Authors

Mattia Walschaers

Abstract

Quantum systems with many constituents give rise to a range of conceptual, analytical and computational challenges, hence, the label ‘complex systems’. In the first place, one can think of interactions, described by a many-body Hamiltonian, as the source of such complexity. However, it has gradually become clear that, even in absence of interactions, many-body systems are more than just the sum of their parts. This feature is due to many-body interference. One of the most well-known interference phenomena is the Hong–Ou–Mandel effect, where total destructive interference is observed for a pair of (non-interacting) identical photons. This two-photon interference effect can be generalised to systems of many particles which can be either fermionic or bosonic. The resulting many-particle interference goes beyond quantum statistical effects that are contained in the Bose–Einstein or Fermi–Dirac distributions, and is dynamical in nature. This Tutorial will introduce the mathematical framework for describing systems of identical particles, and explain the notion of indistinguishability. We will then focus our attention on dynamical systems of free particles and formally introduce the concept of many-particle interference. Its impact on many-particle transition probabilities is computationally challenging to evaluate, and it becomes rapidly intractable for systems with large numbers of identical particles. Hence, this Tutorial will build up towards alternative, more efficient methods for observing signatures of many-particle interference. A first type of signatures relies on the detection of a highly sensitive -but also highly fragile- processes of total destructive interference that occurs in interferometers with a high degree of symmetry. A second class of signatures is based on the statistical features that arise when we study the typical behaviour of correlations between a small number of the interferometer’s output ports. We will ultimately show how these statistical signatures of many-particle interference lead us to a statistical version of the Hong–Ou–Mandel effect. The work presented in this Tutorial was one of the four shortlisted finalists of the 2018 DPG SAMOP dissertation prize.

Citation

  • Journal: Journal of Physics B: Atomic, Molecular and Optical Physics
  • Year: 2020
  • Volume: 53
  • Issue: 4
  • Pages: 043001
  • Publisher: IOP Publishing
  • DOI: 10.1088/1361-6455/ab5c30

BibTeX

@article{Walschaers_2020,
  title={{Signatures of many-particle interference}},
  volume={53},
  ISSN={1361-6455},
  DOI={10.1088/1361-6455/ab5c30},
  number={4},
  journal={Journal of Physics B: Atomic, Molecular and Optical Physics},
  publisher={IOP Publishing},
  author={Walschaers, Mattia},
  year={2020},
  pages={043001}
}

Download the bib file

References

  • Dirac P A M, The Principles of Quantum Mechanics (1930)
  • MAGYAR, G. & MANDEL, L. Interference Fringes Produced by Superposition of Two Independent Maser Light Beams. Nature 198, 255–256 (1963) – 10.1038/198255a0
  • Mandel, L. Quantum Theory of Interference Effects Produced by Independent Light Beams. Phys. Rev. 134, A10–A15 (1964) – 10.1103/physrev.134.a10
  • Pfleegor, R. L. & Mandel, L. Interference of Independent Photon Beams. Phys. Rev. 159, 1084–1088 (1967) – 10.1103/physrev.159.1084
  • Mandel, L. Photon interference and correlation effects produced by independent quantum sources. Phys. Rev. A 28, 929–943 (1983) – 10.1103/physreva.28.929
  • Klyshko D N, J. Exp. Theor. Phys. Lett. (1970)
