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Two-Particle Bosonic-Fermionic Quantum Walk via Integrated Photonics
Open accessAbstract
Quantum walk represents one of the most promising resources for the simulation of physical quantum systems, and has also emerged as an alternative to the standard circuit model for quantum computing. Here we investigate how the particle statistics, either bosonic or fermionic, influences a two-particle discrete quantum walk. Such an experiment has been realized by exploiting polarization entanglement to simulate the bunching-antibunching feature of noninteracting bosons and fermions. To this scope a novel three-dimensional geometry for the waveguide circuit is introduced, which allows accurate polarization independent behavior, maintaining remarkable control on both phase and balancement.
Overview
AI snapshot
Written from the paper’s full text.
TL;DR
The paper experimentally implements a four-step discrete quantum walk in an integrated femtosecond-laser-written waveguide circuit and uses polarization-entangled photon pairs to simulate bosonic, fermionic, and anyonic two-particle statistics. Measured output distributions agree with theory with similarities above 0.97.
Key findings
- The device is polarization insensitive: single-photon distributions for horizontal, vertical, diagonal, and antidiagonal inputs match theory, with mean similarity \(S_{1ph}=0.992\pm0.002\); supplementary table values range from \(0.983\pm0.002\) to \(0.997\pm0.002\).
- Two-photon entangled states reproduce bosonic and fermionic walks: triplet \(|\Psi^+\rangle\) (\(\phi=0\)) gives \(S_{bos}=0.982\pm0.002\), and singlet \(|\Psi^-\rangle\) (\(\phi=\pi\)) gives \(S_{fer}=0.973\pm0.002\).
- Anyonic states \(|\Psi_\phi\rangle\) with \(\phi=\pi/4,\pi/2,3\pi/4\) show mixed bunching/antibunching, with similarities \(S^{\pi/4}_{any}=0.987\pm0.002\), \(S^{\pi/2}_{any}=0.988\pm0.001\), and \(S^{3\pi/4}_{any}=0.980\pm0.002\).
- The fermionic walk-position distribution has nonzero diagonal elements even though the probability of two fermions emerging from the same output spatial mode vanishes, due to the mapping between output ports and lattice positions.
Methods
- A four-step discrete quantum walk was implemented as a network of directional couplers in borosilicate glass using femtosecond laser writing; a three-dimensional tilted geometry (waveguides at \(62^\circ\), \(11\,\mu\text{m}\) spacing, interaction length \(2.1\,\text{mm}\)) gave polarization-insensitive balanced splitters, with a \(32\,\text{mm}\)-long chip.
- Polarization-entangled photon pairs at \(\lambda=806\,\text{nm}\) were generated by type-II non-collinear spontaneous parametric down conversion in a \(1.5\,\text{mm}\) BBO crystal pumped by a CW diode laser at \(P=50\,\text{mW}\); waveplates and a liquid-crystal phase shifter prepared Bell states, and interference filters set \(\Delta\lambda=6\,\text{nm}\).
- Output photons were collected by multimode fibers and detected via single-photon counting modules for single counts and two-photon coincidences; measured distributions were compared with theory using a similarity \(S\), a generalized fidelity, while changing the Bell-state phase \(\phi\) selected bosonic, fermionic, or anyonic behavior.
Limitations
- The paper does not state a dedicated limitations section. Evident from the text: the demonstration is limited to a four-step discrete quantum walk and a small integrated network, with no demonstration of scaling to many steps.
- Evident from the text: bosonic and fermionic statistics are simulated via polarization entanglement of photons rather than actual non-interacting bosonic or fermionic particles, and anyonic behavior is measured only for selected phases \(\phi=\pi/4,\pi/2,3\pi/4\).
- Stated in the paper: residual birefringence and slightly different guided modes for the two polarizations cause residual polarization dependence in directional couplers; the work mitigates this with the tilted three-dimensional geometry but does not claim perfect elimination.
