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arxiv: 2605.14263 · v1 · submitted 2026-05-14 · ❄️ cond-mat.mes-hall · quant-ph

Recognition: 2 theorem links

· Lean Theorem

Open Quantum Theory of Shot Noise in Dissipative Chiral Transport

Ming Gong , Masahito Ueda
Authors on Pith no claims yet

Pith reviewed 2026-05-15 02:31 UTC · model grok-4.3

classification ❄️ cond-mat.mes-hall quant-ph
keywords shot noisedissipative chiral transportopen quantum systemsquantum circuit mappingU(1) symmetrynoise cumulantsoccupancy distribution
0
0 comments X

The pith

Current noise in dissipative chiral transport arises from the competition between average occupancy and particle-number fluctuations.

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

The paper maps a dissipative chiral system onto a quantum circuit and shows that the resulting current noise splits into two parts: one set by how electrons occupy energy levels on average and the other by fluctuations in particle number. When the system relaxes completely, electrons stack into lower states, which removes most partition noise and leaves only a small residual contribution enforced by strict particle-number conservation. Selectively raising the temperature of the source while keeping the bath cold exposes the underlying competition and produces a sign change in the noise measured between different channels. The authors give a concrete inversion procedure that turns measured noise cumulants back into the hidden occupancy distribution.

Core claim

Mapping the open dissipative chiral transport problem onto a quantum circuit yields an exact decomposition of current noise into occupancy-distribution and particle-number-fluctuation contributions; complete energy relaxation suppresses all but the U(1)-protected residual noise.

What carries the argument

Quantum-circuit mapping that decomposes noise into separate occupancy-distribution and particle-number-fluctuation terms.

If this is right

  • Shot noise is strongly suppressed once energy relaxation is complete.
  • Inter-channel noise correlations reverse sign under selective source heating.
  • The occupancy distribution can be reconstructed from measured noise cumulants via the proposed inversion scheme.
  • Only the component of noise protected by particle-number conservation survives full relaxation.

Where Pith is reading between the lines

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

  • The same circuit decomposition may apply to other open quantum transport geometries with chiral edges.
  • The residual U(1)-protected noise could serve as a stable reference signal in experiments where thermal noise dominates.
  • Varying the bath coupling strength offers a direct experimental knob to tune between the two noise contributions.

Load-bearing premise

The open-system dynamics of the dissipative chiral transport can be captured exactly by the quantum-circuit representation without further uncontrolled approximations.

What would settle it

Failure to observe a sign reversal in inter-channel correlation noise when the source is selectively heated while the bath remains cold would contradict the claimed decomposition.

Figures

Figures reproduced from arXiv: 2605.14263 by Masahito Ueda, Ming Gong.

Figure 1
Figure 1. Figure 1: FIG. 1. Illustration of the multi-channel chiral transport system and [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2. Cumulant generating function (CGF) and shot noise suppres [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3. Impacts of the origins of thermal fluctuations on noise dynam [PITH_FULL_IMAGE:figures/full_fig_p004_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4. Reconstruction of the occupancy distribution from noise cu [PITH_FULL_IMAGE:figures/full_fig_p004_4.png] view at source ↗
read the original abstract

We develop an open quantum theory for shot-noise dynamics in dissipative chiral transport. By mapping a system under consideration onto a quantum circuit, we show that current noise is governed by two competing factors: the average occupancy distribution and particle-number fluctuations. With energy fully relaxed, shot noise is strongly suppressed, reflecting the stacking of electrons into lower energy states due to dissipation. This process quenches the partition noise from partially occupied levels, and finally isolates the residual noise protected by strong $U(1)$ symmetry. Moreover, selectively heating the source against the bath uncovers the underlying competition between the noise contributions from the occupancy distribution and those from the particle-number fluctuations. It triggers a sign reversal in inter-channel correlation noise, a signature masked by seemingly identical single-channel thermal noises. We propose an inversion scheme to experimentally reconstruct the hidden occupancy distribution directly from measurable noise cumulants.

