pith. sign in

arxiv: 2405.10685 · v3 · submitted 2024-05-17 · 🪐 quant-ph

Tunable non-Markovian dynamics in a collision model: an application to coherent transport

Simone Rijavec , Giuseppe Di Pietra This is my paper

Pith reviewed 2026-05-24 01:21 UTC · model grok-4.3

classification 🪐 quant-ph
keywords collision modelnon-Markovianitydepolarising channelcoherent transportthree-qubit chainopen quantum systemsinformation dynamicssystem-environment coupling
0
0 comments X

The pith

Applying a depolarising channel to a qubit reservoir tunes non-Markovianity in a collision model, and Markovian cases can sometimes reduce information loss during coherent transport on a three-qubit chain.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper introduces a collision model in which a depolarising channel applied to a fixed reservoir of qubits controls the degree of non-Markovianity experienced by the system. This tunable setup is then used to examine information flow during coherent transport along a chain of three interacting qubits. The results show that both the system-environment coupling probability and the tuned non-Markovianity strength shape how much information is preserved or lost. In certain regimes the memoryless Markovian limit outperforms environments with memory, suggesting that memory effects are not always beneficial for transport fidelity.

Core claim

We propose a collision model to investigate the information dynamics of a system coupled to an environment with varying degrees of non-Markovianity. We control the degree of non-Markovianity by applying a depolarising channel to a fixed and rigid reservoir of qubits. We characterise the effect of the depolarising channel and apply the model to study the coherent transport of information on a chain of three interacting qubits. We show how the system-environment coupling probability and the degree of non-Markovianity affect the process. Interestingly, in some cases a Markovian environment is preferable to reduce information loss and enhance the coherent transport.

What carries the argument

Collision model in which a depolarising channel applied to a rigid qubit reservoir independently tunes the non-Markovianity of the system-environment interaction while the system evolves under repeated collisions.

If this is right

  • The system-environment coupling probability directly modulates information loss during coherent transport on the three-qubit chain.
  • Increasing the depolarising strength on the reservoir reduces the memory effects in the dynamics.
  • For some values of coupling probability the Markovian limit yields higher transport fidelity than non-Markovian regimes.
  • The model provides a controllable platform for studying how environment memory influences open-system transport.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • The same depolarising tuning mechanism could be tested on longer chains or different interaction graphs to check whether the Markovian preference persists at larger scales.
  • Engineering the bath via depolarising operations might offer a practical route to suppress unwanted memory effects in quantum transport devices.
  • The observed preference for Markovian baths raises the question of whether similar behaviour appears in continuous-time master-equation descriptions of the same three-qubit chain.

Load-bearing premise

The depolarising channel applied to the reservoir tunes the degree of non-Markovianity without introducing other uncontrolled effects in the collision dynamics.

What would settle it

Measuring that the non-Markovianity measure remains unchanged when the depolarising probability is varied, or that coherent transport fidelity does not increase in the predicted Markovian parameter regimes.

Figures

Figures reproduced from arXiv: 2405.10685 by Giuseppe Di Pietra, Simone Rijavec.

Figure 1
Figure 1. Figure 1: FIG. 1. Four steps of the protocol with three chain qubits and three reservoir qubits. a) exchange step: each system qubit [PITH_FULL_IMAGE:figures/full_fig_p003_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2. Degree of non-Markovianity [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3. (a) Von Neumann entropy of the systems qubit [PITH_FULL_IMAGE:figures/full_fig_p005_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4. Coherence element [PITH_FULL_IMAGE:figures/full_fig_p006_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: FIG. 5. Maximum coherence max [PITH_FULL_IMAGE:figures/full_fig_p007_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: FIG. 6. Maximum coherence max [PITH_FULL_IMAGE:figures/full_fig_p008_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: FIG. 7. Population elements [PITH_FULL_IMAGE:figures/full_fig_p009_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: FIG. 8. Difference between the populations [PITH_FULL_IMAGE:figures/full_fig_p010_8.png] view at source ↗
read the original abstract

We propose a collision model to investigate the information dynamics of a system coupled to an environment with varying degrees of non-Markovianity. We control the degree of non-Markovianity by applying a depolarising channel to a fixed and rigid reservoir of qubits. We characterise the effect of the depolarising channel and apply the model to study the coherent transport of information on a chain of three interacting qubits. We show how the system-environment coupling probability and the degree of non-Markovianity affect the process. Interestingly, in some cases a Markovian environment is preferable to reduce information loss and enhance the coherent transport.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

1 major / 0 minor

Summary. The manuscript introduces a collision model in which non-Markovianity of the environment is tuned by applying a depolarizing channel with probability p to each reservoir qubit before collisions. The model is then used to simulate coherent transport of information along a three-qubit chain, with the system-environment coupling strength and the value of p varied to quantify their effects on information backflow and transport efficiency. The central observation is that, for certain parameter regimes, a fully Markovian environment (p=1) yields lower information loss and better transport than environments with memory.

