{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,6]],"date-time":"2026-06-06T02:01:01Z","timestamp":1780711261631,"version":"3.54.1"},"reference-count":70,"publisher":"Verein zur Forderung des Open Access Publizierens in den Quantenwissenschaften","license":[{"start":{"date-parts":[[2026,4,15]],"date-time":"2026-04-15T00:00:00Z","timestamp":1776211200000},"content-version":"unspecified","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100011033","name":"MICIU\/AEI (Agencia Estatal de Investigaci\u00f3n) and the European Union","doi-asserted-by":"publisher","award":["PCI2024-153449"],"award-info":[{"award-number":["PCI2024-153449"]}],"id":[{"id":"10.13039\/501100011033","id-type":"DOI","asserted-by":"publisher"}]},{"name":"Bavarian state government","award":["Munich Quantum Valley"],"award-info":[{"award-number":["Munich Quantum Valley"]}]}],"content-domain":{"domain":["quantum-journal.org"],"crossmark-restriction":false},"short-container-title":["Quantum"],"abstract":"<jats:p>We describe a novel scheme for the generation of stationary entanglement between two separated qubits that are driven by a purely thermal photon source. While in this scenario the qubits remain in a separable state at all times when the source is broadband, i.e. Markovian, the qubits relax into an entangled steady state once the bandwidth of the thermal source is sufficiently reduced. We explain this phenomenon by the appearance of a quasiadiabatic dark state and identify the most relevant nonadiabatic corrections that eventually lead to a breakdown of the entangled state, once the temperature is too high. This effect demonstrates how the non-Markovianity of an otherwise incoherent reservoir can be harnessed for quantum communication applications in optical, microwave, and phononic networks. As two specific examples, we discuss the use of filtered room-temperature noise as a passive resource for entangling distant superconducting qubits in a cryogenic quantum link or solid-state spin qubits in a phononic quantum channel.<\/jats:p>","DOI":"10.22331\/q-2026-04-15-2066","type":"journal-article","created":{"date-parts":[[2026,4,15]],"date-time":"2026-04-15T06:57:11Z","timestamp":1776236231000},"page":"2066","update-policy":"https:\/\/doi.org\/10.22331\/q-crossmark-policy-page","source":"Crossref","is-referenced-by-count":2,"title":["Non-Markovian thermal reservoirs for autonomous entanglement distribution"],"prefix":"10.22331","volume":"10","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-9883-1958","authenticated-orcid":false,"given":"Joan","family":"Agust\u00ed","sequence":"first","affiliation":[{"name":"Technical University of Munich, TUM School of Natural Sciences, Physics Department, 85748 Garching, Germany"},{"name":"Walther-Mei\u00dfner-Institut, Bayerische Akademie der Wissenschaften, 85748 Garching, Germany"},{"name":"Munich Center for Quantum Science and Technology (MCQST), 80799 Munich, Germany"},{"name":"Institute of Fundamental Physics IFF-CSIC, Calle Serrano 113b, 28006 Madrid, Spain"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-5766-7979","authenticated-orcid":false,"given":"Christian M. F.","family":"Schneider","sequence":"additional","affiliation":[{"name":"Technical University of Munich, TUM School of Natural Sciences, Physics Department, 85748 Garching, Germany"},{"name":"Walther-Mei\u00dfner-Institut, Bayerische Akademie der Wissenschaften, 85748 Garching, Germany"},{"name":"Munich Center for Quantum Science and