- Open Access
Quantum resource theory of lasers
Phys. Rev. Research 8, 013170 – Published 13 February, 2026
DOI: https://doi.org/10.1103/nchs-mvlw
Abstract
Lasers serve as the fundamental workhorses of photonic quantum technologies, with perfectly coherent light fields being essential for many protocols that generate nonclassical light, implement coherent control schemes, and initialize qubits. However, no laser is absolutely ideal and the implications of deviations from perfect coherence in quantum technological tasks remain unclear. In this study, we theoretically and experimentally explore the quantum coherence properties of lasers from a resourcetheory perspective, establishing a significant connection between photonics, quantum optics, and quantum information science. We demonstrate that the maximum achievable quantum coherence for laser light is constrained by spontaneous emission and the purity of the dephased laser field state. As a critical example application in quantum information protocols, we show that the quantum coherence of a laser field with a given mean photon number directly governs the maximum purity attainable when initializing a qubit in a superposition state through resonant driving. Our findings are highly relevant for bridging applied physics and engineering with integrated photonic quantum technologies and resource theories, paving the way for reliable benchmarking of various coherent light sources for applications in photonics and quantum protocols.
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References (80)
- E. Chitambar and G. Gour, Quantum resource theories, Rev. Mod. Phys. 91, 025001 (2019).
- T. H. Maiman, Stimulated optical radiation in ruby, Nature (London) 187, 493 (1960).
- C. T. Santis, S. T. Steger, Y. Vilenchik, A. Vasilyev, and A. Yariv, High-coherence semiconductor lasers based on integral high-Q-resonators in hybrid Si/III-V platforms, Proc. Natl. Acad. Sci. USA 111, 2879 (2014).
- S. Kim, B. Zhang, Z. Wang, J. Fischer, S. Brodbeck, M. Kamp, C. Schneider, S. Höfling, and H. Deng, Coherent polariton laser, Phys. Rev. X 6, 011026 (2016).
- T. Baumgratz, M. Cramer, and M. B. Plenio, Quantifying coherence, Phys. Rev. Lett. 113, 140401 (2014).
- I. Marvian and R. W. Spekkens, How to quantify coherence: Distinguishing speakable and unspeakable notions, Phys. Rev. A 94, 052324 (2016).
- A. Streltsov, H. Kampermann, S. Wölk, M. Gessner, and D. Bruß, Maximal coherence and the resource theory of purity, New J. Phys. 20, 053058 (2018).
- J. Ma, B. Yadin, D. Girolami, V. Vedral, and M. Gu, Converting coherence to quantum correlations, Phys. Rev. Lett. 116, 160407 (2016).
- H. Zhu, Z. Ma, Z. Cao, S.-M. Fei, and V. Vedral, Operational one-to-one mapping between coherence and entanglement measures, Phys. Rev. A 96, 032316 (2017).
- H. J. Kimble, M. Dagenais, and L. Mandel, Photon antibunching in resonance fluorescence, Phys. Rev. Lett. 39, 691 (1977).
- F. Diedrich and H. Walther, Nonclassical radiation of a single stored ion, Phys. Rev. Lett. 58, 203 (1987).
- R. Horodecki, P. Horodecki, M. Horodecki, and K. Horodecki, Quantum entanglement, Rev. Mod. Phys. 81, 865 (2009).
- D. F. Walls, Squeezed states of light, Nature (London) 306, 141 (1983).
- E. Knill, R. Laflamme, and G. J. Milburn, A scheme for efficient quantum computation with linear optics, Nature (London) 409, 46 (2001).
- H. Wang, J. Qin, X. Ding, M.-C. Chen, S. Chen, X. You, Y.-M. He, X. Jiang, L. You, Z. Wang, C. Schneider, J. J. Renema, S. Höfling, C.-Y. Lu, and J.-W. Pan, Boson sampling with 20 input photons and a 60-mode interferometer in a -dimensional Hilbert space, Phys. Rev. Lett. 123, 250503 (2019).
- N. Maring et al., A versatile single-photon-based quantum computing platform, Nat. Photonics 18, 603 (2024).
