{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,10]],"date-time":"2026-06-10T01:57:16Z","timestamp":1781056636093,"version":"3.54.1"},"reference-count":81,"publisher":"Verein zur Forderung des Open Access Publizierens in den Quantenwissenschaften","license":[{"start":{"date-parts":[[2022,12,7]],"date-time":"2022-12-07T00:00:00Z","timestamp":1670371200000},"content-version":"unspecified","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100001711","name":"Swiss National Science Foundation","doi-asserted-by":"crossref","award":["PZ00P2-186067"],"award-info":[{"award-number":["PZ00P2-186067"]}],"id":[{"id":"10.13039\/501100001711","id-type":"DOI","asserted-by":"crossref"}]},{"DOI":"10.13039\/501100001711","name":"Swiss National Science Foundation","doi-asserted-by":"crossref","award":["NCCR SwissMap"],"award-info":[{"award-number":["NCCR SwissMap"]}],"id":[{"id":"10.13039\/501100001711","id-type":"DOI","asserted-by":"crossref"}]}],"content-domain":{"domain":["quantum-journal.org"],"crossmark-restriction":false},"short-container-title":["Quantum"],"abstract":"<jats:p>What is the minimum time required to take a temperature? In this paper, we solve this question for a large class of processes where temperature is inferred by measuring a probe (the thermometer) weakly coupled to the sample of interest, so that the probe's evolution is well described by a quantum Markovian master equation. Considering the most general control strategy on the probe (adaptive measurements, arbitrary control on the probe's state and Hamiltonian), we provide bounds on the achievable measurement precision in a finite amount of time, and show that in many scenarios these fundamental limits can be saturated with a relatively simple experiment. We find that for a general class of sample-probe interactions the scaling of the measurement uncertainty is inversely proportional to the time of the process, a shot-noise like behaviour that arises due to the dissipative nature of thermometry. As a side result, we show that the Lamb shift induced by the probe-sample interaction can play a relevant role in thermometry, allowing for finite measurement resolution in the low-temperature regime. More precisely, the measurement uncertainty decays polynomially with the temperature as <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mml:mi>T<\/mml:mi><mml:mo stretchy=\"false\">&amp;#x2192;<\/mml:mo><mml:mn>0<\/mml:mn><\/mml:math>, in contrast to the usual exponential decay with <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mml:msup><mml:mi>T<\/mml:mi><mml:mrow class=\"MJX-TeXAtom-ORD\"><mml:mo>&amp;#x2212;<\/mml:mo><mml:mn>1<\/mml:mn><\/mml:mrow><\/mml:msup><\/mml:math>. We illustrate these general results for (i) a qubit probe interacting with a bosonic sample, where the role of the Lamb shift is highlighted, and (ii) a collective superradiant coupling between a <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mml:mi>N<\/mml:mi><\/mml:math>-qubit probe and a sample, which enables a quadratic decay with <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mml:mi>N<\/mml:mi><\/mml:math> of the measurement uncertainty.