Technology (MCQST), 80799 Munich, Germany"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-3243-4343","authenticated-orcid":false,"given":"Kirill G.","family":"Fedorov","sequence":"additional","affiliation":[{"name":"Technical University of Munich, TUM School of Natural Sciences, Physics Department, 85748 Garching, Germany"},{"name":"Walther-Mei\u00dfner-Institut, Bayerische Akademie der Wissenschaften, 85748 Garching, Germany"},{"name":"Munich Center for Quantum Science and Technology (MCQST), 80799 Munich, Germany"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-1976-1817","authenticated-orcid":false,"given":"Stefan","family":"Filipp","sequence":"additional","affiliation":[{"name":"Technical University of Munich, TUM School of Natural Sciences, Physics Department, 85748 Garching, Germany"},{"name":"Walther-Mei\u00dfner-Institut, Bayerische Akademie der Wissenschaften, 85748 Garching, Germany"},{"name":"Munich Center for Quantum Science and Technology (MCQST), 80799 Munich, Germany"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-2560-8835","authenticated-orcid":false,"given":"Peter","family":"Rabl","sequence":"additional","affiliation":[{"name":"Technical University of Munich, TUM School of Natural Sciences, Physics Department, 85748 Garching, Germany"},{"name":"Walther-Mei\u00dfner-Institut, Bayerische Akademie der Wissenschaften, 85748 Garching, Germany"},{"name":"Munich Center for Quantum Science and Technology (MCQST), 80799 Munich, Germany"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"9598","published-online":{"date-parts":[[2026,4,15]]},"reference":[{"key":"0","doi-asserted-by":"publisher","unstructured":"J. I. Cirac, P. Zoller, H. J. Kimble, and H. Mabuchi, Quantum state transfer and entanglement distribution among distant nodes in a quantum network, Phys. Rev. Lett. 78, 3221 (1997).","DOI":"10.1103\/PhysRevLett.78.3221"},{"key":"1","doi-asserted-by":"publisher","unstructured":"H. J. Kimble, The quantum internet, Nature 453, 1023-1030 (2008).","DOI":"10.1038\/nature07127"},{"key":"2","doi-asserted-by":"publisher","unstructured":"T. E. Northup and R. Blatt, Quantum information transfer using photons, Nature Photon 8, 356 (2014).","DOI":"10.1038\/nphoton.2014.53"},{"key":"3","doi-asserted-by":"publisher","unstructured":"Z.-L. Xiang, M. Zhang, L. Jiang, and P. Rabl, Intracity Quantum Communication via Thermal Microwave Networks, Phys. Rev. X 7, 011035 (2017).","DOI":"10.1103\/PhysRevX.7.011035"},{"key":"4","doi-asserted-by":"publisher","unstructured":"B. Vermersch, P.-O. Guimond, H. Pichler, and P. Zoller, Quantum State Transfer via Noisy Photonic and Phononic Waveguides, Phys. Rev. Lett. 118, 133601 (2017).","DOI":"10.1103\/PhysRevLett.118.133601"},{"key":"5","doi-asserted-by":"publisher","unstructured":"Z.-L. Xiang, D. Gonzalez Olivares, J. J. Garcia-Ripoll, and P. Rabl, Universal Time-Dependent Control Scheme for Realizing Arbitrary Linear Bosonic Transformations, Phys. Rev. Lett. 130, 050801 (2023).","DOI":"10.1103\/PhysRevLett.130.050801"},{"key":"6","doi-asserted-by":"publisher","unstructured":"A. Reiserer and G. Rempe, Cavity-based quantum networks with single atoms and optical photons, Rev. Mod. Phys. 87, 1379 (2015).","DOI":"10.1103\/RevModPhys.87.1379"},{"key":"7","doi-asserted-by":"publisher","unstructured":"P. Magnard, S. Storz, P. Kurpiers, J. Sch\u00e4r, F. Marxer, J. L\u00fctolf, T. Walter, J.