References
Akkermans, E. & Montambaux, G. Mesoscopic Physics of Electrons and Photons (Cambridge Univ. Press, 2007).
Cao, H., Mosk, A. & Rotter, S. Shaping the propagation of light in complex media. Nat. Phys. https://doi.org/10.1038/s41567-022-01677-x (2022).
Gerry, C., Knight, P. & Knight, P. L. Introductory Quantum Optics (Cambridge Univ. Press, 2005).
Patra, M. & Beenakker, C. W. J. Propagation of squeezed radiation through amplifying or absorbing random media. Phys. Rev. A 61, 063805 (2000).
Starshynov, I., Bertolotti, J. & Anders, J. Quantum correlation of light scattered by disordered media. Opt. Express 24, 4662–4671 (2016).
Lodahl, P., Mosk, A. & Lagendijk, A. Spatial quantum correlations in multiple scattered light. Phys. Rev. Lett. 95, 173901 (2005).
Skipetrov, S. E. Quantum theory of dynamic multiple light scattering in fluctuating disordered media. Phys. Rev. A 75, (2007).
Lodahl, P. & Lagendijk, A. Transport of quantum noise through random media. Phys. Rev. Lett. 94, 153905 (2005).
Smolka, S., Huck, A., Andersen, U. L., Lagendijk, A. & Lodahl, P. Observation of spatial quantum correlations induced by multiple scattering of nonclassical light. Phys. Rev. Lett. 102, 193901 (2009).
Smolka, S., Ott, J. R., Huck, A., Andersen, U. L. & Lodahl, P. Continuous-wave spatial quantum correlations of light induced by multiple scattering. Phys. Rev. A 86, 033814 (2012).
Aiello, A. & Woerdman, J. P. Intrinsic entanglement degradation by multimode detection. Phys. Rev. A 70, 023808 (2004).
Candé, M., Goetschy, A. & Skipetrov, S. E. Transmission of quantum entanglement through a random medium. Europhys. Lett. 107, 54004 (2014).
Beenakker, C. W. J., Venderbos, J. W. F. & van Exter, M. P. Two-photon speckle as a probe of multi-dimensional entanglement. Phys. Rev. Lett. 102, 193601 (2009).
Peeters, W. H., Moerman, J. J. D. & van Exter, M. P. Observation of two-photon speckle patterns. Phys. Rev. Lett. 104, 173601 (2010).
Pires, H. D. L., Woudenberg, J. & Van Exter, M. Statistical properties of two-photon speckles. Phys. Rev. A 85, 033807 (2012).
Van Exter, M., Woudenberg, J., Pires, H. D. L. & Peeters, W. Bosonic, fermionic, and anyonic symmetry in two-photon random scattering. Phys. Rev. A 85, 033823 (2012).
Safadi, M. et al. Coherent backscattering of entangled photon pairs. Preprint at https://arxiv.org/abs/2203.09650 (2022).
Segev, M., Silberberg, Y. & Christodoulides, D. N. Anderson localization of light. Nat. Photon. 7, 197–204 (2013).
Aharonov, Y., Davidovich, L. & Zagury, N. Quantum random walks. Phys. Rev. A 48, 1687–1690 (1993).
Childs, A. M. Universal computation by quantum walk. Phys. Rev. Lett. 102, 180501 (2009).
Perets, H. B. et al. Realization of quantum walks with negligible decoherence in waveguide lattices. Phys. Rev. Lett. 100, 170506 (2008).
Schreiber, A. et al. A 2D quantum walk simulation of two-particle dynamics. Science 336, 55–58 (2012).
Peruzzo, A. et al. Quantum walks of correlated photons. Science 329, 1500–1503 (2010).
Crespi, A. et al. Anderson localization of entangled photons in an integrated quantum walk. Nat. Photon. 7, 322–328 (2013).
Lahini, Y., Bromberg, Y., Christodoulides, D. N. & Silberberg, Y. Quantum correlations in two-particle Anderson localization. Phys. Rev. Lett. 105, 163905 (2010).
Gilead, Y., Verbin, M. & Silberberg, Y. Ensemble-averaged quantum correlations between path-entangled photons undergoing Anderson localization. Phys. Rev. Lett. 115, 133602 (2015).
Di Giuseppe, G. et al. Einstein-Podolsky-Rosen spatial entanglement in ordered and Anderson photonic lattices. Phys. Rev. Lett. 110, 150503 (2013).
Jiao, Z.-Q. et al. Two-dimensional quantum walks of correlated photons. Optica 8, 1129–1135 (2021).