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

2 major / 2 minor

Summary. The manuscript develops an open quantum theory of shot noise in dissipative chiral transport. By mapping the system onto a quantum circuit, it decomposes current noise into competing contributions from the average occupancy distribution and particle-number fluctuations. Full energy relaxation is shown to strongly suppress shot noise via electron stacking into lower states, quenching partition noise and isolating only the residual component protected by U(1) symmetry. Selective heating of the source is used to expose the competition, producing a sign reversal in inter-channel correlation noise, and an inversion scheme is proposed to reconstruct the hidden occupancy distribution from measurable noise cumulants.

Significance. If the quantum-circuit mapping is shown to be exact and free of hidden approximations, the work would supply a useful framework for noise analysis in open dissipative systems, clarifying how dissipation suppresses partition noise while preserving symmetry-protected residuals. The proposed inversion from cumulants to occupancy could enable new experimental probes of non-equilibrium distributions in mesoscopic chiral devices.

major comments (2)
  1. [Quantum-circuit mapping section (likely §III)] The central claim of exact noise decomposition and strong suppression rests on the quantum-circuit mapping of the dissipative chiral system. The manuscript must demonstrate explicitly (with the relevant Lindblad equation and circuit construction) that this mapping reproduces the full steady-state noise spectrum without additional Markovian, weak-coupling, or perturbative assumptions; any uncontrolled approximation here would render the suppression result and the isolation of U(1)-protected noise non-exact.
  2. [Results on energy relaxation and selective heating (likely §IV)] The suppression result and the sign-reversal prediction require validation against known limits. Direct comparison of the derived noise expressions to the equilibrium thermal-noise limit and to the non-dissipative chiral case (with explicit equations) is needed to confirm that the quenching of partition noise is not an artifact of the mapping.
minor comments (2)
  1. [Inversion scheme paragraph] Define all noise cumulants and the precise form of the inversion scheme with explicit formulas so that the reconstruction procedure can be reproduced from the text alone.
  2. [Figure captions and associated text] Add uncertainty estimates or parameter-sensitivity analysis to the plots showing sign reversal in inter-channel correlations.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the careful reading of our manuscript and the constructive comments. We address each major comment below and will revise the manuscript to provide the requested explicit demonstrations and validations.

read point-by-point responses

  1. Referee: [Quantum-circuit mapping section (likely §III)] The central claim of exact noise decomposition and strong suppression rests on the quantum-circuit mapping of the dissipative chiral system. The manuscript must demonstrate explicitly (with the relevant Lindblad equation and circuit construction) that this mapping reproduces the full steady-state noise spectrum without additional Markovian, weak-coupling, or perturbative assumptions; any uncontrolled approximation here would render the suppression result and the isolation of U(1)-protected noise non-exact.

    Authors: We agree that the quantum-circuit mapping requires a fully explicit presentation to establish its validity. In the revised manuscript we will add a dedicated subsection that states the Lindblad master equation for the dissipative chiral system, details the circuit construction, and derives the steady-state noise spectrum directly from it. Within the standard Lindblad framework (which assumes Markovian dynamics and weak system-bath coupling by construction), no further perturbative or uncontrolled approximations are introduced; the noise decomposition follows exactly from the mapping. We will emphasize these points to confirm that the suppression of partition noise and the isolation of the U(1)-protected residual are exact results inside the model. revision: yes

  2. Referee: [Results on energy relaxation and selective heating (likely §IV)] The suppression result and the sign-reversal prediction require validation against known limits. Direct comparison of the derived noise expressions to the equilibrium thermal-noise limit and to the non-dissipative chiral case (with explicit equations) is needed to confirm that the quenching of partition noise is not an artifact of the mapping.

    Authors: We concur that direct validation against known limits is necessary. In the revised manuscript we will insert explicit comparisons in §IV: (i) the equilibrium limit (zero bias voltage, finite temperature) will be shown to recover the Johnson-Nyquist thermal noise with the corresponding equation; (ii) the non-dissipative limit (vanishing relaxation rate) will be shown to reproduce the standard partition-noise formula for chiral transport. These reductions will be derived step-by-step from the general noise expressions, demonstrating that the quenching of partition noise is a physical consequence of energy relaxation rather than an artifact of the mapping. revision: yes

Circularity Check

0 steps flagged

No significant circularity detected in derivation chain

full rationale

The abstract and provided context describe a mapping of the dissipative chiral system onto a quantum circuit that permits decomposition of noise into occupancy and fluctuation terms. No equations, self-definitions, fitted parameters renamed as predictions, or load-bearing self-citations are quoted that would reduce the central claims to their own inputs by construction. The derivation is presented as an independent construction within the open-system Lindblad framework and remains self-contained against external benchmarks such as the master equation itself.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

Only the abstract is available; no explicit free parameters, axioms, or invented entities are stated. The mapping to a quantum circuit is presented as a modeling choice whose validity is not detailed.

pith-pipeline@v0.9.0 · 5441 in / 1114 out tokens · 48666 ms · 2026-05-15T02:31:05.515002+00:00 · methodology

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Lean theorems connected to this paper

Citations machine-checked in the Pith Canon. Every link opens the source theorem in the public Lean library.