-C. Besse, M. Gabureac, K. Reuer, A. Akin, B. Royer, A. Blais, and A. Wallraff, Microwave Quantum Link between Superconducting Circuits Housed in Spatially Separated Cryogenic Systems, Phys. Rev. Lett. 125, 260502 (2020).","DOI":"10.1103\/PhysRevLett.125.260502"},{"key":"8","doi-asserted-by":"publisher","unstructured":"W. K. Yam, M. Renger, S. Gandorfer et al., Cryogenic microwave link for quantum local area networks. npj Quantum Inf. 11, 87 (2025).","DOI":"10.1038\/s41534-025-01046-5"},{"key":"9","doi-asserted-by":"publisher","unstructured":"J. Qiu, Z. Zhang, Z. Wang, L. Zhang, Y. Zhou, X. Sun, J. Zhang, X. Linpeng, S. Liu, J. Niu, Y. Zhong, and D. Yu, A thermal-noise-resilient microwave quantum network traversing 4 K, arXiv:2503.01133 (2025).","DOI":"10.48550\/arXiv.2503.01133"},{"key":"10","doi-asserted-by":"publisher","unstructured":"M. Mollenhauer, A. Irfan, X. Cao, S. Mandal, and W. Pfaff, A high-efficiency elementary network of interchangeable superconducting qubit devices, Nat Electron 8, 610-619 (2025).","DOI":"10.1038\/s41928-025-01404-3"},{"key":"11","doi-asserted-by":"publisher","unstructured":"S. J. M. Habraken, K. Stannigel, M. D. Lukin, P. Zoller, and P. Rabl, Continuous mode cooling and phonon routers for phononic quantum networks, New J. Phys. 14, 115004 (2012).","DOI":"10.1088\/1367-2630\/14\/11\/115004"},{"key":"12","doi-asserted-by":"publisher","unstructured":"M. V. Gustafsson, T. Aref, A. F. Kockum, M. K. Ekstr\u00f6m, G. Johansson, and P. Delsing, Propagating phonons coupled to an artificial atom, Science 346, 207 (2014).","DOI":"10.1126\/science.1257219"},{"key":"13","doi-asserted-by":"publisher","unstructured":"M. J. A. Schuetz, E. M. Kessler, G. Giedke, L. M. K. Vandersypen, M. D. Lukin, and J. I. Cirac, Universal quantum transducers based on surface acoustic waves, Phys. Rev. X 5, 031031 (2015).","DOI":"10.1103\/PhysRevX.5.031031"},{"key":"14","doi-asserted-by":"publisher","unstructured":"M.-A. Lemonde, S. Meesala, A. Sipahigil, M. J. A. Schuetz, M. D. Lukin, M. Loncar, and P. Rabl, Phonon networks with silicon-vacancy centers in diamond waveguides, Phys. Rev. Lett. 120, 213603 (2018).","DOI":"10.1103\/PhysRevLett.120.213603"},{"key":"15","doi-asserted-by":"publisher","unstructured":"A. Bienfait, K. J. Satzinger, Y. P. Zhong, H.-S. Chang, M.-H. Chou, C. R. Conner, E. Dumur, J. Grebel, G. A. Peairs, R. G. Povey, and A. N. Cleland, Phonon-mediated quantum state transfer and remote qubit entanglement, Science 364, 368 (2019).","DOI":"10.1126\/science.aaw8415"},{"key":"16","doi-asserted-by":"publisher","unstructured":"E. Dumur, K. J. Satzinger, G. A. Peairs, M.-H. Chou, A. Bienfait, H.-S. Chang, C. R. Conner, J. Grebel, R. G. Povey, Y. P. Zhong, and A. N. Cleland, Quantum communication with itinerant surface acoustic wave phonons, npj Quantum Inf. 7, 173 (2021).","DOI":"10.1038\/s41534-021-00511-1"},{"key":"17","doi-asserted-by":"publisher","unstructured":"J. B. Brask, G. Haack, N. Brunner, and M. Huber, Autonomous quantum thermal machine for generating steady-state entanglement, New J. Phys. 17, 113029 (2015).","DOI":"10.1088\/1367-2630\/17\/11\/113029"},{"key":"18","doi-asserted-by":"publisher","unstructured":"S. Khandelwal, B. Annby-Andersson, G. F. Diotallevi, A. Wacker, and A. Tavakoli, Maximal steady-state entanglement in autonomous quantum thermal machines, npj Quantum Inf. 11, 28 (2025).","DOI":"10.1038\/s41534-025-00981-7"},{"key":"19","doi-asserted-by":"publisher","unstructured":"C. H. Bennett, G. Brassard, S. Popescu, B. Schumacher, J. A. Smolin, and W. K. Wootters, Purification of Noisy Entanglement and Faithful Teleportation via Noisy Channels, Phys. Rev. Lett. 76, 722 (1996).","DOI":"10.1103\/PhysRevLett.76.722"},{"key":"20","doi-asserted-by":"publisher","unstructured":"W. D\u00fcr, H.