic uncertainty relations for two incompatible measurements. Explicitly, we observe the dynamics of the entropic uncertainty in the presence of quantum memory under two canonical categories of noisy environments: unital (phase flip) and nonunital (amplitude damping). Our study shows that the measurement uncertainty exhibits a non-monotonic dynamical behavior—that is, the amount of the uncertainty will first inflate, and subsequently decrease, with the growth of decoherence strengths in the two channels. In contrast, the uncertainty decreases monotonically with the growth of the purity of the initial state shared in prior. In order to reduce the measurement uncertainty in noisy environments, we put forward a remarkably effective strategy to steer the magnitude of uncertainty by means of a local non-unitary operation (i.e. weak measurement) on the qubit of interest. It turns out that this non-unitary operation can greatly reduce the entropic uncertainty, upon tuning the operation strength. Our investigations might thereby offer an insight into the dynamics and steering of entropic uncertainty in open systems.
Abstract The uncertainty principle is one of the most remarkable features of quantum mechanics, originally expressed in terms of the standard deviation of two incompatible observables. Alternatively, it can be modified and written in the form of entropy to eliminate the defect in the form of standard deviation, and can also be generalized by including a memory particle that is entangled with the particle to be measured. Herein we consider a realistic scenario where the particle A to be measured is in an open environment and B as quantum memory is under an environment typically characterized by non-Markovian regimes. Specifically, it shows that the quantum memory and the non-Markovian effect can essentially inhibit the increase of uncertainty, however, the quantum memory-assisted uncertainty will finally inflate inevitably, due to that the quantum correlation of the system will be damaged gradually by the noise from the surrounding environments. To be explicit, we study the dynamic evolution of the entropic uncertainty and correlation in open system where both particles experience the noise channels. Meanwhile, we put forward some effective operation strategies to reduce the magnitude of the measurement uncertainty under the open systems. Furthermore, we explore the applications of the uncertainty relation investigated on entanglement witness and quantum channel capacity. Thus, our investigations might offer an insight into quantum measurement estimation in open systems.
Abstract In this work, we investigate the dynamics of quantum-memory-assisted entropic uncertainty relations under open systems, and how to steer the uncertainty under different types of decoherence. Specifically, we develop the dynamical behaviors of the uncertainty of interest under two typical categories of noise; bit flipping and depolarizing channels. It has been shown that the measurement uncertainty firstly increases and then decreases with the growth of the decoherence strength in bit flipping channels. In contrast, the uncertainty monotonically increases with the increase of the decoherence strength in depolarizing channels. Notably, and to a large degree, it is shown that the uncertainty depends on both the systematic quantum correlation and the minimal conditional entropy of the observed subsystem. Moreover, we present a possible physical interpretation for these distinctive behaviors of the uncertainty within such scenarios. Furthermore, we propose a simple and effective strategy to reduce the entropic uncertainty by means of a partially collapsed operation—quantum weak measurement. Therefore, our investigations might offer an insight into the dynamics of the measurment uncertainty under decoherence, and be of importance to quantum precision measurement in open systems.
The entropic uncertainty principle imposes a limit on how precisely two incompatible observables can be measured, which can be reduced when quantum memory is involved. We theoretically investigate the dynamics of the quantum-memory-assisted entropic uncertainty relation when either quantum memory alone or both the measured particle and the quantum memory interact with a squeezed-vacuum bath through energy-preserving interactions. We show that in both scenarios, the squeezing phase of the reservoir decreases the entropic uncertainty (EU), whereas the squeezing strength increases the EU. In addition, we find that EU can be significantly reduced when both the measured particle and quantum memory are subjected to a common squeezed-vacuum bath. Furthermore, we explore the key factors controlling the behavior of EU by exploring the competition between quantum discord and minimal missing information. Moreover, we examine the tightness of the entropic uncertainty bound (EUB) in both system-environment setups and observe that the EUB is less tight when both the measured particle and quantum memory are coupled to a common squeezed-vacuum bath.
The uncertainty principle imposes a limitation on the measurement accuracy of two incompatible observables and has potential applications in quantum information science. We explore the bipartite entropic uncertainty relation and dense coding for two qubits coupled via dipole–dipole interaction and subject to a bosonic reservoir. It is shown that there exists a trade-off between the uncertainty bound and the dense coding capacity which results in their opposite dynamical behaviors. Moreover, the behaviors of the measurement uncertainty and the dense coding capacity rely crucially on the initial system–reservoir correlation, the strength of the dipole–dipole interaction, and the degree of non-Markovianity, and one can reduce the measurement uncertainty and enhance the dense coding capacity by tuning these parameters to appropriate values.
The entropic uncertainty relation imposes a limit on the accuracy of measurement outcomes of two conjugate observables, which can be reduced in the presence of quantum memory. We theoretically study the dynamical behaviors of the quantum-memory-assisted entropic uncertainty relation for a bipartite system under local nonequilibrium dephasing environments and a common nonequilibrium dephasing environment. Particularly, we study the influence of the competition between nonequilibrium and non-Markovianity in controlling the entropic uncertainty bound (EUB) in weak- and strong-coupling regimes. We find that the nonequilibrium nature renders a promising protocol to efficiently harness the EUB in both regimes without requiring any operations on the main system. Further, we reveal that the EUB can be significantly reduced in a common bath case compared to the case of local baths. Moreover, we elucidate the primary factor responsible for governing the dynamical behaviors of EUB by examining the interplay between quantum discord and the minimal missing information about the particle to be measured. In addition, we investigate the state preparation and measurement choice (SPMC) condition in both environmental setups with weak- and strong-coupling regimes. Remarkably, we show that the SPMC condition does not hold in the common environment scenario.