Bertolotti, J. & Katz, O. Imaging in complex media. Nat. Phys. https://doi.org/10.1038/s41567-022-01723-8 (2022).
Carolan, J. et al. Universal linear optics. Science 349, 711–716 (2015).
Huisman, T. J., Huisman, S. R., Mosk, A. P. & Pinkse, P. W. Controlling single-photon Fock-state propagation through opaque scattering media. Appl. Phys. B 116, 603–607 (2014).
Defienne, H. et al. Nonclassical light manipulation in a multiple-scattering medium. Opt. Lett. 39, 6090–6093 (2014).
Wolterink, T. A. et al. Programmable two-photon quantum interference in 103 channels in opaque scattering media. Phys. Rev. A 93, 053817 (2016).
Defienne, H., Barbieri, M., Walmsley, I. A., Smith, B. J. & Gigan, S. Two-photon quantum walk in a multimode fiber. Sci. Adv. 2, e1501054 (2016).
Carpenter, J. et al. Mode multiplexed single-photon and classical channels in a few-mode fiber. Opt. Express 21, 28794–28800 (2013).
Liu, J. et al. Multidimensional entanglement transport through single-mode fiber. Sci. Adv. 6, eaay0837 (2020).
Defienne, H., Reichert, M. & Fleischer, J. W. Adaptive quantum optics with spatially entangled photon pairs. Phys. Rev. Lett. 121, 233601 (2018).
Liu, C. et al. Single-end adaptive optics compensation for emulated turbulence in a bi-directional 10-mbit/s per channel free-space quantum communication link using orbital-angular-momentum encoding. Research 2019, 8326701 (2019).
Zhao, J. et al. Performance of real-time adaptive optics compensation in a turbulent channel with high-dimensional spatial-mode encoding. Opt. Express 28, 15376–15391 (2020).
Cao, Y. et al. Long-distance free-space measurement-device-independent quantum key distribution. Phys. Rev. Lett. 125, 260503 (2020).
Lib, O., Hasson, G. & Bromberg, Y. Real-time shaping of entangled photons by classical control and feedback. Sci. Adv. 6, eabb6298 (2020).
Ndagano, B. et al. Characterizing quantum channels with non-separable states of classical light. Nat. Phys. 13, 397–402 (2017).
Valencia, N. H., Goel, S., McCutcheon, W., Defienne, H. & Malik, M. Unscrambling entanglement through a complex medium. Nat. Phys. 16, 1112–1116 (2020).
Konrad, T. et al. Evolution equation for quantum entanglement. Nat. Phys. 4, 99–102 (2008).
Liao, S.-K. et al. Satellite-to-ground quantum key distribution. Nature 549, 43–47 (2017).
Bedington, R., Arrazola, J. M. & Ling, A. Progress in satellite quantum key distribution. npj Quantum Inf. 3, 30 (2017).
Paterson, C. Atmospheric turbulence and orbital angular momentum of single photons for optical communication. Phys. Rev. Lett. 94, 153901 (2005).
Hamadou Ibrahim, A., Roux, F. S., McLaren, M., Konrad, T. & Forbes, A. Orbital-angular-momentum entanglement in turbulence. Phys. Rev. A 88, 012312 (2013).
Malik, M. et al. Influence of atmospheric turbulence on optical communications using orbital angular momentum for encoding. Opt. Express 20, 13195–13200 (2012).
Goyal, S. K., Roux, F. S., Konrad, T. & Forbes, A. et al. The effect of turbulence on entanglement-based free-space quantum key distribution with photonic orbital angular momentum. J. Opt. 18, 064002 (2016).
Sit, A. et al. High-dimensional intracity quantum cryptography with structured photons. Optica 4, 1006–1010 (2017).
Goorden, S. A., Horstmann, M., Mosk, A. P., Škorić, B. & Pinkse, P. W. H. Quantum-secure authentication of a physical unclonable key. Optica 1, 421–424 (2014).
Amitonova, L. V. et al. Quantum key establishment via a multimode fiber. Opt. Express 28, 5965–5981 (2020).
Leedumrongwatthanakun, S. et al. Programmable linear quantum networks with a multimode fibre. Nat. Photon. 14, 139–142 (2020).
Goel, S. et al. Inverse-design of high-dimensional quantum optical circuits in a complex medium. Preprint at https://arxiv.org/abs/2204.00578 (2022).
Aaronson, S. & Arkhipov, A. The computational complexity of linear optics. In Proc. Forty-Third Annual ACM Symposium on Theory of Computing 333–342 (Association for Computing Machinery, 2011).