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Claims the paper makes
12 Own result · 6 Own interpretation · 6 No basis given · 4 Couldn’t confirm · 4 Own method · 2 Not checked yet · accuracy not yet measured
The cited sources that could be checked couldn’t confirm or dispute this claim.
In the paper
“Furthermore, by considering a generic phase φ (dif- ferent from 0 and π), it is possible to simulate the be- haviour of the quantum walk of two anyons, particles with a non semi-integer spin that represent a generaliza- tion of fermions and bosons [30].”
What the sources say
- Could not verifycites [30] sourceExperimental — accuracy not yet measured
The Introduction (p. 1) describes a continuous-time quantum walk of a particle on a one-dimensional lattice, and the Discussion (p. 7) addresses disorder and decoherence. Searches for anyons and a generic phase φ yielded no passage about simulating a two-anyon walk, so our copy does not verify the attributed claim. (LLM, conf=0.74)
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In the paper
“By changing the symmetry of entanglement we can simulate the quan- tum dynamics of the walks of two particles with bosonic or fermionic statistic.”
- Also stated in: § Introduction · plain
“By changing the symmetry of the entangled state we can simulate the quantum walk of two particles with integer or semi- integer spin [29].”
What the sources say
- Could not verifycites [29] sourceExperimental — accuracy not yet measured
The discussion of the quantum walk on Gₙ (pp. 1–2) describes a particle moving on a graph, while the discussion of symmetry (p. 2) concerns imperfections in the graph. Searches for entanglement symmetry and two-particle bosonic or fermionic walks found no passage addressing the attributed claim. (LLM, conf=0.76)
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- Also stated in: § Introduction · plain
The cited sources that could be checked couldn’t confirm or dispute this claim.
In the paper
“In fact, the expected probability to measure two fermions over the same output spatial mode is vanishing [29].”
What the sources say
- Could not verifycites [29] sourceExperimental — accuracy not yet measured
The discussion on pp. 1–3 concerns the probability of finding a single particle at a graph node and how localization affects its propagation. The passage on p. 4 mentions small numbers of excitations but does not address two fermions occupying the same output spatial mode. Searches for that phrase and for fermions and the Pauli exclusion principle found no supporting passage. (LLM, conf=0.76)
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In the paper
“Birefringence of these waveguides is on the order of B = 7× 10−5, as characterized in [1].”
What the sources say
- Could not verifycites [1] sourceExperimental — accuracy not yet measured
The cited paper discusses theoretical quantum-walk wires and scattering widgets (III. UNIVERSAL GATE SET, p. 3; IV. MOMENTUM FILTERING, p. 5). Searches for waveguide birefringence, polarization characterization, and B = 7×10−5 found no passage reporting that measurement. (LLM, conf=0.76)
plain- Asserted: passes — The authors put it forward as true.
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- Could not verify
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In the paper
“Note that some of the diagonal ele- ments of the fermionic two-particle walk are nonzero both in the theoretical and experimental distribution.”
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In the paper
“In particular there exists an angle for which the ratio between the two coefficients is one, i.e. the coupler becomes polarization insensitive.”
plain- Asserted: passes — The authors put it forward as true.
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In the paper
“In Fig. 4 we observe how the particle symmetry affects the quantum walks.”
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In the paper
“Such experiment has been realized by exploiting polarization entanglement to simulate the bunching-antibunching feature of non interacting bosons and fermions.”
plaindirect- Asserted: passes — The authors put it forward as true.
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In the paper
“The mean value over the tested input polarization states is S1ph = 0.992± 0.002.”
plain- Asserted: passes — The authors put it forward as true.
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In the paper
“It can be observed that the ratio between the measured coupling coefficients for the two polarizations (CV and CH) depends on θ, as shown in Fig. 2b.”
plaincorrelational- Asserted: passes — The authors put it forward as true.