<\/jats:p>","DOI":"10.22331\/q-2022-12-07-869","type":"journal-article","created":{"date-parts":[[2022,12,7]],"date-time":"2022-12-07T13:22:52Z","timestamp":1670419372000},"page":"869","update-policy":"https:\/\/doi.org\/10.22331\/q-crossmark-policy-page","source":"Crossref","is-referenced-by-count":25,"title":["Optimal nonequilibrium thermometry in Markovian environments"],"prefix":"10.22331","volume":"6","author":[{"given":"Pavel","family":"Sekatski","sequence":"first","affiliation":[{"name":"Department of Applied Physics, University of Geneva, 1211 Geneva, Switzerland"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Mart\u00ed","family":"Perarnau-Llobet","sequence":"additional","affiliation":[{"name":"Department of Applied Physics, University of Geneva, 1211 Geneva, Switzerland"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"9598","published-online":{"date-parts":[[2022,12,7]]},"reference":[{"key":"0","doi-asserted-by":"publisher","unstructured":"F. Giazotto, T. T. Heikkil\u00e4, A. Luukanen, A. M. Savin, and J. P. Pekola, Rev. Mod. Phys. 78, 217 (2006).","DOI":"10.1103\/RevModPhys.78.217"},{"key":"1","doi-asserted-by":"publisher","unstructured":"Y. Yue and X. Wang, Nano Rev. 3, 11586 (2012).","DOI":"10.3402\/nano.v3i0.11586"},{"key":"2","doi-asserted-by":"publisher","unstructured":"M. Mehboudi, A. Sanpera, and L. A. Correa, J. Phys. A 52, 303001 (2019).","DOI":"10.1088\/1751-8121\/ab2828"},{"key":"3","doi-asserted-by":"publisher","unstructured":"L. D. Carlos and F. Palacio, eds., Thermometry at the Nanoscale, Nanoscience & Nanotechnology Series (The Royal Society of Chemistry, 2016) pp. P007\u2013522.","DOI":"10.1039\/9781782622031"},{"key":"4","doi-asserted-by":"publisher","unstructured":"A. D. Pasquale and T. M. Stace, in Fundamental Theories of Physics (Springer International Publishing, 2018) pp. 503\u2013527.","DOI":"10.1007\/978-3-319-99046-0_21"},{"key":"5","doi-asserted-by":"publisher","unstructured":"S. L. Braunstein and C. M. Caves, Phys. Rev. Lett. 72, 3439 (1994).","DOI":"10.1103\/PhysRevLett.72.3439"},{"key":"6","doi-asserted-by":"publisher","unstructured":"M. G. A. Paris, J. Phys. A 49, 03LT02 (2015).","DOI":"10.1088\/1751-8113\/49\/3\/03lt02"},{"key":"7","doi-asserted-by":"publisher","unstructured":"L. A. Correa, M. Mehboudi, G. Adesso, and A. Sanpera, Phys. Rev. Lett. 114, 220405 (2015).","DOI":"10.1103\/PhysRevLett.114.220405"},{"key":"8","doi-asserted-by":"publisher","unstructured":"L.-S. Guo, B.-M. Xu, J. Zou, and B. Shao, Phys. Rev. A 92, 052112 (2015).","DOI":"10.1103\/PhysRevA.92.052112"},{"key":"9","doi-asserted-by":"publisher","unstructured":"S. Campbell, M. Mehboudi, G. D. Chiara, and M. Paternostro, New Journal of Physics 19, 103003 (2017).","DOI":"10.1088\/1367-2630\/aa7fac"},{"key":"10","doi-asserted-by":"publisher","unstructured":"S. Campbell, M. G. Genoni, and S. Deffner, Quantum Science and Technology 3, 025002 (2018).","DOI":"10.1088\/2058-9565\/aaa641"},{"key":"11","doi-asserted-by":"publisher","unstructured":"M. P\u0142odzie\u0144, R. Demkowicz-Dobrza\u0144ski, and T. Sowi\u0144ski, Phys. Rev. A 97, 063619 (2018).","DOI":"10.1103\/PhysRevA.97.063619"},{"key":"12","doi-asserted-by":"publisher","unstructured":"G. Ruppeiner, Phys. Rev. A 20, 1608 (1979).","DOI":"10.1103\/PhysRevA.20.1608"},{"key":"13","doi-asserted-by":"publisher","unstructured":"T. Jahnke, S. Lan\u00e9ry, and G. Mahler, Phys. Rev. E 83, 011109 (2011).","DOI":"10.1103\/PhysRevE.83.011109"},{"key":"14","doi-asserted-by":"publisher","unstructured":"M. Salado-Mej\u00eda, R. Rom\u00e1n-Ancheyta, F. Soto-Eguibar, and