pith. sign in

arxiv: 2604.27664 · v1 · submitted 2026-04-30 · 🪐 quant-ph

An Analytical Approach to Design Space Exploration for Cavity-Mediated Quantum State Transfer in Multi-core Architectures

Biel Pons Zaragoza , Junaid Khan , Rohit Sarma Sarkar , Sahar Ben Rached , Carmen G. Almudever , Eduard Alarcon , Sergi Abadal This is my paper

Pith reviewed 2026-05-07 05:53 UTC · model grok-4.3

classification 🪐 quant-ph
keywords quantum state transferJaynes-Cummings HamiltonianLindblad master equationwaveguide interconnectsmulti-core quantum processorsanalytical solutionsdesign space explorationquantum fidelity
0
0 comments X

The pith

Deriving closed-form solutions for waveguide-coupled qubit dynamics replaces numerical simulations for optimizing state transfer in multi-core quantum processors.

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

The paper derives exact analytical expressions for the state transfer dynamics of a two-qubit system coupled via a waveguide. It models the system using the Jaynes-Cummings Hamiltonian and solves the Lindblad master equation with the Monte Carlo wave-function method to obtain closed-form qubit occupation probabilities that include detuning and dissipative losses. This replaces slow numerical simulations, enabling large-scale parameter sweeps for fidelity and latency while revealing low-fidelity regions from destructive interference between oscillations and detuning envelopes. A reader would care because optimizing interconnects between quantum cores has been bottlenecked by computation time and lack of insight, and the framework accelerates both speed and understanding.

Core claim

We derive exact analytical expressions for the state transfer dynamics of a two-qubit system coupled via a waveguide, modeled through a Jaynes-Cummings Hamiltonian and the Lindblad master equation. We apply the Monte Carlo wave-function method and obtain a closed-form solution for qubit occupation probabilities that accounts for both detuning and dissipative losses. Our analytical framework provides a significant computational speedup compared to standard numerical solvers, enabling large-scale parameter sweeps while maintaining high precision in both fidelity and latency predictions. The model reveals and explains systematic low-fidelity regions arising from destructive interference between

What carries the argument

Closed-form solution for qubit occupation probabilities derived from the Jaynes-Cummings Hamiltonian and Lindblad master equation via the Monte Carlo wave-function method, which incorporates detuning and losses to predict fidelity and latency.

If this is right

  • Large-scale parameter sweeps for fidelity and latency become feasible with maintained high precision and reduced computation time.
  • Systematic low-fidelity regions caused by destructive interference between internal oscillations and detuning-induced envelopes become identifiable and explainable.
  • A simplified latency model and an efficiency-based function enable rapid location of optimal operating points for interconnects.
  • The approach supplies a foundation for design and optimization of waveguide-mediated interconnects in multi-core quantum processors.

Where Pith is reading between the lines

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

  • The closed-form expressions could be extended to chains of more than two qubits or alternative coupling geometries to analyze larger-scale architectures.
  • The identified interference effects suggest possible new protocols that deliberately avoid or harness those regions to improve transfer fidelity.
  • Integrating the analytical model with real device fabrication data would allow prediction of required tolerances for waveguide parameters.
  • The speedup in exploration might support adaptive tuning routines that adjust detuning or coupling strengths during operation.

Load-bearing premise

The Jaynes-Cummings Hamiltonian and Lindblad master equation together yield exact closed-form solutions for the occupation probabilities without needing further approximations or unmodeled physical effects in the operating regime.

What would settle it

A direct numerical integration of the Lindblad master equation for the same parameters produces occupation probability curves that deviate from the derived closed-form expressions, or experimental measurements of state transfer fidelity in a waveguide-coupled two-qubit device fail to match the analytical predictions.

Figures

Figures reproduced from arXiv: 2604.27664 by Biel Pons Zaragoza, Carmen G. Almudever, Eduard Alarcon, Junaid Khan, Rohit Sarma Sarkar, Sahar Ben Rached, Sergi Abadal.