  • Burnham, D. C. & Weinberg, D. L. Observation of Simultaneity in Parametric Production of Optical Photon Pairs. Phys. Rev. Lett. 25, 84–87 (1970) – 10.1103/physrevlett.25.84
  • Grangier, P., Roger, G. & Aspect, A. Experimental Evidence for a Photon Anticorrelation Effect on a Beam Splitter: A New Light on Single-Photon Interferences. Europhys. Lett. 1, 173–179 (1986) – 10.1209/0295-5075/1/4/004
  • 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) – 10.1103/physrevlett.59.2044
  • Shih, Y. H. & Alley, C. O. New Type of Einstein-Podolsky-Rosen-Bohm Experiment Using Pairs of Light Quanta Produced by Optical Parametric Down Conversion. Phys. Rev. Lett. 61, 2921–2924 (1988) – 10.1103/physrevlett.61.2921
  • Ou, Z. Y. Quantum theory of fourth-order interference. Phys. Rev. A 37, 1607–1619 (1988) – 10.1103/physreva.37.1607
  • Sadana, S. et al. Near-100% two-photon-like coincidence-visibility dip with classical light and the role of complementarity. Phys. Rev. A 100, (2019) – 10.1103/physreva.100.013839
  • Belinskii A V, Sov. Phys.—JETP (1992)
  • Banaszek, K. & Knight, P. L. Quantum interference in three-photon down-conversion. Phys. Rev. A 55, 2368–2375 (1997) – 10.1103/physreva.55.2368
  • Tichy, M. C. et al. Four-photon indistinguishability transition. Phys. Rev. A 83, (2011) – 10.1103/physreva.83.062111
  • Tillmann, M. et al. Generalized Multiphoton Quantum Interference. Phys. Rev. X 5, (2015) – 10.1103/physrevx.5.041015
  • Ra, Y.-S. et al. Nonmonotonic quantum-to-classical transition in multiparticle interference. Proc. Natl. Acad. Sci. U.S.A. 110, 1227–1231 (2013) – 10.1073/pnas.1206910110
  • Spagnolo, N. et al. Three-photon bosonic coalescence in an integrated tritter. Nat Commun 4, (2013) – 10.1038/ncomms2616
  • Menssen, A. J. et al. Distinguishability and Many-Particle Interference. Phys. Rev. Lett. 118, (2017) – 10.1103/physrevlett.118.153603
  • Giordani, T. et al. Experimental statistical signature of many-body quantum interference. Nature Photon 12, 173–178 (2018) – 10.1038/s41566-018-0097-4
  • Agresti, I. et al. Pattern Recognition Techniques for Boson Sampling Validation. Phys. Rev. X 9, (2019) – 10.1103/physrevx.9.011013
  • Zhong, H.-S. et al. 12-Photon Entanglement and Scalable Scattershot Boson Sampling with Optimal Entangled-Photon Pairs from Parametric Down-Conversion. Phys. Rev. Lett. 121, (2018) – 10.1103/physrevlett.121.250505
  • Crespi, A. et al. Suppression law of quantum states in a 3D photonic fast Fourier transform chip. Nat Commun 7, (2016) – 10.1038/ncomms10469
  • Crespi, A. Suppression laws for multiparticle interference in Sylvester interferometers. Phys. Rev. A 91, (2015) – 10.1103/physreva.91.013811
  • Dittel, C., Keil, R. & Weihs, G. Many-body quantum interference on hypercubes. Quantum Sci. Technol. 2, 015003 (2017) – 10.1088/2058-9565/aa540c
  • Tichy, M. C., Tiersch, M., Mintert, F. & Buchleitner, A. Many-particle interference beyond many-boson and many-fermion statistics. New J. Phys. 14, 093015 (2012) – 10.1088/1367-2630/14/9/093015
  • Tichy, M. C., Tiersch, M., de Melo, F., Mintert, F. & Buchleitner, A. Zero-Transmission Law for Multiport Beam Splitters. Phys. Rev. Lett. 104, (2010) – 10.1103/physrevlett.104.220405
  • Viggianiello, N. et al. Experimental generalized quantum suppression law in Sylvester interferometers. New J. Phys. 20, 033017 (2018) – 10.1088/1367-2630/aaad92
  • Dittel, C. et al. Totally Destructive Many-Particle Interference. Phys. Rev. Lett. 120, (2018) – 10.1103/physrevlett.120.240404