  • IndisputableMonolith/Cost/FunctionalEquation.lean washburn_uniqueness_aczel unclear
    ?
    unclear

    Relation between the paper passage and the cited Recognition theorem.

    We map this transport process onto a fermionic quantum circuit... intra-layer random unitary gates U(m) and inter-layer dissipative jump operators Kα... both commute with Ntot, strictly enforcing a strong U(1) symmetry

  • IndisputableMonolith/Foundation/ArrowOfTime.lean z_monotone_absolute echoes
    ?
    echoes

    ECHOES: this paper passage has the same mathematical shape or conceptual pattern as the Recognition theorem, but is not a direct formal dependency.

    dissipation forces electrons to pack into lower energy states... quenches the partition noise... isolates the residual noise protected by strong U(1) symmetry

What do these tags mean?
matches
The paper's claim is directly supported by a theorem in the formal canon.
supports
The theorem supports part of the paper's argument, but the paper may add assumptions or extra steps.
extends
The paper goes beyond the formal theorem; the theorem is a base layer rather than the whole result.
uses
The paper appears to rely on the theorem as machinery.
contradicts
The paper's claim conflicts with a theorem or certificate in the canon.
unclear
Pith found a possible connection, but the passage is too broad, indirect, or ambiguous to say the theorem truly supports the claim.

Reference graph

Works this paper leans on

74 extracted references · 74 canonical work pages

  1. [1]

    J. B. Johnson, Thermal agitation of electricity in conductors, Phys. Rev.32, 97 (1928)

    work page 1928

  2. [2]

    Nyquist, Thermal agitation of electric charge in conductors, Phys

    H. Nyquist, Thermal agitation of electric charge in conductors, Phys. Rev.32, 110 (1928)

    work page 1928

  3. [3]

    Brillouin, Fluctuations de courant dans un conducteur, Helv

    L. Brillouin, Fluctuations de courant dans un conducteur, Helv. Phys. Acta7, 47 (1934)

    work page 1934

  4. [4]

    Y . M. Blanter and M. Büttiker, Shot noise in mesoscopic con- ductors, Phys. Rep.336, 1 (2000)

    work page 2000

  5. [5]

    C. W. J. Beenakker and H. van Houten, Semiclassical theory of shot noise and its suppression in a conductor with deterministic scattering, Phys. Rev. B43, 12066 (1991)

    work page 1991

  6. [6]

    Shimizu and M

    A. Shimizu and M. Ueda, Effects of dephasing and dissipation on quantum noise in conductors, Phys. Rev. Lett.69, 1403 (1992)

    work page 1992

  7. [7]

    C. W. J. Beenakker, Suppression of shot noise in metallic diffu- sive conductors, Phys. Rev. B46, 1889 (1992)

    work page 1992

  8. [8]

    R. C. Liu and Y . Yamamoto, Suppression of quantum partition noise in mesoscopic electron branching circuits, Phys. Rev. B 49, 10520 (1994)

    work page 1994

  9. [9]

    R. C. Liu and Y . Yamamoto, Nyquist noise in the transition from mesoscopic to macroscopic transport, Phys. Rev. B50, 17411 (1994)

    work page 1994

  10. [10]

    M. J. M. de Jong and C. W. J. Beenakker, Semiclassical theory of shot-noise suppression, Phys. Rev. B51, 16867 (1995)

    work page 1995

  11. [11]

    A. H. Steinbach, J. M. Martinis, and M. H. Devoret, Observation of hot-electron shot noise in a metallic resistor, Phys. Rev. Lett. 76, 3806 (1996)

    work page 1996

  12. [12]