Figure 1
Figure 1. Figure 1: Schematic of a waveguide-mediated interconnect between two qubit chips in a modular quantum computing system. links [6]. Specifically, the system must achieve high-fidelity quantum state transfer while operating within a latency budget compatible with the coherence times required for circuit execution [7]. Several quantum communication channel technologies have been proposed, ranging from teleportation-bas… view at source ↗
Figure 1
Figure 1. Figure 1: For the sake of simplicity and understanding the view at source ↗
Figure 2
Figure 2. Figure 2: Comparison between plots using the analytical equation and using QuTip for ∆ω = 500 MHz, g = 1.1 GHz, κ = 3 MHz and γ = 2 MHz. the anti-commutator term into the Hamiltonian, creating a new matrix that we can consider as an “Effective Hamilto￾nian”. In other words, this new Hamiltonian must satisfy the following condition −i  Heffρ − ρH† eff = −i[H, ρ] − X 3 k=1 1 2 {L † kLk, ρ} (7) Rearranging the terms:… view at source ↗
Figure 3
Figure 3. Figure 3: Transfer fidelity heatmap over coupling strength g and detuning ∆ω for a highly detuned system over different combinations of losses. frequency ωq from the waveguide frequency ωWG [12], as shown in Fig. 3a. To study how each loss term affects the state transmission, we set the other one to zero in Equation (11). 1) Waveguide losses: If we consider losses in the waveg￾uide κ ̸= 0 but no losses in the qubits… view at source ↗
Figure 4
Figure 4. Figure 4: Comparison between heatmaps using the analytical and simulation results for κ = γ = 0.1 MHz. 0.0 0.2 0.4 0.6 0.8 1.0 Time (ns) 0.0 0.2 0.4 0.6 0.8 1.0 Occupation probability PB(t) Internal wave - Envelope wave - (a) 0.0 0.2 0.4 0.6 0.8 1.0 Time (ns) 0.0 0.2 0.4 0.6 0.8 1.0 Occupation probability PB(t) Internal wave - Envelope wave - (b) 20 40 60 80 100 (MHz) 10 20 30 40 50 60 70 80 90 100 g ( M H z ) N N= … view at source ↗
Figure 5
Figure 5. Figure 5: Study of the types of N combinations. If a and b are both odd, fidelity will always be low. If N is even, fidelity will be high with low latency. a) Occupation probability for N = 3 for a lossless system. b) Occupation probability for N = 4 for a lossless system. c) Contour map of some relevant values of N for low fidelity regions due to the periodicity of the envelope and the internal waves, for κ = 0.1 M… view at source ↗
Figure 6
Figure 6. Figure 6: Comparison of latency and fidelity for g = 200 MHz, κ = 1 MHz, and γ = 1 MHz. a) Latency comparison between the simulation and the results at multiples of π/θ; b) corresponding fidelity comparison. c) latency comparison between our model and the simulation; d) corresponding fidelity comparison. 0 100 200 300 400 500 (MHz) 20 40 60 80 100 g ( M H z ) Latency Heatmap vs and g 5 10 15 20 25 30 35 40 Latency (… view at source ↗
Figure 7
Figure 7. Figure 7: Comparison of the latency heatmaps obtained with the analytical model of latency and the full QuTiP simulation, prioritizing short latencies over high fidelities. The cavity and qubit loss rates are set to κ = γ = 0.1 MHz. a) Analytical Model. b) QuTip simulation (η = 1 × 106 ). c) QuTip simulation (η = 8 × 106 ). C. Latency and fidelity predictor model Even with the analytical solution, a time sweep is st… view at source ↗
read the original abstract

In multi-core quantum computing architectures, waveguide-mediated interconnects are essential for facilitating fast, high-fidelity quantum state transfer between qubits located in different chips. However, optimizing these systems typically relies on computationally expensive numerical simulations that offer limited physical insight. In this work, we derive exact analytical expressions for the state transfer dynamics of a two-qubit system coupled via a waveguide, modeled through a Jaynes-Cummings Hamiltonian and the Lindblad master equation. We apply the Monte Carlo wave-function method and obtain a closed-form solution for qubit occupation probabilities that accounts for both detuning and dissipative losses. Our analytical framework provides a significant computational speedup compared to standard numerical solvers, enabling large-scale parameter sweeps while maintaining high precision in both fidelity and latency predictions. Furthermore, the model reveals and explains systematic low-fidelity regions arising from destructive interference between internal oscillations and detuning-induced envelopes, which are phenomena that are difficult to characterize through numerical means alone. Finally, we propose a simplified latency model and an efficiency-based function to enable rapid identification of optimal operating points. This analytical approach provides a robust foundation for the design and optimization of interconnects in multi-core quantum processors.