-J. Briegel, J. Cirac, and P. Zoller, Quantum repeaters based on entanglement purification, Phys. Rev. A 59, 169 (1999).","DOI":"10.1103\/PhysRevA.59.169"},{"key":"21","doi-asserted-by":"publisher","unstructured":"J. I. Cirac, A. K. Ekert, S. F. Huelga, and C. Macchiavello, Distributed quantum computation over noisy channels, Phys. Rev. A 59, 4249 (1999).","DOI":"10.1103\/PhysRevA.59.4249"},{"key":"22","doi-asserted-by":"publisher","unstructured":"H. Yan, Y. Zhong, H.-S. Chang, A. Bienfait, M. -H. Chou, C. R. Conner, E. Dumur, J. Grebel, R. G. Povey, and A. N. Cleland, Entanglement Purification and Protection in a Superconducting Quantum Network, Phys. Rev. Lett. 128, 080504 (2022).","DOI":"10.1103\/PhysRevLett.128.080504"},{"key":"23","doi-asserted-by":"publisher","unstructured":"K. M. Sliwa, M. Hatridge, A. Narla, S. Shankar, L. Frunzio, R. J. Schoelkopf, and M. H. Devoret, Reconfigurable Josephson Circulator\/Directional Amplifier, Phys. Rev. X 5, 041020 (2015).","DOI":"10.1103\/PhysRevX.5.041020"},{"key":"24","doi-asserted-by":"publisher","unstructured":"J. Kerckhoff, K. Lalumiere, B. J. Chapman, A. Blais, and K. W. Lehnert, On-Chip Superconducting Microwave Circulator from Synthetic Rotation, Phys. Rev. Applied 4, 034002 (2015).","DOI":"10.1103\/PhysRevApplied.4.034002"},{"key":"25","doi-asserted-by":"publisher","unstructured":"B. J. Chapman, E. I. Rosenthal, J. Kerckhoff, B. A. Moores, L. R. Vale, J. A. B. Mates, G. C. Hilton, K. Lalumiere, A. Blais, and K. W. Lehnert, Widely Tunable On-Chip Microwave Circulator for Superconducting Quantum Circuits, Phys. Rev. X 7, 041043 (2017).","DOI":"10.1103\/PhysRevX.7.041043"},{"key":"26","doi-asserted-by":"publisher","unstructured":"F. Lecocq, L. Ranzani, G. A. Peterson, K. Cicak, R. W. Simmonds, J. D. Teufel, and J. Aumentado, Nonreciprocal Microwave Signal Processing with a Field-Programmable Josephson Amplifier, Phys. Rev. Appl. 7, 024028 (2017).","DOI":"10.1103\/PhysRevApplied.7.024028"},{"key":"27","doi-asserted-by":"publisher","unstructured":"S. Masuda, S. Kono, K. Suzuki, Y. Tokunaga, Y. Nakamura, and K. Koshino, Nonreciprocal microwave transmission based on Gebhard-Ruckenstein hopping, Phys. Rev. A 99, 013816 (2019).","DOI":"10.1103\/PhysRevA.99.013816"},{"key":"28","doi-asserted-by":"publisher","unstructured":"Y.-Y. Wang, S. van Geldern, T. Connolly, Y.-X. Wang, A. Shilcusky, A. McDonald, A. A. Clerk, and C. Wang, Low-Loss Ferrite Circulator as a Tunable Chiral Quantum System, Phys. Rev. Applied 16, 064066 (2021).","DOI":"10.1103\/PhysRevApplied.16.064066"},{"key":"29","doi-asserted-by":"publisher","unstructured":"P.-O. Guimond, B. Vermersch, M. L. Juan, A. Sharafiev, G. Kirchmair, and P. Zoller, A unidirectional on-chip photonic interface for superconducting circuits, npj Quantum Inf. 6, 32 (2020).","DOI":"10.1038\/s41534-020-0261-9"},{"key":"30","doi-asserted-by":"publisher","unstructured":"N. Gheeraert, S. Kono, and Y. Nakamura, Programmable directional emitter and receiver of itinerant microwave photons in a waveguide, Phys. Rev. A 102, 053720 (2020).","DOI":"10.1103\/PhysRevA.102.053720"},{"key":"31","doi-asserted-by":"publisher","unstructured":"B. Kannan, et al., On-demand directional microwave photon emission using waveguide quantum electrodynamics, Nature Phys. 19, 