    Y . V . Nazarov, ed.,Quantum Noise in Mesoscopic Physics, NATO Science Series II: Mathematics, Physics and Chemistry No. 97 (Springer Netherlands, 2003)

    work page 2003

  13. [13]

    M. G. Pala and G. Iannaccone, Effect of dephasing on the current statistics of mesoscopic devices, Phys. Rev. Lett.93, 256803 (2004)

    work page 2004

  14. [14]

    Kumada, F

    N. Kumada, F. D. Parmentier, H. Hibino, D. C. Glattli, and P. Roulleau, Shot noise generated by graphene p−n junctions in the quantum Hall effect regime, Nat. Commun.6, 8068 (2015)

    work page 2015

  15. [15]

    C. W. J. Beenakker, Pure dephasing increases partition noise in the quantum Hall effect, Phys. Rev. B113, 075416 (2026)

    work page 2026

  16. [16]

    Chang, J

    C.-Z. Chang, J. Zhang, X. Feng, J. Shen, Z. Zhang, M. Guo, K. Li, Y . Ou, P. Wei, L.-L. Wang, Z.-Q. Ji, Y . Feng, S. Ji, X. Chen, J. Jia, X. Dai, Z. Fang, S.-C. Zhang, K. He, Y . Wang, L. Lu, X.-C. Ma, and Q.-K. Xue, Experimental observation of the quan- tum anomalous Hall effect in a magnetic topological insulator, Science340, 167 (2013)

    work page 2013

  17. [17]

    Kou, S.-T

    X. Kou, S.-T. Guo, Y . Fan, L. Pan, M. Lang, Y . Jiang, Q. Shao, T. Nie, K. Murata, J. Tang, Y . Wang, L. He, T.-K. Lee, W.-L. Lee, and K. L. Wang, Scale-invariant quantum anomalous Hall effect in magnetic topological insulators beyond the two-dimensional limit, Phys. Rev. Lett.113, 137201 (2014)

    work page 2014

  18. [18]

    Chang, W

    C.-Z. Chang, W. Zhao, D. Y . Kim, P. Wei, J. K. Jain, C. Liu, M. H. W. Chan, and J. S. Moodera, Zero-field dissipationless chiral edge transport and the nature of dissipation in the quantum anomalous Hall state, Phys. Rev. Lett.115, 057206 (2015)

    work page 2015

  19. [19]

    Yasuda, M

    K. Yasuda, M. Mogi, R. Yoshimi, A. Tsukazaki, K. S. Takahashi, M. Kawasaki, F. Kagawa, and Y . Tokura, Quantized chiral edge conduction on domain walls of a magnetic topological insulator, Science358, 1311 (2017)

    work page 2017

  20. [20]

    Marguerite, J

    A. Marguerite, J. Birkbeck, A. Aharon-Steinberg, D. Halbertal, K. Bagani, Y . Myasoedov, A. K. Geim, D. J. Perello, and E. Zel- dov, Imaging work and dissipation in the quantum Hall state in graphene, Nature575, 628 (2019)

    work page 2019

  21. [21]

    Y .-F. Zhao, R. Zhang, R. Mei, L.-J. Zhou, H. Yi, Y .-Q. Zhang, J. Yu, R. Xiao, K. Wang, N. Samarth, M. H. W. Chan, C.-X. Liu, and C.-Z. Chang, Tuning the Chern number in quantum anomalous Hall insulators, Nature588, 419 (2020)

    work page 2020

  22. [22]

    Chang, C.-X

    C.-Z. Chang, C.-X. Liu, and A. H. MacDonald, Colloquium: Quantum anomalous Hall effect, Rev. Mod. Phys.95, 011002 (2023)

    work page 2023

  23. [23]

    H. Li, H. Jiang, Q.-F. Sun, and X. C. Xie, Emergent energy dissipation in quantum limit, Science Bulletin69, 1221 (2024)

    work page 2024

  24. [24]

    Q. Yan, H. Li, H. Jiang, Q.-F. Sun, and X. C. Xie, Rules for dissi- pationless topotronics, Science Advances10, eado4756 (2024)

    work page 2024

  25. [25]

    K. M. Fijalkowski, N. Liu, M. Klement, S. Schreyeck, K. Brun- ner, C. Gould, and L. W. Molenkamp, A balanced quantum Hall resistor, Nat. Electron.7, 438 (2024)

    work page 2024

  26. [26]