H. M. Moya-Cessa, Quantum Science and Technology 6, 025010 (2021).","DOI":"10.1088\/2058-9565\/abdca5"},{"key":"15","doi-asserted-by":"publisher","unstructured":"D. Reeb and M. M. Wolf, New Journal of Physics 16, 103011 (2014).","DOI":"10.1088\/1367-2630\/16\/10\/103011"},{"key":"16","doi-asserted-by":"publisher","unstructured":"M. Brunelli, S. Olivares, and M. G. A. Paris, Phys. Rev. A 84, 032105 (2011).","DOI":"10.1103\/PhysRevA.84.032105"},{"key":"17","doi-asserted-by":"publisher","unstructured":"M. Brunelli, S. Olivares, M. Paternostro, and M. G. A. Paris, Phys. Rev. A 86, 012125 (2012).","DOI":"10.1103\/PhysRevA.86.012125"},{"key":"18","doi-asserted-by":"publisher","unstructured":"S. Jevtic, D. Newman, T. Rudolph, and T. M. Stace, Phys. Rev. A 91, 012331 (2015).","DOI":"10.1103\/PhysRevA.91.012331"},{"key":"19","doi-asserted-by":"publisher","unstructured":"W. K. Tham, H. Ferretti, A. V. Sadashivan, and A. M. Steinberg, Scientific Reports 6 (2016), 10.1038\/srep38822.","DOI":"10.1038\/srep38822"},{"key":"20","doi-asserted-by":"publisher","unstructured":"A. De Pasquale, K. Yuasa, and V. Giovannetti, Phys. Rev. A 96, 012316 (2017).","DOI":"10.1103\/PhysRevA.96.012316"},{"key":"21","doi-asserted-by":"publisher","unstructured":"P. P. Hofer, J. B. Brask, M. Perarnau-Llobet, and N. Brunner, Phys. Rev. Lett. 119, 090603 (2017a).","DOI":"10.1103\/PhysRevLett.119.090603"},{"key":"22","doi-asserted-by":"publisher","unstructured":"V. Cavina, L. Mancino, A. De Pasquale, I. Gianani, M. Sbroscia, R. I. Booth, E. Roccia, R. Raimondi, V. Giovannetti, and M. Barbieri, Phys. Rev. A 98, 050101 (2018).","DOI":"10.1103\/PhysRevA.98.050101"},{"key":"23","doi-asserted-by":"publisher","unstructured":"R. Rom\u00e1n-Ancheyta, B. \u00c7akmak, and \u00d6zg\u00fcr E M\u00fcstecapl\u0131o\u011flu, Quantum Science and Technology 5, 015003 (2019).","DOI":"10.1088\/2058-9565\/ab5e4f"},{"key":"24","doi-asserted-by":"publisher","unstructured":"M. T. Mitchison, T. Fogarty, G. Guarnieri, S. Campbell, T. Busch, and J. Goold, Phys. Rev. Lett. 125, 080402 (2020).","DOI":"10.1103\/PhysRevLett.125.080402"},{"key":"25","doi-asserted-by":"publisher","unstructured":"L. Mancino, M. G. Genoni, M. Barbieri, and M. Paternostro, Phys. Rev. Research 2, 033498 (2020).","DOI":"10.1103\/PhysRevResearch.2.033498"},{"key":"26","doi-asserted-by":"publisher","unstructured":"M. R. J\u00f8rgensen, P. P. Potts, M. G. A. Paris, and J. B. Brask, Physical Review Research 2 (2020), 10.1103\/physrevresearch.2.033394.","DOI":"10.1103\/physrevresearch.2.033394"},{"key":"27","doi-asserted-by":"publisher","unstructured":"S. Seah, S. Nimmrichter, D. Grimmer, J. P. Santos, V. Scarani, and G. T. Landi, Phys. Rev. Lett. 123, 180602 (2019).","DOI":"10.1103\/PhysRevLett.123.180602"},{"key":"28","doi-asserted-by":"publisher","unstructured":"A. Shu, S. Seah, and V. Scarani, Phys. Rev. A 102, 042417 (2020).","DOI":"10.1103\/PhysRevA.102.042417"},{"key":"29","doi-asserted-by":"publisher","unstructured":"I. Henao and R. Uzdin, Quantum 5, 547 (2021).","DOI":"10.22331\/q-2021-09-21-547"},{"key":"30","doi-asserted-by":"publisher","unstructured":"Q. Bouton, J. Nettersheim, D. Adam, F. Schmidt, D. Mayer, T. Lausch, E. Tiemann, and A. Widera, Phys. Rev. X 10, 011018 (2020).","DOI":"10.1103\/PhysRevX.10.011018"},{"key":"31","doi-asserted-by":"publisher","unstructured":"K. V. Hovhannisyan, M. R. J\u00f8rgensen, G. T. Landi, A. M. Alhambra, J. B. Brask, and