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:0912.2879 · Physical Review A

Proposed method for direct measurement of the non-Markovian character of the qubits coupled to bosonic reservoirs

Z. Y. Xu, W. L. Yang, Mang Feng

Published Apr 16, 2010• 72 citations
arXivHTMLPDF

Abstract

Non-Markovianity is a recently proposed characterization of the non-Markovian behavior in an open quantum system, based on which we first present a practical idea for directly measuring the non-Markovian character of a single qubit coupled to a zero-temperature bosonic reservoir, and then extend to investigate the dynamics of two noninteracting qubits subject to two reservoirs, respectively, with a lower bound of non-Markovianity. Our scheme, with no need for optimization procedures and quantum state tomography, is helpful for experimental implementation.

DOI
10.1103/physreva.81.044105

Related papers

Non-Markovianity of a two-level system transversally coupled to multiple bosonic reservoirs

Zhong‐Xiao Man, Nguyen Ba An, Yun‐Jie Xia

Dynamics of a two-level open system transversally coupled to a single zero-temperature bosonic reservoir may be Markovian or non-Markovian, depending on whether the system-reservoir coupling is weak or strong. In this paper, we show that when the system is simultaneously coupled to $N$ reservoirs its dynamics is always non-Markovian, provided that $N\ensuremath{\ge}{N}_{\mathrm{cr}},$ with ${N}_{\mathrm{cr}}$ a critical number depending on the reservoirs' parameters. Quantitatively, the non-Markovianity $\mathcal{N}$ is shown proportional to the number of contributed reservoirs. We explain our results in terms of the pseudomode theory, finding out that when $N\ensuremath{\ge}{N}_{\mathrm{cr}}$ the pseudomodes of all the reservoirs can always partially return information back to the system, no matter how strong the couplings between the system and each individual reservoir.

Physical Review A•Dec 1, 2014•48 citations

Harnessing non-Markovian quantum memory by environmental coupling

Zhong‐Xiao Man, Yun‐Jie Xia, Rosario Lo Franco

Controlling the non-Markovian dynamics of open quantum systems is essential in quantum information technology since it plays a crucial role in preserving quantum memory. Albeit in many realistic scenarios the quantum system can simultaneously interact with composite environments, this condition remains little understood, particularly regarding the effect of the coupling between environmental parts. We analyze the non-Markovian behavior of a qubit interacting at the same time with two coupled single-mode cavities which in turn dissipate into memoryless or memory-keeping reservoirs. We show that increasing the control parameter, that is the two-mode coupling, allows for triggering and enhancing a non-Markovian dynamics for the qubit starting from a Markovian one in the absence of coupling. Surprisingly, if the qubit dynamics is non-Markovian for the zero control parameter, increasing the latter enables multiple transitions from non-Markovian to Markovian regimes. These results hold independently on the nature of the reservoirs. This work highlights that suitably engineering the coupling between parts of a compound environment can efficiently harness the quantum memory, stored in a qubit, based on non-Markovianity.

arXiv:1506.08293•Physical Review A•Jul 13, 2015•93 citations

Characterization of non-Markovianity with maximal extractable qubit-reservoir entanglement

Pei‐Rong Han, Fan Wu, Xin-Jie Huang +5 more

Understanding the dynamical behavior of a qubit in a reservoir is critical to applications in quantum technological protocols, ranging from quantum computation to quantum metrology. The effect of the reservoir depends on the reservoir's spectral structure as well as on the qubit-reservoir coupling strength. We here propose a measure for quantifying the non-Markovian effect of a reservoir with a Lorentzian spectrum, based on the maximum qubit-reservoir quantum entanglement that can be extracted. Numerical simulation shows that this entanglement exhibits a monotonous behavior in response to the variation of the coupling strength. We confirm the validity of this measure with an experiment where a superconducting qubit is controllably coupled to a lossy resonator, which acts as a reservoir for the qubit. The experimental results illustrate that the maximal extractable entanglement is progressively increased with the strengthening of non-Markovianity.

arXiv:2403.01967•Applied Physics Letters•Sep 16, 2024•3 citations

Characterization of non-Markovianity with maximal extractable qubit-reservoir entanglement