Significance. If the depolarizing channel can be shown to modulate only the memory kernel without altering the collision map or the fixed point of the reduced dynamics, the construction would supply a controllable platform for isolating non-Markovian contributions to quantum transport. The numerical results on the three-qubit chain would then constitute a concrete, falsifiable illustration of when memory is detrimental rather than beneficial.

major comments (1)
  1. [Model description and abstract] The central claim that the depolarizing probability p independently tunes the degree of non-Markovianity while leaving the system-reservoir collision map otherwise unchanged is not supported by any auxiliary diagnostics. Depolarization reduces the Bloch-vector length of each reservoir qubit and shifts its steady-state population; both effects can modify the effective decay rate and the fixed point of the reduced collision map. No plots or tables compare the collision-induced decay constant or the steady-state populations across different p values, so it remains possible that the reported preference for the Markovian case (p=1) arises from these side effects rather than from the absence of memory alone.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for the careful reading and constructive feedback. The major comment raises a valid point about the need for explicit verification that p modulates non-Markovianity independently of other dynamical features. We address this below and will revise the manuscript to include the requested diagnostics.

read point-by-point responses

  1. Referee: The central claim that the depolarizing probability p independently tunes the degree of non-Markovianity while leaving the system-reservoir collision map otherwise unchanged is not supported by any auxiliary diagnostics. Depolarization reduces the Bloch-vector length of each reservoir qubit and shifts its steady-state population; both effects can modify the effective decay rate and the fixed point of the reduced collision map. No plots or tables compare the collision-induced decay constant or the steady-state populations across different p values, so it remains possible that the reported preference for the Markovian case (p=1) arises from these side effects rather than from the absence of memory alone.

    Authors: We agree that auxiliary diagnostics are necessary to substantiate the claim. In the model the depolarizing channel is applied to each reservoir qubit immediately before the collision with the system; the collision unitary itself and the system-environment coupling strength remain fixed. Nevertheless, we acknowledge that the manuscript does not explicitly demonstrate that the effective decay rate and fixed point of the reduced map are independent of p. In the revised version we will add a new figure (or table) that reports the collision-induced decay constant and the steady-state populations of the reduced dynamics for representative values of p (including p=0 and p=1). This will allow readers to verify that the dominant effect of p is on the memory kernel rather than on the Markovian decay parameters. With these diagnostics in place, the numerical results on the three-qubit chain can be interpreted more confidently as evidence that memory can be detrimental to transport in the studied regime. revision: yes

Circularity Check

0 steps flagged

No significant circularity; model and application are independently defined

full rationale

The paper introduces a collision model for a system coupled to a qubit reservoir and defines non-Markovianity tuning via an explicit depolarising channel applied to the reservoir qubits. The subsequent application to coherent transport on a three-qubit chain follows directly from the defined collision maps and channel parameters without any reduction of outputs to fitted inputs, self-definitional loops, or load-bearing self-citations. No equations or claims in the provided text equate a derived quantity (such as transport efficiency or information backflow) to the tuning parameter by construction. The derivation chain remains self-contained against external benchmarks.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

Based on abstract only; no specific free parameters or invented entities mentioned. The depolarizing channel is a standard tool.

axioms (1)
  • domain assumption The collision model framework accurately represents open quantum system dynamics.
    Standard in the field but assumed here.

pith-pipeline@v0.9.0 · 5626 in / 1164 out tokens · 26543 ms · 2026-05-24T01:21:06.832155+00:00 · methodology

discussion (0)

Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.