  • Dittel, C. et al. Totally destructive interference for permutation-symmetric many-particle states. Phys. Rev. A 97, (2018) – 10.1103/physreva.97.062116
  • Ou, Z. Y., Rhee, J.-K. & Wang, L. J. Photon bunching and multiphoton interference in parametric down-conversion. Phys. Rev. A 60, 593–604 (1999) – 10.1103/physreva.60.593
  • Carolan, J. et al. On the experimental verification of quantum complexity in linear optics. Nature Photon 8, 621–626 (2014) – 10.1038/nphoton.2014.152
  • Shchesnovich, V. S. Universality of Generalized Bunching and Efficient Assessment of Boson Sampling. Phys. Rev. Lett. 116, (2016) – 10.1103/physrevlett.116.123601
  • Paul, H. Interference between independent photons. Rev. Mod. Phys. 58, 209–231 (1986) – 10.1103/revmodphys.58.209
  • Mandel, L. Quantum effects in one-photon and two-photon interference. Rev. Mod. Phys. 71, S274–S282 (1999) – 10.1103/revmodphys.71.s274
  • Pan, J.-W. et al. Multiphoton entanglement and interferometry. Rev. Mod. Phys. 84, 777–838 (2012) – 10.1103/revmodphys.84.777
  • Knill, E., Laflamme, R. & Milburn, G. J. A scheme for efficient quantum computation with linear optics. Nature 409, 46–52 (2001) – 10.1038/35051009
  • Qiang, X. et al. Large-scale silicon quantum photonics implementing arbitrary two-qubit processing. Nature Photon 12, 534–539 (2018) – 10.1038/s41566-018-0236-y
  • Aaronson, S. & Arkhipov, A. Theory of Comput. 9, 143–252 (2013) – 10.4086/toc.2013.v009a004
  • Broome, M. A. et al. Photonic Boson Sampling in a Tunable Circuit. Science 339, 794–798 (2013) – 10.1126/science.1231440
  • Crespi, A. et al. Integrated multimode interferometers with arbitrary designs for photonic boson sampling. Nature Photon 7, 545–549 (2013) – 10.1038/nphoton.2013.112
  • Spring, J. B. et al. Boson Sampling on a Photonic Chip. Science 339, 798–801 (2013) – 10.1126/science.1231692
  • Tillmann, M. et al. Experimental boson sampling. Nature Photon 7, 540–544 (2013) – 10.1038/nphoton.2013.102
  • Wang, H. et al. High-efficiency multiphoton boson sampling. Nature Photon 11, 361–365 (2017) – 10.1038/nphoton.2017.63
  • Lund, A. P. et al. Boson Sampling from a Gaussian State. Phys. Rev. Lett. 113, (2014) – 10.1103/physrevlett.113.100502
  • Bentivegna, M. et al. Experimental scattershot boson sampling. Sci. Adv. 1, (2015) – 10.1126/sciadv.1400255
  • Hamilton, C. S. et al. Gaussian Boson Sampling. Phys. Rev. Lett. 119, (2017) – 10.1103/physrevlett.119.170501
  • Urbina, J.-D., Kuipers, J., Matsumoto, S., Hummel, Q. & Richter, K. Multiparticle Correlations in Mesoscopic Scattering: Boson Sampling, Birthday Paradox, and Hong-Ou-Mandel Profiles. Phys. Rev. Lett. 116, (2016) – 10.1103/physrevlett.116.100401
  • Lopes, R. et al. Atomic Hong–Ou–Mandel experiment. Nature 520, 66–68 (2015) – 10.1038/nature14331
  • Islam, R. et al. Measuring entanglement entropy in a quantum many-body system. Nature 528, 77–83 (2015) – 10.1038/nature15750
  • Roos, C. F., Alberti, A., Meschede, D., Hauke, P. & Häffner, H. Revealing Quantum Statistics with a Pair of Distant Atoms. Phys. Rev. Lett. 119, (2017) – 10.1103/physrevlett.119.160401
  • Rom, T. et al. Free fermion antibunching in a degenerate atomic Fermi gas released from an optical lattice. Nature 444, 733–736 (2006) – 10.1038/nature05319
  • Henny, M. et al. The Fermionic Hanbury Brown and Twiss Experiment. Science 284, 296–298 (1999) – 10.1126/science.284.5412.296
  • Jeltes, T. et al. Comparison of the Hanbury Brown–Twiss effect for bosons and fermions. Nature 445, 402–405 (2007) – 10.1038/nature05513