- A. Acín, N. Gisin, and L. Masanes, From Bell's theorem to secure quantum key distribution, Phys. Rev. Lett. 97, 120405 (2006).
- U. Vazirani and T. Vidick, Fully device-independent quantum key distribution, Phys. Rev. Lett. 113, 140501 (2014).
- V. Zapatero, T. van Leent, R. Arnon-Friedman, W.-Z. Liu, Q. Zhang, H. Weinfurter, and M. Curty, Advances in device-independent quantum key distribution, npj Quantum Inf. 9, 10 (2023).
- S. L. Braunstein and H. J. Kimble, Teleportation of continuous quantum variables, Phys. Rev. Lett. 80, 869 (1998).
- A. Furusawa, J. L. Sørensen, S. L. Braunstein, C. A. Fuchs, H. J. Kimble, and E. S. Polzik, Unconditional quantum teleportation, Science 282, 706 (1998).
- S. Scheel and D.-G. Welsch, Entanglement generation and degradation by passive optical devices, Phys. Rev. A 64, 063811 (2001).
- C. S. Hamilton, R. Kruse, L. Sansoni, S. Barkhofen, C. Silberhorn, and I. Jex, Gaussian boson sampling, Phys. Rev. Lett. 119, 170501 (2017).
- H.-S. Zhong et al., Quantum computational advantage using photons, Science 370, 1460 (2020).
- R. Schnabel, Squeezed states of light and their applications in laser interferometers, Phys. Rep. 684, 1 (2017).
- M. Avesani, D. G. Marangon, G. Vallone, and P. Villoresi, Source-device-independent heterodyne-based quantum random number generator at 17 Gbps, Nat. Commun. 9, 5365 (2018).
- C. Bruynsteen, T. Gehring, C. Lupo, J. Bauwelinck, and X. Yin, 100-Gbit/s integrated quantum random number generator based on vacuum fluctuations, PRX Quantum 4, 010330 (2023).
- B. Qi, True randomness from an incoherent source, Rev. Sci. Instrum. 88, 113101 (2017).
- J. Thewes, C. Lüders, and M. Aßmann, Eavesdropping attack on a trusted continuous-variable quantum random-number generator, Phys. Rev. A 100, 052318 (2019).
- E. Agudelo, J. Sperling, and W. Vogel, Quasiprobabilities for multipartite quantum correlations of light, Phys. Rev. A 87, 033811 (2013).
- F. Shahandeh, A. P. Lund, and T. C. Ralph, Quantum correlations in nonlocal boson sampling, Phys. Rev. Lett. 119, 120502 (2017).
- A. Ferraro and M. G. A. Paris, Nonclassicality criteria from phase-space representations and information-theoretical constraints are maximally inequivalent, Phys. Rev. Lett. 108, 260403 (2012).
- A. P. Lund, Estimating Fock-state linear optics evolution using coherent states, AVS Quantum Sci. 5, 011405 (2023).
- J. I. Cirac and P. Zoller, Quantum computations with cold trapped ions, Phys. Rev. Lett. 74, 4091 (1995).
- Q. A. Turchette, C. S. Wood, B. E. King, C. J. Myatt, D. Leibfried, W. M. Itano, C. Monroe, and D. J. Wineland, Deterministic entanglement of two trapped ions, Phys. Rev. Lett. 81, 3631 (1998).
- S. Ahn, A. S. Moskalenko, V. Y. Chernyak, and S. Mukamel, Qubit entanglement generated by classical light driving an optical cavity, Phys. Rev. Res. 5, 043195 (2023).
- D. Press, T. D. Ladd, B. Zhang, and Y. Yamamoto, Complete quantum control of a single quantum dot spin using ultrafast optical pulses, Nature (London) 456, 218 (2008).
- D. Tiarks, S. Schmidt, G. Rempe, and S. Dürr, Optical π phase shift created with a single-photon pulse, Sci. Adv. 2, e1600036 (2016).
- J. M. Matera, D. Egloff, N. Killoran, and M. B. Plenio, Coherent control of quantum systems as a resource theory, Quantum Sci. Technol. 1, 01LT01 (2016).
- G. S. Uhrig, Keeping a quantum bit alive by optimized -pulse sequences, Phys. Rev. Lett. 98, 100504 (2007).