394 (2023).","DOI":"10.1038\/s41567-022-01869-5"},{"key":"32","doi-asserted-by":"publisher","unstructured":"C. Joshi, F. Yang, and M. Mirhosseini, Resonance Fluorescence of a Chiral Artificial Atom, Phys. Rev. X 13, 021039 (2023).","DOI":"10.1103\/PhysRevX.13.021039"},{"key":"33","doi-asserted-by":"publisher","unstructured":"P. Lodahl, S. Mahmoodian, S. Stobbe, P. Schneeweiss, J. Volz, A. Rauschenbeutel, H. Pichler, and P. Zoller, Chiral quantum optics, Nature (London) 541, 473 (2017).","DOI":"10.1038\/nature21037"},{"key":"34","doi-asserted-by":"publisher","unstructured":"H. J. Carmichael, Quantum Trajectory Theory for Cascaded Open Systems, Phys. Rev. Lett. 70, 2273 (1993).","DOI":"10.1103\/PhysRevLett.70.2273"},{"key":"35","doi-asserted-by":"publisher","unstructured":"C. W. Gardiner, Driving a Quantum System with the Output Field From Another Driven Quantum System, Phys. Rev. Lett. 70, 2269 (1993).","DOI":"10.1103\/PhysRevLett.70.2269"},{"key":"36","unstructured":"C. W. Gardiner and P. Zoller, Quantum noise, Springer, Berlin (2004). ISBN: 978-3-540-22301-6."},{"key":"37","doi-asserted-by":"publisher","unstructured":"J. Agust\u00ed, Y. Minoguchi, J. M. Fink, and P. Rabl, Long-distance distribution of qubit-qubit entanglement using Gaussian-correlated photonic beams, Phys. Rev. A 105, 062454 (2022).","DOI":"10.1103\/PhysRevA.105.062454"},{"key":"38","doi-asserted-by":"publisher","unstructured":"H. Ritsch and P. Zoller, Systems driven by colored squeezed noise: The atomic absorption spectrum, Phys. Rev. A 38, 4657 (1988).","DOI":"10.1103\/PhysRevA.38.4657"},{"key":"39","doi-asserted-by":"publisher","unstructured":"H. Risken, The Fokker-Planck Equation: Methods of Solution and Applications, Springer, Berlin (1996).","DOI":"10.1007\/978-3-642-61544-3"},{"key":"40","doi-asserted-by":"publisher","unstructured":"S. Hill and W. K. Wootters, Entanglement of a Pair of Quantum Bits, Phys. Rev. Lett. 78, 5022 (1997).","DOI":"10.1103\/PhysRevLett.78.5022"},{"key":"41","doi-asserted-by":"publisher","unstructured":"R. Horodecki, P. Horodecki, M. Horodecki, and K. Horodecki, Quantum entanglement, Rev. Mod. Phys. 81, 865 (2009).","DOI":"10.1103\/RevModPhys.81.865"},{"key":"42","doi-asserted-by":"publisher","unstructured":"C. Gonzalez-Ballestero, Tutorial: projector approach to master equations for open quantum systems, Quantum 8, 1454 (2024).","DOI":"10.22331\/q-2024-08-29-1454"},{"key":"43","doi-asserted-by":"publisher","unstructured":"H. J. Carmichael, Statistical methods in quantum optics 2: Non-classical fields, Springer, Berlin (2007).","DOI":"10.1007\/978-3-540-71320-3"},{"key":"44","doi-asserted-by":"publisher","unstructured":"K. Stannigel, P. Rabl, and P. Zoller, Driven-dissipative preparation of entangled states in cascaded quantum-optical networks, New J. Phys. 14, 063014 (2012).","DOI":"10.1088\/1367-2630\/14\/6\/063014"},{"key":"45","doi-asserted-by":"publisher","unstructured":"H. Pichler, T. Ramos, A. J. Daley, and P. Zoller, Quantum optics of chiral spin networks, Phys. Rev. A 91, 042116 (2015).","DOI":"10.1103\/PhysRevA.91.042116"},{"key":"46","doi-asserted-by":"publisher","unstructured":"P. Groszkowski, A. Seif, J. Koch, and A. A. Clerk, Simple master equations for describing driven systems subject to classical non-Markovian noise, Quantum 7, 972 (2023).","DOI":"10.22331\/q-2023-04-06-972"},{"key":"47","doi-asserted-by":"publisher","unstructured":"C. Gardiner and P. Zoller, The quantum world of ultra-cold atoms and light. Book