    X.-L. Qi, T. L. Hughes, and S.-C. Zhang, Chiral topological superconductor from the quantum Hall state, Phys. Rev. B82, 184516 (2010)

    work page 2010

  27. [27]

    C. W. J. Beenakker, Search for Majorana fermions in supercon- ductors, Annu. Rev. Condens. Matter Phys.4, 113 (2013)

    work page 2013

  28. [28]

    Sato and Y

    M. Sato and Y . Ando, Topological superconductors: a review, Rep. Prog. Phys.80, 076501 (2017). 6

    work page 2017

  29. [29]

    Lian, X.-Q

    B. Lian, X.-Q. Sun, A. Vaezi, X.-L. Qi, and S.-C. Zhang, Topo- logical quantum computation based on chiral Majorana fermions, Proc. Natl. Acad. Sci. USA115, 10938 (2018)

    work page 2018

  30. [30]

    Büttiker, Absence of backscattering in the quantum Hall effect in multiprobe conductors, Phys

    M. Büttiker, Absence of backscattering in the quantum Hall effect in multiprobe conductors, Phys. Rev. B38, 9375 (1988)

    work page 1988

  31. [31]

    C. W. J. Beenakker, Random-matrix theory of quantum transport, Rev. Mod. Phys.69, 731 (1997)

    work page 1997

  32. [32]

    Q. Ma, F. D. Parmentier, P. Roulleau, and G. Fleury, Graphene n−p junctions in the quantum Hall regime: Numerical study of incoherent scattering effects, Phys. Rev. B97, 205445 (2018)

    work page 2018

  33. [33]

    C. W. J. Beenakker and J.-F. Chen, Monitored quantum trans- port: full counting statistics of a quantum Hall interferometer, Quantum9, 1874 (2025)

    work page 2025

  34. [34]

    C. W. J. Beenakker, Shot noise from which-path detection in a chiral Majorana interferometer, Phys. Rev. B112, L081402 (2025)

    work page 2025

  35. [35]

    Datta,Electronic Transport in Mesoscopic Systems, Cam- bridge Studies in Semiconductor Physics and Microelectronic Engineering (Cambridge University Press, Cambridge, 1995)

    S. Datta,Electronic Transport in Mesoscopic Systems, Cam- bridge Studies in Semiconductor Physics and Microelectronic Engineering (Cambridge University Press, Cambridge, 1995)

    work page 1995

  36. [36]

    Haug and A.-P

    H. Haug and A.-P. Jauho,Quantum Kinetics in Transport and Optics of Semiconductors, 2nd ed., Solid-State Sciences No. 123 (Springer, Berlin, Heidelberg, 2008)

    work page 2008

  37. [37]

    Y . V . Nazarov and Y . M. Blanter,Quantum Transport: Introduc- tion to Nanoscience(Cambridge University Press, Cambridge, 2009)

    work page 2009

  38. [38]

    Henny, S

    M. Henny, S. Oberholzer, C. Strunk, T. Heinzel, K. Ensslin, M. Holland, and C. Schönenberger, The fermionic Hanbury Brown and Twiss experiment, Science284, 296 (1999)

    work page 1999

  39. [39]

    W. D. Oliver, J. Kim, R. C. Liu, and Y . Yamamoto, Hanbury Brown and Twiss-type experiment with electrons, Science284, 299 (1999)

    work page 1999

  40. [40]

    Buˇca and T

    B. Buˇca and T. Prosen, A note on symmetry reductions of the Lindblad equation: transport in constrained open spin chains, New J. Phys.14, 073007 (2012)

    work page 2012

  41. [41]

    V . V . Albert and L. Jiang, Symmetries and conserved quantities in lindblad master equations, Phys. Rev. A89, 022118 (2014)

    work page 2014

  42. [42]

    D. A. Abanin and L. S. Levitov, Quantized transport in graphene p−njunctions in a magnetic field, Science317, 641 (2007)

    work page 2007

  43. [43]

    J. R. Williams, L. DiCarlo, and C. M. Marcus, Quantum Hall effect in a gate-controlledp−n junction of graphene, Science 317, 638 (2007)

    work page 2007

  44. [44]

