General Rules for Bosonic Bunching in Multimode Interferometers

Spagnolo, Nicolò; Vitelli, Chiara; Sansoni, Linda; Maiorino, Enrico; Mataloni, Paolo; Sciarrino, Fabio; Brod, Daniel J.; Galvão, Ernesto F.; Crespi, Andrea; Ramponi, Roberta; Osellame, Roberto

doi:10.1103/physrevlett.111.130503

Cited by 81 publications

(63 citation statements)

References 29 publications

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“…, however if m = p 2 the equivalence does not emerge, as can be seen in Figure 2(c) where a separation emerges between P Q (p-fold) and P C (p-fold) [26].…”

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confidence: 85%

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On the experimental verification of quantum complexity in linear optics

Carolan¹,

et al. 2014

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The first quantum technologies to solve computational problems that are beyond the capabilities of classical computers are likely to be devices that exploit characteristics inherent to a particular physical system, to tackle a bespoke problem suited to those characteristics. Evidence implies that the detection of ensembles of photons, which have propagated through a linear optical circuit, is equivalent to sampling from a probability distribution that is intractable to classical simulation. However, it is probable that the complexity of this type of sampling problem means that its solution is classically unverifiable within a feasible number of trials, and the task of establishing correct operation becomes one of gathering sufficiently convincing circumstantial evidence. Here, we develop scalable methods to experimentally establish correct operation for this class of sampling algorithm, which we implement with two different types of optical circuits for 3, 4, and 5 photons, on Hilbert spaces of up to 50, 000 dimensions. With only a small number of trials, we establish a confidence > 99% that we are not sampling from a uniform distribution or a classical distribution, and we demonstrate a unitary specific witness that functions robustly for small amounts of data. Like the algorithmic operations they endorse, our methods exploit the characteristics native to the quantum system in question. Here we observe and make an application of a "bosonic clouding" phenomenon, interesting in its own right, where photons are found in local groups of modes superposed across two locations. Our broad approach is likely to be practical for all architectures for quantum technologies where formal verification methods for quantum algorithms are either intractable or unknown.The construction of a universal quantum computer, capable of implementing any quantum computation or quantum simulation, is a major long term experimental objective. However, it is expected that non-universal quantum machines, that exploit characteristics of their own physical system to solve specific problems, will outperform classical computers in the near-term [1]. Ensembles of single photons in linear optical circuits are a recently proposed example: despite being non-interacting particles, their detection statistics are described by functions that are intractable to classical computers -matrix permanents [2]. It is therefore believed that linear optics constitutes a platform for the efficient sampling of probability distributions that cannot be simulated by classical computers, with strong evidence provided in the case of circuits described by large random matrices [3][4][5][6][7].A universal quantum computer, running for example Shor's factoring algorithm [8], creates an exponentially large probability distribution with individual peaks at highly regular intervals that facilitate the solution to the factoring problem allowing efficient classical verification, as is the case for all problems in the NP complexity class [9]. Accordingly, correct operation of the...

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“…, however if m = p 2 the equivalence does not emerge, as can be seen in Figure 2(c) where a separation emerges between P Q (p-fold) and P C (p-fold) [26].…”

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confidence: 85%

“…Due to the non deterministic nature of the downconversion process, we employ the method of [26] to calculate P (p-fold) . We found P Q (p-fold) = 0.450 ± 0.028 compared to an expected value 0.509, while P C (p-fold) = 0.680 ± 0.0002 compared to an expected value of 0.691.…”

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confidence: 99%

On the experimental verification of quantum complexity in linear optics

Carolan¹,

et al. 2014

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“…The anti-symmetrization requirements [1] for fermionic wavefunctions lead to vanishing probability of finding more than one particle on the same site (Pauli principle). Bosons, on the contrary, show a remarked tendency to bunch together, with increased probability of coalesce on the same site [2,3] or to cluster in nearby sites (bosonic clouding [4]). …”

Section: Introductionmentioning

confidence: 99%

“…This enhancement factor for full bunching events is indeed a general law for all unitary processes [3]. With regard to antibunching events (particles in all different ports), it is not difficult to observe that for n = m > 2 they are instead never suppressed for bosons: the scattering matrix for such an event would be a full Sylvester matrix, whose permanent is proved [26] to be non-vanishing by observing that for {r 1 , r 2 , .…”

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confidence: 99%

Suppression laws for multiparticle interference in Sylvester interferometers

Crespi

2015

Phys. Rev. A

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Quantum interference of correlated particles is a fundamental quantum phenomenon which carries signatures of the statistics properties of the particles, such as bunching or anti-bunching. In presence of particular symmetries, interference effects take place with high visibility, one of the simplest cases being the suppression of coincident detection in the Hong-Ou-Mandel effect. Tichy et al. recently demonstrated a simple sufficient criterion for the suppression of output events in the more general case of Fourier multi-port beam splitters. Here we study the case in which 2 q particles (either bosonic or fermionic) are injected simultaneously in different ports of a Sylvester interferometer with 2 p ≥ 2 q modes. In particular, we prove a necessary and sufficient criterion for a significant fraction of output states to be suppressed, for specific input configurations. This may find application in assessing the indistinguishability of multiple single photon sources and in the validation of boson sampling machines.

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“…The rapid advance of integrated optics and quantum information makes it possible to manipulate quantum states in a high phase stability as well as highly complex interferometer. Experiments from single-photon generation to multimode interference have been widely demonstrated [7][8][9][10][11][12][13][14]. Photon correlation in one-dimensional structure has been well studied [15][16][17][18][19][20] and finds many applications in quantum information processing and quantum simulation [21][22][23][24][25][26][27][28][29].…”

Section: Introductionmentioning

confidence: 99%

Non-classical photon correlation in a two-dimensional photonic lattice

Gao¹,

Qiao²,

Lin³

et al. 2016

Opt. Express

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Quantum interference and quantum correlation, as two main features of quantum optics, play an essential role in quantum information applications, such as multi-particle quantum walk and boson sampling. While many experimental demonstrations have been done in one-dimensional waveguide arrays, it remains unexplored in higher dimensions due to tight requirement of manipulating and detecting photons in large-scale. Here, we experimentally observe non-classical correlation of two identical photons in a fully coupled two-dimensional structure, i.e. photonic lattice manufactured by three-dimensional femtosecond laser writing. Photon interference consists of 36 Hong-Ou-Mandel interference and 9 bunching. The overlap between measured and simulated distribution is up to 0.890 ± 0.001. Clear photon correlation is observed in the two-dimensional photonic lattice. Combining with controllably engineered disorder, our results open new perspectives towards large-scale implementation of quantum simulation on integrated photonic chips.

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General Rules for Bosonic Bunching in Multimode Interferometers

Cited by 81 publications

References 29 publications

On the experimental verification of quantum complexity in linear optics

On the experimental verification of quantum complexity in linear optics

Suppression laws for multiparticle interference in Sylvester interferometers

Non-classical photon correlation in a two-dimensional photonic lattice

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