M. Perarnau-Llobet, PRX Quantum 2, 020322 (2021).","DOI":"10.1103\/PRXQuantum.2.020322"},{"key":"32","doi-asserted-by":"publisher","unstructured":"M. T. Mitchison, A. Purkayastha, M. Brenes, A. Silva, and J. Goold, Phys. Rev. A 105, L030201 (2022).","DOI":"10.1103\/PhysRevA.105.L030201"},{"key":"33","doi-asserted-by":"crossref","unstructured":"K. Huang, Introduction to statistical physics (CRC press, 2009).","DOI":"10.1201\/9781439878132"},{"key":"34","doi-asserted-by":"publisher","unstructured":"J. J. . Bollinger, W. M. Itano, D. J. Wineland, and D. J. Heinzen, Phys. Rev. A 54, R4649 (1996).","DOI":"10.1103\/PhysRevA.54.R4649"},{"key":"35","doi-asserted-by":"publisher","unstructured":"S. F. Huelga, C. Macchiavello, T. Pellizzari, A. K. Ekert, M. B. Plenio, and J. I. Cirac, Phys. Rev. Lett. 79, 3865 (1997).","DOI":"10.1103\/PhysRevLett.79.3865"},{"key":"36","doi-asserted-by":"publisher","unstructured":"P. Sekatski, M. Skotiniotis, J. Ko\u0142ody\u0144ski, and W. D\u00fcr, Quantum 1, 27 (2017).","DOI":"10.22331\/q-2017-09-06-27"},{"key":"37","doi-asserted-by":"publisher","unstructured":"R. Demkowicz-Dobrza\u0144ski, J. Czajkowski, and P. Sekatski, Phys. Rev. X 7, 041009 (2017).","DOI":"10.1103\/PhysRevX.7.041009"},{"key":"38","doi-asserted-by":"publisher","unstructured":"S. Zhou, M. Zhang, J. Preskill, and L. Jiang, Nature communications 9, 1 (2018).","DOI":"10.1038\/s41467-017-02510-3"},{"key":"39","unstructured":"J. Nettersheim, Q. Bouton, D. Adam, and A. Widera, arXiv preprint arXiv:2203.13656 (2022)."},{"key":"40","doi-asserted-by":"publisher","unstructured":"L. A. Correa, M. Perarnau-Llobet, K. V. Hovhannisyan, S. Hern\u00e1ndez-Santana, M. Mehboudi, and A. Sanpera, Phys. Rev. A 96, 062103 (2017).","DOI":"10.1103\/PhysRevA.96.062103"},{"key":"41","doi-asserted-by":"publisher","unstructured":"K. V. Hovhannisyan and L. A. Correa, Phys. Rev. B 98, 045101 (2018).","DOI":"10.1103\/PhysRevB.98.045101"},{"key":"42","doi-asserted-by":"publisher","unstructured":"P. P. Potts, J. B. Brask, and N. Brunner, Quantum 3, 161 (2019).","DOI":"10.22331\/q-2019-07-09-161"},{"key":"43","doi-asserted-by":"publisher","unstructured":"R. H. Dicke, Phys. Rev. 93, 99 (1954).","DOI":"10.1103\/physrev.93.99"},{"key":"44","doi-asserted-by":"publisher","unstructured":"C. L. Latune, I. Sinayskiy, and F. Petruccione, New Journal of Physics 22, 083049 (2020).","DOI":"10.1088\/1367-2630\/aba463"},{"key":"45","doi-asserted-by":"crossref","unstructured":"R. D. Gill and B. Y. Levit, Bernoulli , 59 (1995).","DOI":"10.1007\/978-1-349-13596-7_4"},{"key":"46","doi-asserted-by":"publisher","unstructured":"B. B. Mandelbrot, IRE Trans. Inf. Theory 2, 190 (1956).","DOI":"10.1109\/TIT.1956.1056804"},{"key":"47","doi-asserted-by":"publisher","unstructured":"J. Uffink and J. van Lith, Found. Phys. 29, 655 (1999).","DOI":"10.1023\/A:1018811305766"},{"key":"48","doi-asserted-by":"publisher","unstructured":"A. Fujiwara and H. Imai, Journal of Physics A: Mathematical and Theoretical 41, 255304 (2008).","DOI":"10.1088\/1751-8113\/41\/25\/255304"},{"key":"49","doi-asserted-by":"publisher","unstructured":"V. Giovannetti, S. Lloyd, and L. Maccone, Physical review letters 96, 010401 (2006). href http:\/\/dx.doi.org\/10.1103\/PhysRevLett.96.010401.","DOI":"10.1103\/PhysRevLett.96.010401"},{"key":"50","unstructured":"H.