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Local versus global master equation with common and separate baths: superiority of the global approach in partial secular approximation
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Abstract Open systems of coupled qubits are ubiquitous in quantum physics. Finding a suitable master equation to describe their dynamics is therefore a crucial task that must be addressed with utmost attention. In the recent past, many efforts have been made toward the possibility of employing local master equations, which compute the interaction with the environment neglecting the direct coupling between the qubits, and for this reason may be easier to solve. Here, we provide a detailed derivation of the Markovian master equation for two coupled qubits interacting with common and separate baths, considering pure dephasing as well as dissipation. Then, we explore the differences between the local and global master equation, showing that they intrinsically depend on the way we apply the secular approximation. Our results prove that the global approach with partial secular approximation always provides the most accurate choice for the master equation when Born–Markov approximations hold, even for small inter-system coupling constants. Using different master equations we compute the stationary heat current between two separate baths, the entanglement dynamics generated by a common bath, and the emergence of spontaneous synchronization, showing the importance of the accurate choice of approach.
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“In the dressed picture, the separate baths acting locally on each buffer spins become global baths [102,103] acting collectively on the dressed buffer spins.”
From Quantum Models of Consciousness from a Quantum Information Science Perspective (2025) · cites this paper as [102]
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“Writing the spectral decomposition ˆ ρ u = 4 j =1 λ j | λ j ⟩ ⟨ λ j | , the global U (1) symmetry implies that each | λ j ⟩ is an eigenstate of the operator ˆ S z = ˆ S zA + ˆ S zB .”
BackgroundInfluentialSemi-empirical Haken–Strobl model for molecular spin qubits
Aruachan, K., Colón, Y. J., Aravena, D., et al. (2023) · New Journal of Physics · doi:10.1088/1367-2630/acf2bd · Cited by 7
Does canonical quantization lead to GKSL dynamics?
Tomoi Koide, C., & Nicacio, F. (2023) · Physics Letters A · doi:10.1016/j.physleta.2023.129277 · Cited by 7
Dynamics of the nonequilibrium spin-boson model: A benchmark of master equations and their validity
Suárez, G., Łobejko, M., & Horodecki, M. (2024) · Physical Review A · doi:10.1103/physreva.110.042428 · Cited by 7
“…equation being a CPTP map make it a good alternative to simulate open quantum systems in the weak coupling regime, specially with respect to the several efforts to make the Bloch-Redfield equation completely positive [28–30] From this section forward all simulations shown in plots have ρ (0) = 0 .”
MethodDynamics of Microscale and Nanoscale Systems in the Weak-Memory Regime
Brandner, K. (2025) · Physical Review Letters · doi:10.1103/physrevlett.134.037101 · Cited by 7
Geometry-based circulation of local thermal current in quantum harmonic and Bose-Hubbard systems
Dugar, P., & Chien, C.-C. (2022) · Physical review. E · doi:10.1103/physreve.105.064111 · Cited by 7
Thermodynamics of the Coarse-Graining Master Equation
Schaller, G., & Ablaßmayer, J. (2020) · Entropy · doi:10.3390/e22050525 · Cited by 8
Leveraging Collective Effects for Thermometry in Waveguide Quantum Electrodynamics
Sharafiev, A., Juan, M. L., Cattaneo, M., & Kirchmair, G. (2025) · Physical Review Letters · doi:10.1103/physrevlett.134.213602 · Cited by 6
“Then, we can introduce the lowering operators: j +1 ,j are the jump operators [17, 46] of the local master equation, respectively associated with the jump frequencies ω ( α ) j and − ω ( α ) j .”
InfluentialQuantum consensus dynamics by entangling Maxwell demon
Ryu, S., López, R., & Toral, R. (2022) · New Journal of Physics · doi:10.1088/1367-2630/ac57ea · Cited by 6
“The bit-flip noise can be realized when (a) each qubit observable Xi is weakly coupled to the bosonic bath [38], and (b) the interaction between the qubits is weak J Γflip [4].”
BackgroundParticle and thermal transport through one dimensional topological systems via Lindblad formalism
He, Y., & Chien, C.-C. (2023) · Physics Letters A · doi:10.1016/j.physleta.2023.128826 · Cited by 6
Angeletti, J., Zippilli, S., & Vitali, D. (2023) · Quantum Science and Technology · doi:10.1088/2058-9565/acd4e3 · Cited by 6
Vovchenko, I. V., Zyablovsky, A. A., Pukhov, A. A., & Andrianov, E. S. (2023) · Journal of the Optical Society of America B · doi:10.1364/josab.499439 · Cited by 6
Effect of Inter-System Coupling on Heat Transport in a Microscopic Collision Model
Tian, F., Zou, J., Li, L., Li, H., & Shao, B. (2021) · Entropy · doi:10.3390/e23040471 · Cited by 6
“For two coupled qubits interacting with common and separate baths, it was shown that the global approach with partial secular rather than full secular approximation always provides the most accurate choice for the master equation [24].”
Background
Metadata
- Authors
- Cattaneo, M., Giorgi, G. L., Maniscalco, S., & Zambrini, R.
- Affiliations
- Consejo Superior de Investigaciones Científicas (ES)
- University of Turku (FI)
- Corresponding author
- Cattaneo, Marco
- Venue
- New Journal of Physics
- Publisher
- IOP Publishing
- Published
- 2019-11-01
- Volume
- 21
- Issue
- 11
- Pages
- 113045
- ISSN
- 1367-2630 (ISSN-L)
- OpenAlex
- W2952234744
- Semantic Scholar
- 28c3c80a750a8d571ed3e459850f32da0a76ce16
- Cited by
- 169
- References
- 105
- Citations by year
- 2026: 14 · 2025: 31 · 2024: 30 · 2023: 19 · 2022: 28 · 2021: 33 · 2020: 12 · 2019: 2
- FWCI
- 8.46
- Type
- journal article
- Language
- en
- Open access
- gold
- doi.org
- Licence
- Locations
- New Journal of Physics (publishedVersion, cc-by)
- arXiv (Cornell University) (acceptedVersion)
- Aaltodoc (Aalto University) (submittedVersion, cc-by)
- UTUPub (University of Turku) (submittedVersion)
- UTUPub (University of Turku) (submittedVersion, cc-by)
- DIGITAL.CSIC (Spanish National Research Council (CSIC)) (submittedVersion, cc-by)
- DOAJ (DOAJ: Directory of Open Access Journals) (submittedVersion)
- arXiv (Cornell University)
- Funders
- Ministerio de Econom??a y Competitividad
- Topics
- Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Quantum Information and Cryptography
- Physical Sciences › Physics and Astronomy › Statistical and Nonlinear Physics › Advanced Thermodynamics and Statistical Mechanics
- Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Quantum Mechanics and Applications
- Keywords
- coupled qubits, Born-Markov approximation, Markovian dynamics, pure dephasing, energy dissipation, entanglement dynamics, spontaneous synchronization, open quantum systems
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