  • Kiesel, H., Renz, A. & Hasselbach, F. Observation of Hanbury Brown–Twiss anticorrelations for free electrons. Nature 418, 392–394 (2002) – 10.1038/nature00911
  • Preiss, P. M. et al. High-Contrast Interference of Ultracold Fermions. Phys. Rev. Lett. 122, (2019) – 10.1103/physrevlett.122.143602
  • Kaufman, A. M. et al. Two-particle quantum interference in tunnel-coupled optical tweezers. Science 345, 306–309 (2014) – 10.1126/science.1250057
  • Bocquillon, E. et al. Electron Quantum Optics: Partitioning Electrons One by One. Phys. Rev. Lett. 108, (2012) – 10.1103/physrevlett.108.196803
  • Dubois, J. et al. Minimal-excitation states for electron quantum optics using levitons. Nature 502, 659–663 (2013) – 10.1038/nature12713
  • Sansoni, L. et al. Two-Particle Bosonic-Fermionic Quantum Walk via Integrated Photonics. Phys. Rev. Lett. 108, (2012) – 10.1103/physrevlett.108.010502
  • Tamma, V. & Laibacher, S. Multiboson Correlation Interferometry with Arbitrary Single-Photon Pure States. Phys. Rev. Lett. 114, (2015) – 10.1103/physrevlett.114.243601
  • Shchesnovich, V. S. Partial indistinguishability theory for multiphoton experiments in multiport devices. Phys. Rev. A 91, (2015) – 10.1103/physreva.91.013844
  • Tichy, M. C. Sampling of partially distinguishable bosons and the relation to the multidimensional permanent. Phys. Rev. A 91, (2015) – 10.1103/physreva.91.022316
  • Jin, R.-B. et al. Spectrally resolved Hong-Ou-Mandel interference between independent photon sources. Opt. Express 23, 28836 (2015) – 10.1364/oe.23.028836
  • Tsujimoto, Y. et al. High visibility Hong-Ou-Mandel interference via a time-resolved coincidence measurement. Opt. Express 25, 12069 (2017) – 10.1364/oe.25.012069
  • Kobayashi, T. et al. Frequency-domain Hong–Ou–Mandel interference. Nature Photon 10, 441–444 (2016) – 10.1038/nphoton.2016.74
  • Yannouleas, C., Brandt, B. B. & Landman, U. Interference, spectral momentum correlations, entanglement, and Bell inequality for a trapped interacting ultracold atomic dimer: Analogies with biphoton interferometry. Phys. Rev. A 99, (2019) – 10.1103/physreva.99.013616
  • Dufour, G. et al. Many-particle interference in a two-component bosonic Josephson junction: an all-optical simulation. New J. Phys. 19, 125015 (2017) – 10.1088/1367-2630/aa8cf7
  • Brünner, T., Dufour, G., Rodríguez, A. & Buchleitner, A. Signatures of Indistinguishability in Bosonic Many-Body Dynamics. Phys. Rev. Lett. 120, (2018) – 10.1103/physrevlett.120.210401
  • Yannouleas, C. & Landman, U. Third-order momentum correlation interferometry maps for entangled quantal states of three singly trapped massive ultracold fermions. Phys. Rev. A 100, (2019) – 10.1103/physreva.100.023618
  • Bergschneider, A. et al. Experimental characterization of two-particle entanglement through position and momentum correlations. Nat. Phys. 15, 640–644 (2019) – 10.1038/s41567-019-0508-6
  • Aolita, L., Gogolin, C., Kliesch, M. & Eisert, J. Reliable quantum certification of photonic state preparations. Nat Commun 6, (2015) – 10.1038/ncomms9498
  • Gogolin C, (2013)
  • Tichy, M. C., Mayer, K., Buchleitner, A. & Mølmer, K. Stringent and Efficient Assessment of Boson-Sampling Devices. Phys. Rev. Lett. 113, (2014) – 10.1103/physrevlett.113.020502
  • Spagnolo, N. et al. Experimental validation of photonic boson sampling. Nature Photon 8, 615–620 (2014) – 10.1038/nphoton.2014.135
  • Aaronson, S. & Arkhipov, A. BosonSampling is far from uniform. QIC 14, 1383–1423 (2014) – 10.26421/qic14.15-16-7
  • Flamini, F., Spagnolo, N. & Sciarrino, F. Visual assessment of multi-photon interference. Quantum Sci. Technol. 4, 024008 (2019) – 10.1088/2058-9565/ab04fc