-P. Breuer, F. Petruccione, et al., The theory of open quantum systems (Oxford University Press on Demand, 2002)."},{"key":"51","doi-asserted-by":"publisher","unstructured":"P. P. Hofer, M. Perarnau-Llobet, L. D. M. Miranda, G. Haack, R. Silva, J. B. Brask, and N. Brunner, New Journal of Physics 19, 123037 (2017b).","DOI":"10.1088\/1367-2630\/aa964f"},{"key":"52","doi-asserted-by":"publisher","unstructured":"J. O. Gonz\u00e1lez, L. A. Correa, G. Nocerino, J. P. Palao, D. Alonso, and G. Adesso, Open Systems & Information Dynamics 24, 1740010 (2017).","DOI":"10.1142\/s1230161217400108"},{"key":"53","doi-asserted-by":"publisher","unstructured":"S. Scali, J. Anders, and L. A. Correa, Quantum 5, 451 (2021).","DOI":"10.22331\/q-2021-05-01-451"},{"key":"54","doi-asserted-by":"publisher","unstructured":"T. V. Tscherbul and P. Brumer, The Journal of Chemical Physics 142, 104107 (2015).","DOI":"10.1063\/1.4908130"},{"key":"55","doi-asserted-by":"publisher","unstructured":"D. Farina and V. Giovannetti, Phys. Rev. A 100, 012107 (2019).","DOI":"10.1103\/PhysRevA.100.012107"},{"key":"56","doi-asserted-by":"publisher","unstructured":"M. Cattaneo, G. L. Giorgi, S. Maniscalco, and R. Zambrini, New Journal of Physics 21, 113045 (2019).","DOI":"10.1088\/1367-2630\/ab54ac"},{"key":"57","doi-asserted-by":"publisher","unstructured":"M. Cattaneo, G. L. Giorgi, S. Maniscalco, and R. Zambrini, Physical Review A 101 (2020), 10.1103\/physreva.101.042108.","DOI":"10.1103\/physreva.101.042108"},{"key":"58","doi-asserted-by":"publisher","unstructured":"G. McCauley, B. Cruikshank, D. I. Bondar, and K. Jacobs, npj Quantum Information 6 (2020), 10.1038\/s41534-020-00299-6.","DOI":"10.1038\/s41534-020-00299-6"},{"key":"59","unstructured":"A. Trushechkin, arXiv e-prints , arXiv (2021)."},{"key":"60","doi-asserted-by":"publisher","unstructured":"A. Nazir and G. Schaller, in Fundamental Theories of Physics (Springer International Publishing, 2018) pp. 551\u2013577.","DOI":"10.1007\/978-3-319-99046-0_23"},{"key":"61","doi-asserted-by":"publisher","unstructured":"K. D. B. Higgins, B. W. Lovett, and E. M. Gauger, Phys. Rev. B 88, 155409 (2013).","DOI":"10.1103\/PhysRevB.88.155409"},{"key":"62","doi-asserted-by":"publisher","unstructured":"T. Albash, S. Boixo, D. A. Lidar, and P. Zanardi, New Journal of Physics 14, 123016 (2012).","DOI":"10.1088\/1367-2630\/14\/12\/123016"},{"key":"63","doi-asserted-by":"publisher","unstructured":"R. Dann, A. Levy, and R. Kosloff, Phys. Rev. A 98, 052129 (2018).","DOI":"10.1103\/PhysRevA.98.052129"},{"key":"64","doi-asserted-by":"publisher","unstructured":"R. Demkowicz-Dobrza\u0144ski, M. Jarzyna, and J. Ko\u0142ody\u0144ski, in Progress in Optics (Elsevier, 2015) pp. 345\u2013435.","DOI":"10.1016\/bs.po.2015.02.003"},{"key":"65","doi-asserted-by":"publisher","unstructured":"J. P. Pekola, P. Solinas, A. Shnirman, and D. V. Averin, New Journal of Physics 15, 115006 (2013).","DOI":"10.1088\/1367-2630\/15\/11\/115006"},{"key":"66","doi-asserted-by":"publisher","unstructured":"P. Menczel, C. Flindt, and K. Brandner, Phys. Rev. Research 2, 033449 (2020).","DOI":"10.1103\/PhysRevResearch.2.033449"},{"key":"67","doi-asserted-by":"publisher","unstructured":"S. Gasparinetti, K. L. Viisanen, O.