Zhen‐Biao Yang, Pei‐Rong Han, Fan Wu +5 more

Abstract Understanding the dynamical behavior of a qubit in a reservoir is critical to applications in quantum technological protocols, ranging from quantum computation to quantum metrology. The effect of the reservoir depends on reservoir’s spectral structure, as well as on the qubit-reservoir coupling strength. We here propose a measure for quantifying the non-Markovian effect of a reservoir with a Lorentzian spectrum, based on the maximum qubit-reservoir quantum entanglement that can be extracted. Numerical simulation shows this entanglement exhibits a monotonous behavior in response to the variation of the coupling strength. We confirm the validity of this measure with an experiment, where a superconducting qubit is controllably coupled to a lossy resonator, which acts as a reservoir for the qubit. The experimental results illustrate the maximal extractable entanglement is progressively increased with the strengthening of the non-Markovianity.

•Apr 18, 2024•0 citations

Non-Markovian open quantum systems

Maike Gail Zinterl

We examine different nonlinear open quantum systems and calculate the non-Markovianity based on the distinguishability between two density matrices. We show that for a single spin (qubit) coupled to a bosonic field the non-Markovianity depends on the spectral density function and can take on any number N with 0 ≤ N ≤ 1, meaning the dynamics can be Markovian or highly non-Markovian. For the main result we consider a system of Ntot identical spins coupled to an environment in the mean-field way. Each spin is coupled to a local and the common reservoir. There are only indirect interactions between the spins through the common reservoir. In limit Ntot → 1 the subsystem consisting of a fixed set of n particles reduces to a factorized state in which each factor is a single spin evolving according to a nonlinear Hartree-Lindblad equation which is exactly solvable. For non-stationary initial spin states the non-Markovianity diverges. In this instance we can never approximate the dynamics of the quantum system by a Markovian master equation and this implies that in the mean field models, memory effects are significant.

•Jul 1, 2019•0 citations

Enabling quantum non-Markovian dynamics by injection of classical colored noise

Jose Inacio Costa-Filho, R. B. B. Lima, Rafael Rothganger de Paiva +4 more

The non-Markovian nature of quantum systems recently turned to be a key subject for investigations on open quantum system dynamics. Many studies, from its theoretical grounding to its usefulness as a resource for quantum information processing and experimental demonstrations, have been reported in the literature. Typically, in these studies, a structured reservoir is required to make non-Markovian dynamics emerge. Here, we investigate the dynamics of a qubit interacting with a bosonic bath and under the injection of a classical stochastic colored noise. A canonical Lindblad-like master equation for the system is derived by using the stochastic wave function formalism. Then, the non-Markovianity of the evolution is witnessed by using the measure of Andersson, Cresser, Hall, and Li. We evaluate the measure for three different noises and study the interplay between environment and noise pump necessary to generate quantum non-Markovianity, as well as the energy balance of the system. Finally, we discuss the possibility to experimentally implement the proposed model.