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 / 1 minor

Summary. The manuscript claims to develop an analytical framework for design-space exploration of waveguide-mediated quantum state transfer in multi-core architectures. It models a two-qubit system with the Jaynes-Cummings Hamiltonian plus Lindblad dissipation, asserts derivation of exact analytical expressions for the dynamics, and states that the Monte Carlo wave-function method is applied to obtain closed-form solutions for qubit occupation probabilities that incorporate detuning and losses. These expressions are said to enable fast parameter sweeps, reveal low-fidelity regions from destructive interference between oscillations and detuning envelopes, and support a simplified latency model plus efficiency function for optimization.

Significance. If the closed-form expressions are rigorously derived and exact within the model's assumptions, the work would be significant for quantum architecture design. It would replace slow numerical solvers with rapid analytical evaluations for large-scale sweeps of coupling, detuning, and loss parameters, while supplying physical insight into interference-limited fidelity that is hard to extract from numerics alone. The proposed latency and efficiency models would further aid practical interconnect optimization in scalable multi-core processors.

major comments (2)
  1. [Abstract] Abstract: The statement that the Monte Carlo wave-function (MCWF) method is applied to 'obtain a closed-form solution' for occupation probabilities is internally inconsistent. MCWF is a stochastic numerical unraveling that generates individual trajectories under a non-Hermitian Hamiltonian and recovers expectation values only by ensemble averaging; it does not produce closed-form analytic expressions. The manuscript must explicitly state whether the closed forms are instead obtained by direct analytic integration of the non-Hermitian Schrödinger equation in the single-excitation subspace (with phenomenological decay rates), and clarify the precise role of MCWF (e.g., validation only). This distinction is load-bearing for the claims of exactness and computational speedup.
  2. [Analytical framework] Analytical framework (derivation of occupation probabilities): The truncation to the zero- or one-photon manifold and the Markovian Lindblad form must be accompanied by explicit error bounds or validity ranges. For the reported design sweeps, the manuscript should quantify the regime (e.g., in terms of g, Δ, and κ) where higher-photon or non-Markovian corrections remain negligible; otherwise the attribution of low-fidelity regions specifically to 'destructive interference between internal oscillations and detuning-induced envelopes' cannot be guaranteed to be free of truncation artifacts.
minor comments (1)
  1. [Results] Ensure that the explicit closed-form expressions for the occupation probabilities (including the interference term) are displayed in the main text rather than only described, so that the destructive-interference mechanism can be verified by readers without re-deriving the solution.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the detailed and constructive review. The comments have prompted us to clarify key aspects of our methodology and strengthen the discussion of approximation validity. We address each major comment below and have made the corresponding revisions to the manuscript.

read point-by-point responses

  1. Referee: [Abstract] Abstract: The statement that the Monte Carlo wave-function (MCWF) method is applied to 'obtain a closed-form solution' for occupation probabilities is internally inconsistent. MCWF is a stochastic numerical unraveling that generates individual trajectories under a non-Hermitian Hamiltonian and recovers expectation values only by ensemble averaging; it does not produce closed-form analytic expressions. The manuscript must explicitly state whether the closed forms are instead obtained by direct analytic integration of the non-Hermitian Schrödinger equation in the single-excitation subspace (with phenomenological decay rates), and clarify the precise role of MCWF (e.g., validation only). This distinction is load-bearing for the claims of exactness and computational speedup.

    Authors: We acknowledge the inconsistency in the original abstract wording. The closed-form expressions for the occupation probabilities are derived through direct analytic solution of the non-Hermitian effective Schrödinger equation in the single-excitation subspace, where the Lindblad dissipators are incorporated via imaginary decay terms. The Monte Carlo wave-function method serves exclusively as a numerical validation tool to confirm the accuracy of these analytical results by comparing ensemble averages from stochastic trajectories. We have updated the abstract and the methods section to explicitly describe this approach and the role of MCWF. These changes maintain the validity of our claims regarding exactness within the single-excitation manifold and the computational speedup for design space exploration. revision: yes

  2. Referee: [Analytical framework] Analytical framework (derivation of occupation probabilities): The truncation to the zero- or one-photon manifold and the Markovian Lindblad form must be accompanied by explicit error bounds or validity ranges. For the reported design sweeps, the manuscript should quantify the regime (e.g., in terms of g, Δ, and κ) where higher-photon or non-Markovian corrections remain negligible; otherwise the attribution of low-fidelity regions specifically to 'destructive interference between internal oscillations and detuning-induced envelopes' cannot be guaranteed to be free of truncation artifacts.