-P. Saira, T. Faivre, M. Arzeo, M. Meschke, and J. P. Pekola, Phys. Rev. Applied 3, 014007 (2015).","DOI":"10.1103\/PhysRevApplied.3.014007"},{"key":"68","doi-asserted-by":"publisher","unstructured":"J. Govenius, R. E. Lake, K. Y. Tan, and M. M\u00f6tt\u00f6nen, Phys. Rev. Lett. 117, 030802 (2016).","DOI":"10.1103\/PhysRevLett.117.030802"},{"key":"69","doi-asserted-by":"publisher","unstructured":"B. Karimi, F. Brange, P. Samuelsson, and J. P. Pekola, Nature Communications 11 (2020), 10.1038\/s41467-019-14247-2.","DOI":"10.1038\/s41467-019-14247-2"},{"key":"70","doi-asserted-by":"publisher","unstructured":"L. Pezz\u00e8, A. Smerzi, M. K. Oberthaler, R. Schmied, and P. Treutlein, Rev. Mod. Phys. 90, 035005 (2018).","DOI":"10.1103\/RevModPhys.90.035005"},{"key":"71","doi-asserted-by":"publisher","unstructured":"A. Recati, P. O. Fedichev, W. Zwerger, J. von Delft, and P. Zoller, Phys. Rev. Lett. 94, 040404 (2005).","DOI":"10.1103\/PhysRevLett.94.040404"},{"key":"72","doi-asserted-by":"publisher","unstructured":"C. Sabin, A. White, L. Hackermuller, and I. Fuentes, Sci. Rep. 4, 6436 (2014).","DOI":"10.1038\/srep06436"},{"key":"73","doi-asserted-by":"publisher","unstructured":"E. B. Norrgard, S. P. Eckel, C. L. Holloway, and E. L. Shirley, New Journal of Physics 23, 033037 (2021).","DOI":"10.1088\/1367-2630\/abe8f5"},{"key":"74","doi-asserted-by":"publisher","unstructured":"S. Gr\u00f6blacher, A. Trubarov, N. Prigge, G. D. Cole, M. Aspelmeyer, and J. Eisert, Nature Communications 6 (2015), 10.1038\/ncomms8606.","DOI":"10.1038\/ncomms8606"},{"key":"75","doi-asserted-by":"publisher","unstructured":"A. Lampo, S. H. Lim, M. \u00c1. Garc\u00eda-March, and M. Lewenstein, Quantum 1, 30 (2017).","DOI":"10.22331\/q-2017-09-27-30"},{"key":"76","doi-asserted-by":"publisher","unstructured":"A. Frisk Kockum, A. Miranowicz, S. De Liberato, S. Savasta, and F. Nori, Nature Reviews Physics 1, 19 (2019), arXiv:1807.11636.","DOI":"10.1038\/s42254-018-0006-2"},{"key":"77","doi-asserted-by":"publisher","unstructured":"A. Gonz\u00e1lez-Tudela, V. Paulisch, H. J. Kimble, and J. I. Cirac, Phys. Rev. Lett. 118, 213601 (2017).","DOI":"10.1103\/PhysRevLett.118.213601"},{"key":"78","doi-asserted-by":"publisher","unstructured":"G. Kucsko, P. C. Maurer, N. Y. Yao, M. Kubo, H. J. Noh, P. K. Lo, H. Park, and M. D. Lukin, Nature 500, 54 (2013).","DOI":"10.1038\/nature12373"},{"key":"79","doi-asserted-by":"publisher","unstructured":"S. Deffner and S. Campbell, Journal of Physics A: Mathematical and Theoretical 50, 453001 (2017).","DOI":"10.1088\/1751-8121\/aa86c6"},{"key":"80","doi-asserted-by":"publisher","unstructured":"N. Il&apos;in and O. Lychkovskiy, Phys. Rev. A 103, 062204 (2021).","DOI":"10.1103\/PhysRevA.103.062204"}],"container-title":["Quantum"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/quantum-journal.org\/papers\/q-2022-12-07-869\/pdf\/","content-type":"unspecified","content-version":"vor","intended-application":"text-mining"}],"deposited":{"date-parts":[[2022,12,7]],"date-time":"2022-12-07T13:22:59Z","timestamp":1670419379000},"score":1,"resource":{"primary":{"URL":"https:\/\/quantum-journal.org\/papers\/q-2022-12-07-869\/"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2022,12,7]]},"references-count":81,"URL":"https:\/\/doi.org\/10.22331\/q-2022-12-07-869","archive":["CLOCKSS"],"relation":{},"ISSN":["2521-327X"],"issn-type":[{"value":"2521-327X","type":"electronic"}],"subject":[],"published":{"date-parts":[[2022,12,7]]},"article-number":"869"}}