Reference graph

Works this paper leans on

46 extracted references · 46 canonical work pages

  1. [1]

    exchange step

    The system qubits interact with the nearest reservoir qubits via a partial swap (Eq. (4)) with probability η (Fig. 1a). We will call this step the “exchange step”

    work page

  2. [2]

    depolarising step

    The depolarising channel is applied to the reservoir qubits (Fig. 1b). This step controls the degree of non- Markovianity of the environment. We will call this step the “depolarising step”

    work page

  3. [3]

    transfer via reservoir

    The reservoir qubits evolve according to the Hamiltonian of Eq. (2) for a time interval ∆ t (Fig. 1c). We will call this step the “transfer via reservoir”

    work page

  4. [4]

    transfer via chain

    The system qubits evolve according to the Hamiltonian of Eq. (1) for a time interval ∆ t (Fig. 1d). We will call this step the “transfer via chain”. All the steps of the protocol can be repeated indefinitely. Non-Markovianity . We expect the parameter Ω to control the amount of information the environment loses. When Ω = 0, ∆ m 0 (ρCR) leaves ρCR unchange...

    work page

  5. [5]

    D. V. Alexandrov and A. Y. Zubarev, Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences 379, 20200301 (2021)

    work page 2021

  6. [6]

    D. V. Alexandrov and A. Y. Zubarev, Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences 380, 20210366 (2022)

    work page 2022

  7. [7]

    Lloyd, J

    S. Lloyd, J. Phys.: Conf. Ser. 302, 012037 (2011)

    work page 2011

  8. [8]

    Y. Kim, F. Bertagna, E. M. D’Souza, D. J. Heyes, L. O. Johannissen, E. T. Nery, A. Pantelias, A. Sanchez-Pedre˜ no Jimenez, L. Slocombe, M. G. Spencer, J. Al-Khalili, G. S. Engel, S. Hay, S. M. Hingley-Wilson, K. Jeevaratnam, A. R. Jones, D. R. Kattnig, R. Lewis, M. Sacchi, N. S. Scrutton, S. R. P. Silva, and J. McFadden, Quantum Reports 3, 80 (2021)

    work page 2021

  9. [9]

    M¨ uller, S

    M. M¨ uller, S. Diehl, G. Pupillo, and P. Zoller, inAdvances In Atomic, Molecular, and Optical Physics , Advances in Atomic, Molecular, and Optical Physics, Vol. 61, edited by P. Berman, E. Arimondo, and C. Lin (Academic Press, 2012) pp. 1–80

    work page 2012

  10. [10]

    Civolani, V

    A. Civolani, V. Stanzione, M. L. Chiofalo, and J. Yago Malo, Entropy 26, 20 (2024)

    work page 2024

  11. [11]

    G. S. Engel, T. R. Calhoun, E. L. Read, T.-K. Ahn, T. Manˇ cal, Y.-C. Cheng, R. E. Blankenship, and G. R. Fleming, Nature 446, 782 (2007)

    work page 2007

  12. [12]

    Panitchayangkoon, D

    G. Panitchayangkoon, D. Hayes, K. A. Fransted, J. R. Caram, E. Harel, J. Wen, R. E. Blankenship, and G. S. Engel, Proceedings of the National Academy of Sciences 107, 12766 (2010)

    work page 2010

  13. [13]

    D. M. Wilkins and N. S. Dattani, J. Chem. Theory Comput. 11, 3411 (2015)

    work page 2015

  14. [14]

    H.-G. Duan, V. I. Prokhorenko, R. J. Cogdell, K. Ashraf, A. L. Stevens, M. Thorwart, and R. J. D. Miller, Proceedings of the National Academy of Sciences 114, 8493 (2017)

    work page 2017

  15. [15]

    Tao, N.-N

    M.-J. Tao, N.-N. Zhang, P.-Y. Wen, F.-G. Deng, Q. Ai, and G.-L. Long, Science Bulletin 65, 318 (2020)

    work page 2020

  16. [16]

    Lee, Y.-C

    H. Lee, Y.-C. Cheng, and G. R. Fleming, Science 316, 1462 (2007)

    work page 2007

  17. [17]

    Mohseni, P

    M. Mohseni, P. Rebentrost, S. Lloyd, and A. Aspuru-Guzik, The Journal of Chemical Physics 129, 174106 (2008)

    work page 2008

  18. [18]

    Rebentrost, M

    P. Rebentrost, M. Mohseni, I. Kassal, S. Lloyd, and A. Aspuru-Guzik, New J. Phys. 11, 033003 (2009)

    work page 2009

  19. [19]

    Rebentrost, M

    P. Rebentrost, M. Mohseni, and A. Aspuru-Guzik, J. Phys. Chem. B 113, 9942 (2009)

    work page 2009

  20. [20]

    Str¨ umpfer and K

    J. Str¨ umpfer and K. Schulten, J Chem Phys134, 095102 (2011)

    work page 2011

  21. [21]

    Rebentrost and A

    P. Rebentrost and A. Aspuru-Guzik, The Journal of Chemical Physics 134, 101103 (2011)

    work page 2011

  22. [22]