I, Foundations of Quantum Optics, Imperial College Press, London (2014).","DOI":"10.1142\/p941"},{"key":"48","doi-asserted-by":"publisher","unstructured":"G. S. Agarwal, Quantum statistical theory of optical-resonance phenomena in fluctuating laser fields, Phys. Rev. A 18, 1490 (1978).","DOI":"10.1103\/PhysRevA.18.1490"},{"key":"49","doi-asserted-by":"publisher","unstructured":"P. Zoller, Resonant multiphoton ionization by finite-bandwidth chaotic fields, Phys. Rev. A 19, 1151 (1979).","DOI":"10.1103\/PhysRevA.19.1151"},{"key":"50","doi-asserted-by":"publisher","unstructured":"P. Zoller, ac Stark splitting in double optical resonance and resonance fluorescence by a nonmonochromatic chaotic field, Phys. Rev. A 20, 1019 (1979).","DOI":"10.1103\/PhysRevA.20.1019"},{"key":"51","doi-asserted-by":"publisher","unstructured":"J. I. Cirac, H. Ritsch, and P. Zoller, Two-level system interacting with a finite-bandwidth thermal cavity mode, Phys. Rev. A 44, 4541 (1991).","DOI":"10.1103\/PhysRevA.44.4541"},{"key":"52","doi-asserted-by":"publisher","unstructured":"C. Hepp, T. M\u00fcller, V. Waselowski, J. N. Becker, B. Pingault, H. Sternschulte, D. Steinm\u00fcller-Nethl, A. Gali, J. R. Maze, M. Atat\u00fcre, and C. Becher, Electronic structure of the silicon vacancy color center in diamond, Phys. Rev. Lett. 112, 036405 (2014).","DOI":"10.1103\/PhysRevLett.112.036405"},{"key":"53","doi-asserted-by":"publisher","unstructured":"S. Meesala, Y.-I. Sohn, B. Pingault, L. Shao, H. A. Atikian, J. Holzgrafe, M. G\u00fcndogan, C. Stavrakas, A. Sipahigil, C. Chia, R. Evans, M. J. Burek, M. Zhang, L. Wu, J. L. Pacheco, J. Abraham, E. Bielejec, M. D. Lukin, M. Atat\u00fcre, and M. Loncar, Strain engineering of the silicon vacancy center in diamond, Phys. Rev. B 97, 205444 (2018).","DOI":"10.1103\/PhysRevB.97.205444"},{"key":"54","doi-asserted-by":"publisher","unstructured":"M. C. Kuzyk and H. Wang, Scaling Phononic Quantum Networks of Solid-State Spins with Closed Mechanical Subsystems, Phys. Rev. X 8, 041027 (2018).","DOI":"10.1103\/PhysRevX.8.041027"},{"key":"55","doi-asserted-by":"publisher","unstructured":"S. Maity, L. Shao, S. Bogdanovic, S. Meesala, Y.-I. Sohn, N. Sinclair, B. Pingault, M. Chalupnik, C. Chia, L. Zheng, K. Lai, and M. Loncar, Coherent acoustic control of a single silicon vacancy spin in diamond, Nat. Commun. 11, 193 (2020).","DOI":"10.1038\/s41467-019-13822-x"},{"key":"56","doi-asserted-by":"publisher","unstructured":"T. Neuman, M. Eichenfield, M. E. Trusheim, L. Hackett, P. Narang, and D. Englund, A phononic interface between a superconducting quantum processor and quantum networked spin memories, npj Quantum Inf. 7, 121 (2021).","DOI":"10.1038\/s41534-021-00457-4"},{"key":"57","doi-asserted-by":"publisher","unstructured":"I. Arrazola, Y. Minoguchi, M.-A. Lemonde, A. Sipahigil, and P. Rabl, Toward high-fidelity quantum information processing and quantum simulation with spin qubits and phonons, Phys. Rev. B 110, 045419 (2024).","DOI":"10.1103\/PhysRevB.110.045419"},{"key":"58","doi-asserted-by":"publisher","unstructured":"M. R. Vanner, J. Hofer, G. D. Cole, and M Aspelmeyer, Cooling-by-measurement and mechanical state tomography via pulsed optomechanics, Nat. Commun. 4, 2295 (2013).","DOI":"10.1038\/ncomms3295"},{"key":"59","doi-asserted-by":"publisher","unstructured":"R. Shaniv, C. Reetz, and C. A. Regal, Direct measurement of a spatially varying thermal bath using Brownian motion, Phys. Rev. Research 5, 043121 (2023).","DOI":"10.1103\/PhysRevResearch.5.043121"},{"key":"60","doi-asserted-by":"publisher","unstructured":"M.