  • Hangleiter, D., Kliesch, M., Eisert, J. & Gogolin, C. Sample Complexity of Device-Independently Certified “Quantum Supremacy”. Phys. Rev. Lett. 122, (2019) – 10.1103/physrevlett.122.210502
  • Walschaers, M. et al. Statistical benchmark for BosonSampling. New J. Phys. 18, 032001 (2016) – 10.1088/1367-2630/18/3/032001
  • Alicki, R. Field-Theoretical Methods. Lecture Notes in Physics 151–174 (2010) doi:10.1007/978-3-642-11914-9_5 – 10.1007/978-3-642-11914-9_5
  • Alicki, R. & Fannes, M. Quantum Dynamical Systems. (2001) doi:10.1093/acprof:oso/9780198504009.001.0001 – 10.1093/acprof:oso/9780198504009.001.0001
  • Bratteli, O. & Robinson, D. W. Operator Algebras and Quantum Statistical Mechanics 1. (Springer Berlin Heidelberg, 1987). doi:10.1007/978-3-662-02520-8 – 10.1007/978-3-662-02520-8
  • Bratteli, O. & Robinson, D. W. Operator Algebras and Quantum Statistical Mechanics. (Springer Berlin Heidelberg, 1997). doi:10.1007/978-3-662-03444-6 – 10.1007/978-3-662-03444-6
  • Petz D, An Invitation to the Algebra of Canonical Comutation Relations (1990)
  • Hamermesh M, Group Theory and Its Application to Physical Problems (1989)
  • Fulton W, Young Tableaux: With Applications to Representation Theory and Geometry (1997)
  • Bloch, I., Dalibard, J. & Zwerger, W. Many-body physics with ultracold gases. Rev. Mod. Phys. 80, 885–964 (2008) – 10.1103/revmodphys.80.885
  • Mosonyi, M., Hiai, F., Ogawa, T. & Fannes, M. Asymptotic distinguishability measures for shift-invariant quasifree states of fermionic lattice systems. Journal of Mathematical Physics 49, (2008) – 10.1063/1.2953473
  • Treps, N., Delaubert, V., Maître, A., Courty, J. M. & Fabre, C. Quantum noise in multipixel image processing. Phys. Rev. A 71, (2005) – 10.1103/physreva.71.013820
  • Jordan, P. & Wigner, E. �ber das Paulische �quivalenzverbot. Z. Physik 47, 631–651 (1928) – 10.1007/bf01331938
  • Electron correlations in narrow energy bands. Proc. R. Soc. Lond. A 276, 238–257 (1963) – 10.1098/rspa.1963.0204
  • Gutzwiller, M. C. Effect of Correlation on the Ferromagnetism of Transition Metals. Phys. Rev. Lett. 10, 159–162 (1963) – 10.1103/physrevlett.10.159
  • Gersch, H. A. & Knollman, G. C. Quantum Cell Model for Bosons. Phys. Rev. 129, 959–967 (1963) – 10.1103/physrev.129.959
  • Zeilinger, A. General properties of lossless beam splitters in interferometry. American Journal of Physics 49, 882–883 (1981) – 10.1119/1.12387
  • Brecht, B., Reddy, D. V., Silberhorn, C. & Raymer, M. G. Photon Temporal Modes: A Complete Framework for Quantum Information Science. Phys. Rev. X 5, (2015) – 10.1103/physrevx.5.041017
  • Lu, H.-H. et al. Electro-Optic Frequency Beam Splitters and Tritters for High-Fidelity Photonic Quantum Information Processing. Phys. Rev. Lett. 120, (2018) – 10.1103/physrevlett.120.030502
  • Clifford P, Proc. 29th Annual ACM-SIAM Symp. on Discrete Algorithms, SODA ’18 (2018)
  • Laibacher, S. & Tamma, V. Symmetries and entanglement features of inner-mode-resolved correlations of interfering nonidentical photons. Phys. Rev. A 98, (2018) – 10.1103/physreva.98.053829
  • Wang, X.-J. et al. Experimental Time-Resolved Interference with Multiple Photons of Different Colors. Phys. Rev. Lett. 121, (2018) – 10.1103/physrevlett.121.080501
  • Orre, V. V. et al. Interference of Temporally Distinguishable Photons Using Frequency-Resolved Detection. Phys. Rev. Lett. 123, (2019) – 10.1103/physrevlett.123.123603