    Butkus, D

    V. Butkus, D. Zigmantas, L. Valkunas, and D. Abramavicius, Chemical Physics Letters 545, 40 (2012)

    work page 2012

  23. [23]

    Huelga and M

    S. Huelga and M. Plenio, Contemporary Physics 54, 181 (2013)

    work page 2013

  24. [24]

    Tempelaar, T

    R. Tempelaar, T. L. C. Jansen, and J. Knoester, J. Phys. Chem. B 118, 12865 (2014)

    work page 2014

  25. [25]

    Halpin, P

    A. Halpin, P. J. M. Johnson, R. Tempelaar, R. S. Murphy, J. Knoester, T. L. C. Jansen, and R. J. D. Miller, Nature Chem 6, 196 (2014)

    work page 2014

  26. [26]

    H.-G. Duan, P. Nalbach, V. I. Prokhorenko, S. Mukamel, and M. Thorwart, New J. Phys. 17, 072002 (2015)

    work page 2015

  27. [27]

    Reppert and P

    M. Reppert and P. Brumer, The Journal of Chemical Physics 149, 234102 (2018)

    work page 2018

  28. [28]

    S. V. Moreira, B. Marques, R. R. Paiva, L. S. Cruz, D. O. Soares-Pinto, and F. L. Semi˜ ao, Phys. Rev. A 101, 012123 (2020)

    work page 2020

  29. [29]

    Di Pietra and C

    G. Di Pietra and C. Marletto, J. Phys. A: Math. Theor. 56, 265305 (2023)

    work page 2023

  30. [30]

    Di Pietra, V

    G. Di Pietra, V. Vedral, and C. Marletto, Scientific Reports 14, 20094 (2024)

    work page 2024

  31. [31]

    Campbell and B

    S. Campbell and B. Vacchini, EPL 133, 60001 (2021)

    work page 2021

  32. [32]

    Ciccarello, S

    F. Ciccarello, S. Lorenzo, V. Giovannetti, and G. M. Palma, Physics Reports Quantum collision models: Open system dynamics from repeated interactions, 954, 1 (2022)

    work page 2022

  33. [33]

    Ziman, P

    M. Ziman, P. ˇStelmachoviˇ c, V. Buˇ zek, M. Hillery, V. Scarani, and N. Gisin, Phys. Rev. A65, 042105 (2002)

    work page 2002

  34. [34]

    Ziman, P

    M. Ziman, P. ˇStelmachoviˇ c, and V. Buˇ zek, Open Syst Inf Dyn12, 81 (2005)

    work page 2005

  35. [35]

    Ziman and V

    M. Ziman and V. Buˇ zek, Phys. Rev. A72, 022110 (2005)

    work page 2005

  36. [36]

    Ciccarello, G

    F. Ciccarello, G. M. Palma, and V. Giovannetti, Phys. Rev. A 87, 040103(R) (2013)

    work page 2013

  37. [37]

    McCloskey and M

    R. McCloskey and M. Paternostro, Phys. Rev. A 89, 052120 (2014)

    work page 2014

  38. [38]

    Kretschmer, K

    S. Kretschmer, K. Luoma, and W. T. Strunz, Phys. Rev. A 94, 012106 (2016)

    work page 2016

  39. [39]

    Man, Y.-J

    Z.-X. Man, Y.-J. Xia, and R. Lo Franco, Phys. Rev. A 97, 062104 (2018)

    work page 2018

  40. [40]

    T. Saha, A. Das, and S. Ghosh, New J. Phys. 26, 023011 (2024)

    work page 2024

  41. [41]

    Kay, Int

    A. Kay, Int. J. Quantum Inform. 08, 641 (2010)

    work page 2010

  42. [42]

    Breuer, E.-M

    H.-P. Breuer, E.-M. Laine, and J. Piilo, Phys. Rev. Lett. 103, 210401 (2009)

    work page 2009

  43. [43]

    Qiskit contributors, Qiskit: An open-source framework for quantum computing (2023)

    work page 2023

  44. [44]

    B. W. Matthews, R. E. Fenna, M. C. Bolognesi, M. F. Schmid, and J. M. Olson, Journal of Molecular Biology 131, 259 (1979)

    work page 1979

  45. [45]

    Uzdin, S

    R. Uzdin, S. Gasparinetti, R. Ozeri, and R. Kosloff, New J. Phys. 20, 063030 (2018)

    work page 2018

  46. [46]

    Leontica, F

    S. Leontica, F. Tennie, and T. Farrow, Commun Phys 4, 1 (2021)

    work page 2021