-A. Lemonde, V. Peano, P. Rabl, and D. G. Angelakis, Quantum state transfer via acoustic edge states in a 2D optomechanical array, New J. Phys. 21, 113030 (2019).","DOI":"10.1088\/1367-2630\/ab51f5"},{"key":"61","doi-asserted-by":"publisher","unstructured":"P. S. Shah, F. Yang, C. Joshi, and M. Mirhosseini, Stabilizing Remote Entanglement via Waveguide Dissipation, PRX Quantum 5, 030346 (2024).","DOI":"10.1103\/PRXQuantum.5.030346"},{"key":"62","doi-asserted-by":"publisher","unstructured":"A. Irfan, K. Singirikonda, M. Yao, A. Lingenfelter, M. Mollenhauer, X. Cao, A. A. Clerk, and W. Pfaff, Autonomous stabilization of remote entanglement in a cascaded quantum network, arXiv:2509.11872 (2025).","DOI":"10.48550\/arXiv.2509.11872"},{"key":"63","doi-asserted-by":"publisher","unstructured":"G. Joe, C. Chia, B. Pingault, M. Haas, M. Chalupnik, E. Cornell, K. Kuruma, B. Machielse, N. Sinclair, S. Meesala, and M. Loncar, High Q-factor diamond optomechanical resonators with silicon vacancy centers at millikelvin temperatures, Nano Lett. 24, 6831 (2024).","DOI":"10.1021\/acs.nanolett.3c04953"},{"key":"64","doi-asserted-by":"publisher","unstructured":"D. D. Sukachev, A. Sipahigil, C. T. Nguyen, M. K. Bhaskar, R. E. Evans, F. Jelezko, and M. D. Lukin, The silicon-vacancy spin qubit in diamond: Quantum memory exceeding ten milliseconds and single-shot state readout, Phys. Rev. Lett. 119, 223602 (2017).","DOI":"10.1103\/PhysRevLett.119.223602"},{"key":"65","doi-asserted-by":"publisher","unstructured":"P. Flajolet and R. Sedgewick, Analytic combinatorics, Cambridge University Press (2009).","DOI":"10.1017\/CBO9780511801655"},{"key":"66","doi-asserted-by":"publisher","unstructured":"H. Pichler and P. Zoller, Photonic Circuits with Time Delays and Quantum Feedback, Phys. Rev. Lett. 116, 093601 (2016).","DOI":"10.1103\/PhysRevLett.116.093601"},{"key":"67","doi-asserted-by":"publisher","unstructured":"N. Fayard, L. Henriet, A. Asenjo-Garcia, and D. Chang, Many-body localization in waveguide quantum electrodynamics, Phys. Rev. Research 3, 033233 (2021).","DOI":"10.1103\/PhysRevResearch.3.033233"},{"key":"68","doi-asserted-by":"publisher","unstructured":"N. Lambert, E. Gigu\u00e8re, P. Menczel, B. Li, P. Hopf, G. Su\u00e1rez, M. Gali, J. Lishman, R. Gadhvi, R. Agarwal, A. Galicia, N. Shammah, P. Nation, J. R. Johansson, S. Ahmed, S. Cross, A. Pitchford, and F. Nori, QuTiP 5: The quantum toolbox in Python, Phys. Rep. 1153, 1 (2026).","DOI":"10.1016\/j.physrep.2025.10.001"},{"key":"69","doi-asserted-by":"publisher","unstructured":"https:\/\/doi.org\/10.5281\/zenodo.15772688.","DOI":"10.5281\/zenodo.15772688"}],"container-title":["Quantum"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/quantum-journal.org\/papers\/q-2026-04-15-2066\/pdf\/","content-type":"unspecified","content-version":"vor","intended-application":"text-mining"}],"deposited":{"date-parts":[[2026,4,15]],"date-time":"2026-04-15T06:57:13Z","timestamp":1776236233000},"score":1,"resource":{"primary":{"URL":"https:\/\/quantum-journal.org\/papers\/q-2026-04-15-2066\/"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2026,4,15]]},"references-count":70,"URL":"https:\/\/doi.org\/10.22331\/q-2026-04-15-2066","archive":["CLOCKSS"],"relation":{},"ISSN":["2521-327X"],"issn-type":[{"value":"2521-327X","type":"electronic"}],"subject":[],"published":{"date-parts":[[2026,4,15]]},"article-number":"2066"}}