    Oberholzer, E

    S. Oberholzer, E. V . Sukhorukov, C. Strunk, and C. Schönen- berger, Shot noise of series quantum point contacts intercalating chaotic cavities, Phys. Rev. B66, 233304 (2002)

    work page 2002

  45. [45]

    Li and S.-Q

    J. Li and S.-Q. Shen, Disorder effects in the quantum Hall effect of graphenep−njunctions, Phys. Rev. B78, 205308 (2008)

    work page 2008

  46. [46]

    See Supplemental Materials for details

    work page

  47. [47]

    Breuer and F

    H.-P. Breuer and F. Petruccione,The Theory of Open Quantum Systems(Oxford University Press, Oxford, 2007)

    work page 2007

  48. [48]

    M. A. Nielsen and I. L. Chuang,Quantum Computation and Quantum Information: 10th Anniversary Edition(Cambridge University Press, 2010)

    work page 2010

  49. [49]

    Verstraete, M

    F. Verstraete, M. M. Wolf, and J. I. Cirac, Quantum computation and quantum-state engineering driven by dissipation, Nat. Phys. 5, 633 (2009)

    work page 2009

  50. [50]

    Schollwöck, The density-matrix renormalization group in the age of matrix product states, Ann

    U. Schollwöck, The density-matrix renormalization group in the age of matrix product states, Ann. Phys. January 2011 Special Issue,326, 96 (2011)

    work page 2011

  51. [51]

    Paeckel, T

    S. Paeckel, T. Köhler, A. Swoboda, S. R. Manmana, U. Scholl- wöck, and C. Hubig, Time-evolution methods for matrix-product states, Ann. Phys.411, 167998 (2019)

    work page 2019

  52. [52]

    Weimer, A

    H. Weimer, A. Kshetrimayum, and R. Orús, Simulation methods for open quantum many-body systems, Rev. Mod. Phys.93, 015008 (2021)

    work page 2021

  53. [53]

    Xiang,Density Matrix and Tensor Network Renormalization (Cambridge University Press, Cambridge, 2023)

    T. Xiang,Density Matrix and Tensor Network Renormalization (Cambridge University Press, Cambridge, 2023)

    work page 2023

  54. [54]

    H. K. Yadalam and M. T. Mitchison, Process-tensor approach to full counting statistics of charge transport in quantum many- body circuits, arXiv:2603.28894 (2026)

    work page arXiv 2026

  55. [55]

    Fishman, S

    M. Fishman, S. R. White, and E. M. Stoudenmire, The ITensor Software Library for Tensor Network Calculations, SciPost Phys. Codebases , 4 (2022)

    work page 2022

  56. [56]

    L. S. Levitov and G. B. Lesovik, Charge distribution in quantum shot noise, JETP Lett.58, 230 (1993)

    work page 1993

  57. [57]

    Y . V . Nazarov, Circuit theory for full counting statistics in multi- terminal circuits, Phys. Rev. Lett.88, 196801 (2002)

    work page 2002

  58. [58]

    Pilgram, P

    S. Pilgram, P. Samuelsson, H. Förster, and M. Büttiker, Full- counting statistics for voltage and dephasing probes, Phys. Rev. Lett.97, 066801 (2006)

    work page 2006

  59. [59]

    Förster, P

    H. Förster, P. Samuelsson, S. Pilgram, and M. Büttiker, V oltage and dephasing probes in mesoscopic conductors: A study of full-counting statistics, Phys. Rev. B75, 035340 (2007)

    work page 2007

  60. [60]

    Both formalisms are equivalent for extracting the cumulants of the fluctuations

    In contrast to the conventional characteristic function with a complex phase eiλ ˆN widely used in quantum transport, we define the generating function using a real parameter λ for algebraic simplicity. Both formalisms are equivalent for extracting the cumulants of the fluctuations

    work page

  61. [61]

    Texier and M

    C. Texier and M. Büttiker, Effect of incoherent scattering on shot noise correlations in the quantum Hall regime, Phys. Rev. B62, 7454 (2000)

    work page 2000

  62. [62]

    Oberholzer, E

    S. Oberholzer, E. Bieri, C. Schönenberger, M. Giovannini, and J. Faist, Positive cross correlations in a normal-conducting fermionic beam splitter, Phys. Rev. Lett.96, 046804 (2006)

    work page 2006

  63. [63]