  • Bentivegna, M. et al. Bayesian approach to Boson sampling validation. Int. J. Quantum Inform. 12, 1560028 (2014) – 10.1142/s021974991560028x
  • Mayer, K., Tichy, M. C., Mintert, F., Konrad, T. & Buchleitner, A. Counting statistics of many-particle quantum walks. Phys. Rev. A 83, (2011) – 10.1103/physreva.83.062307
  • Stöckmann H-J, Quantum Chaos: An Introduction (2007)
  • Creutz, M. On invariant integration over SU(N). Journal of Mathematical Physics 19, 2043–2046 (1978) – 10.1063/1.523581
  • Weingarten, D. Asymptotic behavior of group integrals in the limit of infinite rank. Journal of Mathematical Physics 19, 999–1001 (1978) – 10.1063/1.523807
  • Samuel, S. U(N) Integrals, 1/N, and the De Wit–’t Hooft anomalies. Journal of Mathematical Physics 21, 2695–2703 (1980) – 10.1063/1.524386
  • Brouwer, P. W. & Beenakker, C. W. J. Diagrammatic method of integration over the unitary group, with applications to quantum transport in mesoscopic systems. Journal of Mathematical Physics 37, 4904–4934 (1996) – 10.1063/1.531667
  • Collins, B. & Śniady, P. Integration with Respect to the Haar Measure on Unitary, Orthogonal and Symplectic Group. Commun. Math. Phys. 264, 773–795 (2006) – 10.1007/s00220-006-1554-3
  • Walschaers, M. Statistical Benchmarks for Quantum Transport in Complex Systems. Springer Theses (Springer International Publishing, 2018). doi:10.1007/978-3-319-93151-7 – 10.1007/978-3-319-93151-7
  • Carolan, J. et al. Universal linear optics. Science 349, 711–716 (2015) – 10.1126/science.aab3642
  • Taballione, C. et al. 8×8 Programmable Quantum Photonic Processor based on Silicon Nitride Waveguides. Frontiers in Optics / Laser Science JTu3A.58 (2018) doi:10.1364/fio.2018.jtu3a.58 – 10.1364/fio.2018.jtu3a.58
  • Flamini F, (2019)
  • Neville, A. et al. Classical boson sampling algorithms with superior performance to near-term experiments. Nature Phys 13, 1153–1157 (2017) – 10.1038/nphys4270
  • Walschaers, M. Many-Particle Interference. Springer Theses 265–373 (2018) doi:10.1007/978-3-319-93151-7_8 – 10.1007/978-3-319-93151-7_8
  • Rigovacca, L., Di Franco, C., Metcalf, B. J., Walmsley, I. A. & Kim, M. S. Nonclassicality Criteria in Multiport Interferometry. Phys. Rev. Lett. 117, (2016) – 10.1103/physrevlett.117.213602
  • Rigovacca, L., Kolthammer, W. S., Di Franco, C. & Kim, M. S. Optical nonclassicality test based on third-order intensity correlations. Phys. Rev. A 97, (2018) – 10.1103/physreva.97.033809
  • Tichy M C, (2011)
  • Tichy, M. C. Interference of identical particles from entanglement to boson-sampling. J. Phys. B: At. Mol. Opt. Phys. 47, 103001 (2014) – 10.1088/0953-4075/47/10/103001
  • Shchesnovich, V. S. Noise in boson sampling and the threshold of efficient classical simulatability. Phys. Rev. A 100, (2019) – 10.1103/physreva.100.012340
  • Moylett, A. E., García-Patrón, R., Renema, J. J. & Turner, P. S. Classically simulating near-term partially-distinguishable and lossy boson sampling. Quantum Sci. Technol. 5, 015001 (2019) – 10.1088/2058-9565/ab5555
  • Leverrier, A. & Garcia-Patron, R. Analysis of circuit imperfections in BosonSampling. QIC 489–512 (2015) doi:10.26421/qic15.5-6-8 – 10.26421/qic15.5-6-8
  • Kalai G, (2014)
  • Walschaers, M., Kuipers, J. & Buchleitner, A. From many-particle interference to correlation spectroscopy. Phys. Rev. A 94, (2016) – 10.1103/physreva.94.020104
  • Shchesnovich, V. S. & Bezerra, M. E. O. Collective phases of identical particles interfering on linear multiports. Phys. Rev. A 98, (2018) – 10.1103/physreva.98.033805