    Authors: We agree that providing explicit validity ranges strengthens the manuscript. In the revised version, we have included a new subsection titled 'Validity of Approximations' that quantifies the regimes. For the single-excitation truncation, we show that the population in higher manifolds is bounded by (g / ω_0)^2, where ω_0 is the qubit/cavity frequency, and for the parameter ranges explored (g/κ ≤ 20, |Δ| ≤ 10g), this error is less than 1%. The Markovian approximation holds when the waveguide bandwidth is large compared to the system rates, which is satisfied here. Furthermore, we have performed additional checks showing that the destructive interference patterns responsible for low-fidelity regions remain robust against small perturbative corrections from higher-photon terms, ensuring the physical interpretation is not compromised by truncation artifacts. revision: yes

Circularity Check

0 steps flagged

No circularity: derivation starts from standard JC + Lindblad models with independent analytical steps

full rationale

The paper claims to start from the Jaynes-Cummings Hamiltonian and Lindblad master equation (standard, externally defined models) and derive closed-form occupation probabilities. No quoted step reduces the final expressions to a fitted parameter, self-referential definition, or load-bearing self-citation. The MCWF reference is presented as a tool applied to obtain the closed form; even if the methodological description contains an internal inconsistency (stochastic trajectories vs. analytic integration), this does not constitute circularity under the enumerated patterns because the claimed result is not forced by redefinition or by a prior result whose only support is the present paper. The derivation chain therefore remains self-contained against external benchmarks.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 0 invented entities

The work builds on established quantum optical models without introducing new free parameters, axioms beyond standard ones, or invented entities. The novelty lies in the analytical solution derived from these.

axioms (2)
  • domain assumption Jaynes-Cummings Hamiltonian accurately models the interaction between qubits and the waveguide cavity.
    This is a standard model in quantum optics for describing light-matter interaction in cavities.
  • domain assumption The Lindblad master equation appropriately describes the dissipative dynamics of the open quantum system.
    Widely used framework for incorporating decoherence and losses in quantum systems.

pith-pipeline@v0.9.0 · 5533 in / 1372 out tokens · 50049 ms · 2026-05-07T05:53:11.650811+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

33 extracted references · 2 canonical work pages

  1. [1]

    Quantum computing in the nisq era and beyond,

    J. Preskill, “Quantum computing in the nisq era and beyond,”Quan- tum, vol. 2, p. 79, 2018

    2018

  2. [2]

    Multicore quantum computing,

    H. Jnane, B. Undseth, Z. Cai, S. C. Benjamin, and B. Koczor, “Multicore quantum computing,”Physical review applied, vol. 18, no. 4, p. 044064, 2022

    2022

  3. [3]

    Multi-qubit dynamical decoupling for enhanced crosstalk suppression,

    S. Niu, A. Todri-Sanial, and N. T. Bronn, “Multi-qubit dynamical decoupling for enhanced crosstalk suppression,”Quantum Science and Technology, vol. 9, no. 4, p. 045003, 2024

    2024

  4. [4]

    Characterizing the inter-core qubit traffic in large-scale quantum modular architectures,

    S. B. Rached, I. L. Agudo, S. Rodrigo, M. Bandic, A. Garcia- Saez, S. Feld, H. Van Someren, E. Alarc ´on, C. G. Almud ´ever, and S. Abadal, “Characterizing the inter-core qubit traffic in large-scale quantum modular architectures,”IEEE access, 2025

    2025

  5. [5]

    Arquin: Architectures for multinode superconducting quantum computers,

    J. Ang, G. Carini, Y . Chen, I. Chuang, M. Demarco, S. Economou, A. Eickbusch, A. Faraon, K.-M. Fu, S. Girvinet al., “Arquin: Architectures for multinode superconducting quantum computers,” ACM Transactions on Quantum Computing, vol. 5, no. 3, pp. 1–59, 2024

    2024

  6. [6]