    T. Ota, M. Hashisaka, K. Muraki, and T. Fujisawa, Negative and positive cross-correlations of current noises in quantum Hall edge channels at bulk filling factor ν =1, J. Phys.: Condens. Matter29, 225302 (2017)

    work page 2017

  64. [64]

    Bomze, G

    Y . Bomze, G. Gershon, D. Shovkun, L. S. Levitov, and M. Reznikov, Measurement of counting statistics of electron transport in a tunnel junction, Phys. Rev. Lett.95, 176601 (2005)

    work page 2005

  65. [65]

    Gershon, Y

    G. Gershon, Y . Bomze, E. V . Sukhorukov, and M. Reznikov, De- tection of non-Gaussian fluctuations in a quantum point contact, Phys. Rev. Lett.101, 016803 (2008)

    work page 2008

  66. [66]

    Open Quantum Theory of Shot Noise in Dissipative Chiral Transport

    E. Pinsolle, S. Houle, C. Lupien, and B. Reulet, Non-Gaussian current fluctuations in a short diffusive conductor, Phys. Rev. Lett.121, 027702 (2018). End Matter Inversion Scheme for the Occupancy Distribution—To ob- tain the inverted average occupancy distribution ⟨Mk⟩inv from the measurable joint cumulants Kπ = ∂π ˜F |λ=0, we employ a three-step inversi...

    work page 2018

  67. [67]

    Unitary Scattering S2

    work page

  68. [68]

    Average of Observables S3 D

    Dissipative Kraus Operators S2 C. Average of Observables S3 D. Momentum and Cumulant Generating Function S3 S3. Derivation of the Inversion Scheme S3 A. Definitions of the Effective CGF and the Filter Cumulants and Operators S3

    work page

  69. [69]

    The Effective CGF S3

    work page

  70. [70]

    Effect of the Filter Operator S4 C

    The Filter Cumulant S4 B. Effect of the Filter Operator S4 C. Determining the CoefficientsWm(k) S5 S4. Simulation Parameters S6 S1. CONSTRUCTION OF THE QUANTUM CIRCUIT MODEL A. Kraus Operators for Dissipation For a given channel n between adjacent layers m and m +1, the explicit forms of these Kraus operators ˆK↑, ˆK↓, and ˆK0 are ˆK(m,m+1) ↑,n = √γ↑ˆc† m...

    work page

  71. [71]

    Unitary Scattering SVD U1 U2 U3 FIG. S2. Schematic of the unitary scattering and the subsequent MPS update. The rectangular blocks spanning three adjacent sites (illustrated for N =3) represent the application of the Haar-random unitary operators defined in Eq. (S10). SVD is then employed to factorize the multi-site tensors back into the standard M×N sing...

    work page

  72. [72]

    S1 C, each step of the dissipative evolution entails applying a specific Kraus operator ˆK to the system

    Dissipative Kraus Operators As established in Sec. S1 C, each step of the dissipative evolution entails applying a specific Kraus operator ˆK to the system. Since we consider jumps between the first channels of adjacent energy levels, the corresponding operator spans across all intermediate lattice sites between the two target sites, as schematically illu...

    work page

  73. [73]

    , λN) be the counting field

    The Effective CGF Let λ :=( λ1, . . . , λN) be the counting field. The effective CGF is defined as ˜F(λ)=ln⟨e Ψ(λ)⟩M.(S14) Here,M:=( M0,M 1, . . . ,M N). The microscopic generating function is given by Ψ(λ)= NX k=1 Mk ln " S k(λ)/ N k !# ,(S15) where S k(λ)= P i1<···<ik eλi1 +···+λik . The bracket ⟨· · · ⟩M denotes the statistical average over the configu...

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  74. [74]

    Together with the filter cumulant Qm, we can also define the filter operator ˆQm = X π⊢m C(π)∂π.(S19) Specifically, ˆQm[ ˜F (λ)] λ=0 = Qm

    The Filter Cumulant We define the m-th order filter cumulant Qm as a linear combination of cumulants Qm = X π⊢m C(π)K π.(S17) The sum runs over all integer partitions π of m with the coeffi- cients C(π)=(−1) |π|−1(|π| −1)! m! Q|π| j=1 p j!Q v cv! .(S18) Here, |π| denotes the total number of parts in the partition π, p j represents the value of the j-th pa...

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