arXiv:1612.02628•Physical Review A•May 25, 2017•45 citations
Non-Markovianity is a recently proposed characterization of the non-Markovian behavior in an open quantum system, based on which we first present a practical idea for directly measuring the non-Markovian character of a single qubit coupled to a zero-temperature bosonic reservoir, and then extend to investigate the dynamics of two noninteracting qubits subject to two reservoirs, respectively, with a lower bound of non-Markovianity. Our scheme, with no need for optimization procedures and quantum state tomography, is helpful for experimental implementation.
Dynamics of a two-level open system transversally coupled to a single zero-temperature bosonic reservoir may be Markovian or non-Markovian, depending on whether the system-reservoir coupling is weak or strong. In this paper, we show that when the system is simultaneously coupled to NNN reservoirs its dynamics is always non-Markovian, provided that $N\ensuremath{\ge}{N}_{\mathrm{cr}},$ with Ncr{N}_{\mathrm{cr}}Ncr​ a critical number depending on the reservoirs' parameters. Quantitatively, the non-Markovianity N\mathcal{N}N is shown proportional to the number of contributed reservoirs. We explain our results in terms of the pseudomode theory, finding out that when $N\ensuremath{\ge}{N}_{\mathrm{cr}}$ the pseudomodes of all the reservoirs can always partially return information back to the system, no matter how strong the couplings between the system and each individual reservoir.
Controlling the non-Markovian dynamics of open quantum systems is essential in quantum information technology since it plays a crucial role in preserving quantum memory. Albeit in many realistic scenarios the quantum system can simultaneously interact with composite environments, this condition remains little understood, particularly regarding the effect of the coupling between environmental parts. We analyze the non-Markovian behavior of a qubit interacting at the same time with two coupled single-mode cavities which in turn dissipate into memoryless or memory-keeping reservoirs. We show that increasing the control parameter, that is the two-mode coupling, allows for triggering and enhancing a non-Markovian dynamics for the qubit starting from a Markovian one in the absence of coupling. Surprisingly, if the qubit dynamics is non-Markovian for the zero control parameter, increasing the latter enables multiple transitions from non-Markovian to Markovian regimes. These results hold independently on the nature of the reservoirs. This work highlights that suitably engineering the coupling between parts of a compound environment can efficiently harness the quantum memory, stored in a qubit, based on non-Markovianity.
Understanding the dynamical behavior of a qubit in a reservoir is critical to applications in quantum technological protocols, ranging from quantum computation to quantum metrology. The effect of the reservoir depends on the reservoir's spectral structure as well as on the qubit-reservoir coupling strength. We here propose a measure for quantifying the non-Markovian effect of a reservoir with a Lorentzian spectrum, based on the maximum qubit-reservoir quantum entanglement that can be extracted. Numerical simulation shows that this entanglement exhibits a monotonous behavior in response to the variation of the coupling strength. We confirm the validity of this measure with an experiment where a superconducting qubit is controllably coupled to a lossy resonator, which acts as a reservoir for the qubit. The experimental results illustrate that the maximal extractable entanglement is progressively increased with the strengthening of non-Markovianity.
Abstract Understanding the dynamical behavior of a qubit in a reservoir is critical to applications in quantum technological protocols, ranging from quantum computation to quantum metrology. The effect of the reservoir depends on reservoir’s spectral structure, as well as on the qubit-reservoir coupling strength. We here propose a measure for quantifying the non-Markovian effect of a reservoir with a Lorentzian spectrum, based on the maximum qubit-reservoir quantum entanglement that can be extracted. Numerical simulation shows this entanglement exhibits a monotonous behavior in response to the variation of the coupling strength. We confirm the validity of this measure with an experiment, where a superconducting qubit is controllably coupled to a lossy resonator, which acts as a reservoir for the qubit. The experimental results illustrate the maximal extractable entanglement is progressively increased with the strengthening of the non-Markovianity.
We examine different nonlinear open quantum systems and calculate the non-Markovianity based on the distinguishability between two density matrices. We show that for a single spin (qubit) coupled to a bosonic field the non-Markovianity depends on the spectral density function and can take on any number N with 0 ≤ N ≤ 1, meaning the dynamics can be Markovian or highly non-Markovian. For the main result we consider a system of Ntot identical spins coupled to an environment in the mean-field way. Each spin is coupled to a local and the common reservoir. There are only indirect interactions between the spins through the common reservoir. In limit Ntot → 1 the subsystem consisting of a fixed set of n particles reduces to a factorized state in which each factor is a single spin evolving according to a nonlinear Hartree-Lindblad equation which is exactly solvable. For non-stationary initial spin states the non-Markovianity diverges. In this instance we can never approximate the dynamics of the quantum system by a Markovian master equation and this implies that in the mean field models, memory effects are significant.
The non-Markovian nature of quantum systems recently turned to be a key subject for investigations on open quantum system dynamics. Many studies, from its theoretical grounding to its usefulness as a resource for quantum information processing and experimental demonstrations, have been reported in the literature. Typically, in these studies, a structured reservoir is required to make non-Markovian dynamics emerge. Here, we investigate the dynamics of a qubit interacting with a bosonic bath and under the injection of a classical stochastic colored noise. A canonical Lindblad-like master equation for the system is derived by using the stochastic wave function formalism. Then, the non-Markovianity of the evolution is witnessed by using the measure of Andersson, Cresser, Hall, and Li. We evaluate the measure for three different noises and study the interplay between environment and noise pump necessary to generate quantum non-Markovianity, as well as the energy balance of the system. Finally, we discuss the possibility to experimentally implement the proposed model.