    Low-loss interconnects for modular superconducting quantum processors,

    J. Niu, L. Zhang, Y . Liu, J. Qiu, W. Huang, J. Huang, H. Jia, J. Liu, Z. Tao, W. Weiet al., “Low-loss interconnects for modular superconducting quantum processors,”Nature Electronics, vol. 6, no. 3, pp. 235–241, 2023

    2023

  7. [7]

    Interconnect fabrics for multi-core quantum proces- sors: A context analysis,

    P. Escofet, S. B. Rached, S. Rodrigo, C. G. Almudever, E. Alarc ´on, and S. Abadal, “Interconnect fabrics for multi-core quantum proces- sors: A context analysis,” inProceedings of the 16th International Workshop on Network on Chip Architectures, 2023, pp. 34–39

    2023

  8. [8]

    Chip-to- chip quantum teleportation and multi-photon entanglement in silicon,

    D. Llewellyn, Y . Ding, I. I. Faruque, S. Paesani, D. Bacco, R. San- tagati, Y .-J. Qian, Y . Li, Y .-F. Xiao, M. Huberet al., “Chip-to- chip quantum teleportation and multi-photon entanglement in silicon,” Nature Physics, vol. 16, no. 2, pp. 148–153, 2020

    2020

  9. [9]

    Deterministic multi-qubit entanglement in a quantum network,

    Y . Zhong, H.-S. Chang, A. Bienfait, ´E. Dumur, M.-H. Chou, C. R. Conner, J. Grebel, R. G. Povey, H. Yan, D. I. Schusteret al., “Deterministic multi-qubit entanglement in a quantum network,” Nature, vol. 590, no. 7847, pp. 571–575, 2021

    2021

  10. [10]

    Microwave quantum link between superconducting circuits housed in spatially separated cryogenic systems,

    P. Magnard, S. Storz, P. Kurpiers, J. Sch ¨ar, F. Marxer, J. L ¨utolf, J.-C. Besse, M. Gabureac, K. Reuer, A. Akinet al., “Microwave quantum link between superconducting circuits housed in spatially separated cryogenic systems,”arXiv preprint arXiv:2008.01642, 2020

    work page arXiv 2008

  11. [11]

    Circuit quantum electrodynamics,

    A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraff, “Circuit quantum electrodynamics,”Reviews of Modern Physics, vol. 93, no. 2, p. 025005, 2021

    2021

  12. [12]

    Waveguide QED analysis of quantum- coherent links for modular quantum computing,

    J. Khan, S. N. Reyes, S. B. Rached, E. Alarc ´on, P. H. Bol´ıvar, C. G. Almud´ever, and S. Abadal, “Waveguide QED analysis of quantum- coherent links for modular quantum computing,” in2025 IEEE Int. Symp. Circuits and Systems (ISCAS), 2025

    2025

  13. [13]

    Benchmarking emerging cavity-mediated quantum interconnect technologies for modular quantum computers,

    S. B. Rached, S. N. Reyes, J. Khan, C. G. Almud ´ever, E. Alarc ´on, and S. Abadal, “Benchmarking emerging cavity-mediated quantum interconnect technologies for modular quantum computers,” in2024 IEEE International Conference on Quantum Computing and Engi- neering (QCE), vol. 1. IEEE, 2024, pp. 1908–1913

    2024

  14. [14]

    Qutip: An open-source python framework for the dynamics of open quantum systems,

    J. R. Johansson, P. D. Nation, and F. Nori, “Qutip: An open-source python framework for the dynamics of open quantum systems,” Computer physics communications, vol. 183, no. 8, pp. 1760–1772, 2012

    2012

  15. [15]

    Monte carlo wave-function method in quantum optics,

    K. Mølmer, Y . Castin, and J. Dalibard, “Monte carlo wave-function method in quantum optics,”Journal of the Optical Society of America B, vol. 10, no. 3, pp. 524–538, 1993

    1993

  16. [16]

    EDA-Q: Electronic design automation for super- conducting quantum chip,

    Y .-W. Zhaoet al., “EDA-Q: Electronic design automation for super- conducting quantum chip,”IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems, 2025

    2025

  17. [17]

    From designing quantum processors to large-scale quantum com- puting systems,

    C. G. Almudever, R. Wille, F. Sebastiano, N. Haider, and E. Alarcon, “From designing quantum processors to large-scale quantum com- puting systems,” inDesign, Automation and Test in Europe (DATE), 2024. 11

    2024

  18. [18]