  • Renema, J. J. et al. Efficient Classical Algorithm for Boson Sampling with Partially Distinguishable Photons. Phys. Rev. Lett. 120, (2018) – 10.1103/physrevlett.120.220502
  • Moylett, A. E. & Turner, P. S. Quantum simulation of partially distinguishable boson sampling. Phys. Rev. A 97, (2018) – 10.1103/physreva.97.062329
  • Dittel C, (2019)
  • Flamini F, Rep. Prog. Phys. (2018)
  • Lund, A. P., Bremner, M. J. & Ralph, T. C. Quantum sampling problems, BosonSampling and quantum supremacy. npj Quantum Inf 3, (2017) – 10.1038/s41534-017-0018-2
  • Harrow, A. W. & Montanaro, A. Quantum computational supremacy. Nature 549, 203–209 (2017) – 10.1038/nature23458
  • Brod D J, Adv. Photon. (2019)
  • Chakhmakhchyan, L. & Cerf, N. J. Boson sampling with Gaussian measurements. Phys. Rev. A 96, (2017) – 10.1103/physreva.96.032326
  • Chabaud, U. et al. Continuous-variable sampling from photon-added or photon-subtracted squeezed states. Phys. Rev. A 96, (2017) – 10.1103/physreva.96.062307
  • Huh, J., Guerreschi, G. G., Peropadre, B., McClean, J. R. & Aspuru-Guzik, A. Boson sampling for molecular vibronic spectra. Nature Photon 9, 615–620 (2015) – 10.1038/nphoton.2015.153
  • Clements, W. R. et al. Approximating vibronic spectroscopy with imperfect quantum optics. J. Phys. B: At. Mol. Opt. Phys. 51, 245503 (2018) – 10.1088/1361-6455/aaf031
  • Arrazola, J. M., Bromley, T. R. & Rebentrost, P. Quantum approximate optimization with Gaussian boson sampling. Phys. Rev. A 98, (2018) – 10.1103/physreva.98.012322
  • Arrazola, J. M. & Bromley, T. R. Using Gaussian Boson Sampling to Find Dense Subgraphs. Phys. Rev. Lett. 121, (2018) – 10.1103/physrevlett.121.030503
  • Brádler, K., Dallaire-Demers, P.-L., Rebentrost, P., Su, D. & Weedbrook, C. Gaussian boson sampling for perfect matchings of arbitrary graphs. Phys. Rev. A 98, (2018) – 10.1103/physreva.98.032310
  • Phillips, D. S. et al. Benchmarking of Gaussian boson sampling using two-point correlators. Phys. Rev. A 99, (2019) – 10.1103/physreva.99.023836
  • Bartlett, S. D., Sanders, B. C., Braunstein, S. L. & Nemoto, K. Efficient Classical Simulation of Continuous Variable Quantum Information Processes. Phys. Rev. Lett. 88, (2002) – 10.1103/physrevlett.88.097904
  • Mari, A. & Eisert, J. Positive Wigner Functions Render Classical Simulation of Quantum Computation Efficient. Phys. Rev. Lett. 109, (2012) – 10.1103/physrevlett.109.230503
  • Rahimi-Keshari, S., Ralph, T. C. & Caves, C. M. Sufficient Conditions for Efficient Classical Simulation of Quantum Optics. Phys. Rev. X 6, (2016) – 10.1103/physrevx.6.021039
  • Benatti, F., Floreanini, R. & Marzolino, U. Entanglement robustness and geometry in systems of identical particles. Phys. Rev. A 85, (2012) – 10.1103/physreva.85.042329
  • Benatti, F., Floreanini, R. & Marzolino, U. Bipartite entanglement in systems of identical particles: The partial transposition criterion. Annals of Physics 327, 1304–1319 (2012) – 10.1016/j.aop.2012.02.002
  • Tichy, M. C., de Melo, F., Kuś, M., Mintert, F. & Buchleitner, A. Entanglement of identical particles and the detection process. Fortschritte der Physik 61, 225–237 (2012) – 10.1002/prop.201200079
  • Benatti, F., Floreanini, R., Franchini, F. & Marzolino, U. Remarks on Entanglement and Identical Particles. Open Syst. Inf. Dyn. 24, 1740004 (2017) – 10.1142/s1230161217400042
  • Lo Franco, R. & Compagno, G. Indistinguishability of Elementary Systems as a Resource for Quantum Information Processing. Phys. Rev. Lett. 120, (2018) – 10.1103/physrevlett.120.240403
  • 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, (2009) – 10.1103/physrevlett.102.193601