Brod, D. J. et al. Photonic implementation of boson sampling: a review. Adv. Photon. 1, 034001 (2019).
Zhong, H.-S. et al. Quantum computational advantage using photons. Science 370, 1460–1463 (2020).
van der Meer, R., Huber, S., Pinkse, P., García-Patrón, R. & Renema, J. Boson sampling in low-depth optical systems. Preprint at https://arxiv.org/abs/2110.05099 (2021).
Friis, N., Vitagliano, G., Malik, M. & Huber, M. Entanglement certification from theory to experiment. Nat. Rev. Phys. 1, 72–87 (2019).
Lib, O. & Bromberg, Y. Thermal biphotons. APL Photon. 7, 031301 (2022).
Cherroret, N. & Buchleitner, A. Entanglement and thouless times from coincidence measurements across disordered media. Phys. Rev. A 83, 033827 (2011).
Candé, M. & Skipetrov, S. E. Quantum versus classical effects in two-photon speckle patterns. Phys. Rev. A 87, 013846 (2013).
Pe’Er, A., Dayan, B., Friesem, A. A. & Silberberg, Y. Temporal shaping of entangled photons. Phys. Rev. Lett. 94, 073601 (2005).
Aulbach, J., Gjonaj, B., Johnson, P. M., Mosk, A. P. & Lagendijk, A. Control of light transmission through opaque scattering media in space and time. Phys. Rev. Lett. 106, 103901 (2011).
Mounaix, M. et al. Spatiotemporal coherent control of light through a multiple scattering medium with the multispectral transmission matrix. Phys. Rev. Lett. 116, 253901 (2016).
Gigan, S. et al. Roadmap on wavefront shaping and deep imaging in complex media. J. Phys Photonics https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9/meta (2022).
Tenne, R. et al. Super-resolution enhancement by quantum image scanning microscopy. Nat. Photon. 13, 116–122 (2019).
Brida, G., Genovese, M. & Berchera, I. R. Experimental realization of sub-shot-noise quantum imaging. Nat. Photon. 4, 227–230 (2010).
Defienne, H., Reichert, M., Fleischer, J. W. & Faccio, D. Quantum image distillation. Sci. Adv. 5, eaax0307 (2019).
Lemos, G. B. et al. Quantum imaging with undetected photons. Nature 512, 409–412 (2014).
Defienne, H., Ndagano, B., Lyons, A. & Faccio, D. Polarization entanglement-enabled quantum holography. Nat. Phys. 17, 591–597 (2021).
Shi, L., Galvez, E. J. & Alfano, R. R. Photon entanglement through brain tissue. Sci. Rep. 6, 1–6 (2016).
Lum, D. J. et al. Witnessing the survival of time-energy entanglement through biological tissue and scattering media. Biomed. Opt. Express 12, 3658–3670 (2021).
Sapienza, L. et al. Cavity quantum electrodynamics with Anderson-localized modes. Science 327, 1352–1355 (2010).
Kim, D. & Englund, D. R. Quantum reference beacon–guided superresolution optical focusing in complex media. Science 363, 528–531 (2019).
Brandt, F., Hiekkamäki, M., Bouchard, F., Huber, M. & Fickler, R. High-dimensional quantum gates using full-field spatial modes of photons. Optica 7, 98–107 (2020).
Hiekkamäki, M. & Fickler, R. High-dimensional two-photon interference effects in spatial modes. Phys. Rev. Lett. 126, 123601 (2021).
Lib, O., Sulimany, K. & Bromberg, Y. Reconfigurable synthesizer for quantum information processing of high-dimensional entangled photons. Preprint at https://arxiv.org/abs/2108.02258 (2021).
Defienne, H., Reichert, M. & Fleischer, J. W. General model of photon-pair detection with an image sensor. Phys. Rev. Lett. 120, 203604 (2018).
Gnatiessoro, S., Mosset, A., Lantz, E. & Devaux, F. Imaging spatial quantum correlations through a thin scattering medium. OSA Contin. 2, 3393–3403 (2019).
Madonini, F., Severini, F., Zappa, F. & Villa, F. Single photon avalanche diode arrays for quantum imaging and microscopy. Adv. Quantum Technol. 4, 2100005 (2021).
Brown, R. & Twiss, R. Q. Correlation between photons in two coherent beams of light. Nature 177, 27–29 (1956).
Hong, C. K., Ou, Z. Y. & Mandel, L. Measurement of subpicosecond time intervals between two photons by interference. Phys. Rev. Lett. 59, 2044–2046 (1987).