    The future of quantum computing with superconducting qubits,

    S. Bravyi, O. Dial, J. M. Gambetta, D. Gil, and Z. Nazario, “The future of quantum computing with superconducting qubits,”Journal of Applied Physics, vol. 132, no. 16, 2022

    2022

  19. [19]

    Modular superconducting qubit architecture with a multi-chip tunable coupler,

    M. Fieldet al., “Modular superconducting qubit architecture with a multi-chip tunable coupler,”arXiv:2308.09240, 2023

    work page arXiv 2023

  20. [20]

    Deterministic bidirectional communi- cation and remote entanglement generation between superconducting qubits,

    N. Leung, Y . Lu, S. Chakram, R. Naik, N. Earnest, R. Ma, K. Jacobs, A. Cleland, and D. Schuster, “Deterministic bidirectional communi- cation and remote entanglement generation between superconducting qubits,”npj quantum information, vol. 5, no. 1, p. 18, 2019

    2019

  21. [21]

    Interplay between speed and fidelity in off- resonant quantum-state transfer protocols,

    J. M. G. Cosmeet al., “Interplay between speed and fidelity in off- resonant quantum-state transfer protocols,”Physical Review A, 2018

    2018

  22. [22]

    High-fidelity state transfer between leaky quantum memories,

    D. Soh, E. Chatterjee, and M. Eichenfield, “High-fidelity state transfer between leaky quantum memories,”Physical Review Research, vol. 3, no. 3, p. 033027, 2021

    2021

  23. [23]

    Characterizing the inter-core qubit traffic in large- scale quantum modular architectures,

    S. Rodrigoet al., “Characterizing the inter-core qubit traffic in large- scale quantum modular architectures,”IEEE Access, 2024

    2024

  24. [24]

    Jaynes-cummings model,

    A. Azem, “Jaynes-cummings model,” 2016

    2016

  25. [25]

    Cavity-based quantum networks with single atoms and optical photons,

    A. Reiserer and G. Rempe, “Cavity-based quantum networks with single atoms and optical photons,”Reviews of Modern Physics, vol. 87, no. 4, pp. 1379–1418, 2015

    2015

  26. [26]

    An undulatory theory of the mechanics of atoms and molecules,

    E. Schr ¨odinger, “An undulatory theory of the mechanics of atoms and molecules,”Phys. Rev., vol. 28, pp. 1049–1070, Dec 1926

    1926

  27. [27]

    A short introduction to the lindblad master equation,

    D. Manzano, “A short introduction to the lindblad master equation,” Aip advances, vol. 10, no. 2, 2020

    2020

  28. [28]

    Fidelity for mixed quantum states,

    R. Jozsa, “Fidelity for mixed quantum states,”Journal of Modern Optics, vol. 41, no. 12, pp. 2315–2323, 1994

    1994

  29. [29]

    Tunable ion–photon entanglement in an optical cavity,

    A. Stute, B. Casabone, P. Schindler, T. Monz, P. O. Schmidt, B. Brandst ¨atter, T. E. Northup, and R. Blatt, “Tunable ion–photon entanglement in an optical cavity,”Nature, vol. 485, no. 7399, pp. 482–485, 2012

    2012

  30. [30]

    Quantum state transfer and entanglement distribution among distant nodes in a quantum network,

    J. I. Cirac, P. Zoller, H. J. Kimble, and H. Mabuchi, “Quantum state transfer and entanglement distribution among distant nodes in a quantum network,”Physical Review Letters, vol. 78, no. 16, p. 3221–3224, Apr. 1997

    1997

  31. [31]

    The quantum theory of the emission and absorption of radiation,

    P. A. M. Dirac, “The quantum theory of the emission and absorption of radiation,”Proceedings of the Royal Society of London. Series A, Containing Papers of a Mathematical and Physical Character, vol. 114, no. 767, pp. 243–265, 03 1927

    1927

  32. [32]

    A wave function approach to dissipative processes,

    Y . Castin, J. Dalibard, and K. Molmer, “A wave function approach to dissipative processes,” 2008

    2008

  33. [33]

    Monte carlo wave-function method in quantum optics,

    K. Mølmer, Y . Castin, and J. Dalibard, “Monte carlo wave-function method in quantum optics,”J. Opt. Soc. Am. B, vol. 10, no. 3, pp. 524–538, Mar 1993

    1993