- C. P. Koch, U. Boscain, T. Calarco, G. Dirr, S. Filipp, S. J. Glaser, R. Kosloff, S. Montangero, T. Schulte-Herbrüggen, D. Sugny, and F. K. Wilhelm, Quantum optimal control in quantum technologies. Strategic report on current status, visions and goals for research in Europe, EPJ Quantum Technol. 9, 19 (2022).
- A. Streltsov, G. Adesso, and M. B. Plenio, Colloquium: Quantum coherence as a resource, Rev. Mod. Phys. 89, 041003 (2017).
- G. Chiribella and Y. Yang, Optimal quantum operations at zero energy cost, Phys. Rev. A 96, 022327 (2017).
- F. Bischof, H. Kampermann, and D. Bruß, Resource theory of coherence based on positive-operator-valued measures, Phys. Rev. Lett. 123, 110402 (2019).
- G. Gianfelici, H. Kampermann, and D. Bruß, Hierarchy of continuous-variable quantum resource theories, New J. Phys. 23, 113008 (2021).
- B. Regula, L. Lami, G. Ferrari, and R. Takagi, Operational quantification of continuous-variable quantum resources, Phys. Rev. Lett. 126, 110403 (2021).
- I. M. de Buy Wenniger, S. C. Wein, D. Fioretto, S. E. Thomas, C. Antón-Solanas, A. Lemaître, I. Sagnes, A. Harouri, N. Belabas, N. Somaschi, P. Hilaire, J. Senellart, and P. Senellart, Quantum interferences and gates with emitter-based coherent photon sources, Optica Quantum 2, 404 (2024).
- J. C. Loredo, C. Antón, B. Reznychenko, P. Hilaire, A. Harouri, C. Millet, H. Ollivier, N. Somaschi, L. De Santis, A. Lemaître, I. Sagnes, L. Lanco, A. Auffèves, O. Krebs, and P. Senellart, Generation of non-classical light in a photon-number superposition, Nat. Photonics 13, 803 (2019).
- S. Rana, P. Parashar, and M. Lewenstein, Trace-distance measure of coherence, Phys. Rev. A 93, 012110 (2016).
- J. I. de Vicente and A. Streltsov, Genuine quantum coherence, J. Phys. A: Math. Theor. 50, 045301 (2017).
- C. Lüders, M. Pukrop, E. Rozas, C. Schneider, S. Höfling, J. Sperling, S. Schumacher, and M. Aßmann, Quantifying quantum coherence in polariton condensates, PRX Quantum 2, 030320 (2021).
- I. V. Doronin, E. S. Andrianov, A. A. Zyablovsky, A. A. Pukhov, Y. E. Lozovik, A. P. Vinogradov, and A. A. Lisyansky, Second-order coherence properties of amplified spontaneous emission, Opt. Express 27, 10991 (2019).
- A. I. Lvovsky, Iterative maximum-likelihood reconstruction in quantum homodyne tomography, J. Opt. B: Quantum Semiclassical Opt. 6, S556 (2004).
- U. Leonhardt and H. Paul, Measuring the quantum state of light, Prog. Quantum Electron. 19, 89 (1995).
- K. Mølmer, Optical coherence: A convenient fiction, Phys. Rev. A 55, 3195 (1997).
- J. Gea-Banacloche, Comment on “optical coherence: A convenient fiction”, Phys. Rev. A 58, 4244 (1998).
- H. M. Wiseman, Defending continuous variable teleportation: Why a laser is a clock, not a quantum channel, J. Opt. B: Quantum Semiclassical Opt. 6, S849 (2004).
- S. D. Bartlett, T. Rudolph, and R. W. Spekkens, Dialogue concerning two views on quantum coherence: Factist and fictionist, Int. J. Quantum Inf. 04, 17 (2006).
- K. Nemoto and S. L. Braunstein, Quantum coherence in the presence of unobservable quantities, Phys. Rev. A 68, 042326 (2003).
- J. Thewes, C. Lüders, and M. Aßmann, Conditional spectroscopy via nonstationary optical homodyne quantum state tomography, Phys. Rev. A 101, 023824 (2020).
- C. Lüders, M. Pukrop, F. Barkhausen, E. Rozas, C. Schneider, S. Höfling, J. Sperling, S. Schumacher, and M. Aßmann, Tracking quantum coherence in polariton condensates with time-resolved tomography, Phys. Rev. Lett. 130, 113601 (2023).
- J. H. Eberly, N. B. Narozhny, and J. J. Sanchez-Mondragon, Periodic spontaneous collapse and revival in a simple quantum model, Phys. Rev. Lett. 44, 1323 (1980).
- J. Gea-Banacloche, Collapse and revival of the state vector in the Jaynes-Cummings model: An example of state preparation by a quantum apparatus, Phys. Rev. Lett. 65, 3385 (1990).
- S. J. D. Phoenix and P. L. Knight, Establishment of an entangled atom-field state in the Jaynes-Cummings model, Phys. Rev. A 44, 6023 (1991).
- C. Gardiner and P. Zoller, A Handbook of Markovian and non-Markovian Quantum Stochastic Methods with Applications to Quantum Optics, 3rd ed. (Springer, Berlin, Heidelberg, 2004), p. 171.
- L. Ares and A. Luis, Beam splitter as quantum coherence-maker, Phys. Scr. 98, 015101 (2023).
- G. Díez, L. Ares, and A. Luis, Coherence via reiterated beam splitting, Phys. Rev. A 109, 063706 (2024).
- N. V. Vitanov, A. A. Rangelov, B. W. Shore, and K. Bergmann, Stimulated Raman adiabatic passage in physics, chemistry, and beyond, Rev. Mod. Phys. 89, 015006 (2017).
- D. Jaksch, J. I. Cirac, P. Zoller, S. L. Rolston, R. Côté, and M. D. Lukin, Fast quantum gates for neutral atoms, Phys. Rev. Lett. 85, 2208 (2000).
- I. Schwartz, D. Cogan, E. R. Schmidgall, Y. Don, L. Gantz, O. Kenneth, N. H. Lindner, and D. Gershoni, Deterministic generation of a cluster state of entangled photons, Science 354, 434 (2016).
- T. K. Bracht, M. Cosacchi, T. Seidelmann, M. Cygorek, A. Vagov, V. M. Axt, T. Heindel, and D. E. Reiter, Swing-up of quantum emitter population using detuned pulses, PRX Quantum 2, 040354 (2021).
- J. Gea-Banacloche, Some implications of the quantum nature of laser fields for quantum computations, Phys. Rev. A 65, 022308 (2002).
- K. Igeta, N. Imoto, and M. Koashi, Fundamental limit to qubit control with coherent field, Phys. Rev. A 87, 022321 (2013).
- T. Biswas, M. García Díaz, and A. Winter, Interferometric visibility and coherence, Proc. R. Soc. A 473, 20170170 (2017).
- M. Masini, T. Theurer, and M. B. Plenio, Coherence of operations and interferometry, Phys. Rev. A 103, 042426 (2021).
- J. Klaers, J. Schmitt, F. Vewinger, and M. Weitz, Bose–Einstein condensation of photons in an optical microcavity, Nature (London) 468, 545 (2010).
- J. Kasprzak, M. Richard, S. Kundermann, A. Baas, P. Jeambrun, J. M. J. Keeling, F. M. Marchetti, M. H. Szymańska, R. André, J. L. Staehli, V. Savona, P. B. Littlewood, B. Deveaud, and L. S. Dang, Bose–Einstein condensation of exciton polaritons, Nature (London) 443, 409 (2006).
- C. Pellegrini, A. Marinelli, and S. Reiche, The physics of x-ray free-electron lasers, Rev. Mod. Phys. 88, 015006 (2016).
- A. Karnieli, N. Rivera, A. Arie, and I. Kaminer, The coherence of light is fundamentally tied to the quantum coherence of the emitting particle, Sci. Adv. 7, eabf8096 (2021).
- Y. Brune, M. Cizauskas, and M. Aßmann, Replication data for: Quantum resource theory of lasers (TUDOdata), 2025, https://doi.org/10.17877/TUDODATA-2025-MF2721GU.