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- It may state two separate claims as one. 8
- Probably not a substantial claim. 7
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In the paper
“Anyway the guided modes for the two polarizations are still slightly different (as shown in Fig. 2a) and this results in a resid- ual polarization dependence in the properties of the fab- ricated DCs.”
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In the paper
“The fermionic and bosonic behaviors drastically influence the dynamics of their quantum walk on the line.”
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In the paper
“The measured bosonic and fermionic distributions compared with expected ones are reported in Fig. 4a-b for |Φ+〉 and |Ψ−〉.”
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In the paper
“It is clear from the plot that the behaviours are polarization independent, as confirmed by the simi- larities associated to each distribution, whose values are reported in table I, both for photons injected in mode kA and kB .”
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“Measured propagation losses are 0.5dB/cm and coupling losses to single mode fiber arrays at the input facet are about 1dB.”
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In the paper
“Our approach exploits an integrated waveguide architec- ture, which allows to concentrate a large number of opti- cal elements on a small chip and to achieve intrinsic phase stability due to the monolithic structure.”
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In the paper
“The length of the interaction region is chosen as L = 2.1mm in order to obtain a balanced splitting ratio.”
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In the paper
“To this scope a novel three-dimensional geometry for the waveguide circuit is introduced, which allows accurate polarization independent behaviour, maintaining a remarkable control on both phase and balancement.”
plaindirect- Asserted: passes — The authors put it forward as true.
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In the paper
“In these femtosecond laser written waveguides, birefringence is low and does not affect sig- nificantly the coherence of the photons.”
What the sources say
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In the paper
“The basic cell of the network, depicted in Fig. 2d, acts as a Mach-Zehnder interferom- eter.”
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In the paper
“The insensitivity to photon polarization, high-accuracy in the phase control and intrinsic scalability of the in- tegrated multi-DC network presented in this work, pave the way to further advanced investigations on complexity physics phenomena.”
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In the paper
“the symmetrization postulate of quantum mechanics makes the probability of the photons emerging from the same output of the BS array to be zero -i.e. PBSJJ = 0-, all the same, according to the relations (3) generalized to the case of two-particle walk, a probability pwalkjj 6= 0 for the walk distribution can be observed.”
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In the paper
“It is easy to show that p+(I, J ;K,L) and p−(I, J ;K,L) respectively correspond to the probabilities of detecting at positionsK and L two bosons or fermions injected into the modes I ad J of the quantum walk.”
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Claims other papers make about this one
Each is checked against this paper’s own text: does it say what the citing paper says it does?
The source backs part of the claim, not all of it — or backs it for a different population, condition or comparison.
In the citing paper
“Integrated optical circuits permitting nearest-neighbor coupling between a few tens of modes have been the key technology used in the nascent field of multiphoton quantum walks (20–22).”
From Two-photon quantum walk in a multimode fiber (2016) · cites this paper as [20]
Experimental — accuracy not yet measuredThe cited source says what the claim attributes to it.
In the citing paper
“The additional dimension allowed by the direct laser write technique has also been employed to compensate for polarization dependent coupling [30] and altering the boundary conditions of 1D QWs [31].”
From Quantum Walks of Correlated Photon Pairs in Two-Dimensional Waveguide Arrays (2014) · cites this paper as [31]
The cited source says what the claim attributes to it.
In the citing paper
“This technique is capable of producing high-quality waveguides with low birefringence, which are indeed suited for the propagation of polarization-encoded qubits, as we recently reported in refs 22,23, where a polarization-insensitive directional coupler has been demonstrated.”
From Integrated photonic quantum gates for polarization qubits (2011) · cites this paper as [23]
The cited source says what the claim attributes to it.
In the citing paper
“It is important to note that the polarization sensitivity/insensitivity of the directional coupler can be selected by acting on geometrical parameters and not on physical properties of the waveguides22,23.”
From Integrated photonic quantum gates for polarization qubits (2011) · cites this paper as [23]
The cited source says what the claim attributes to it.
In the citing paper
“Polarization encoding has always played an important role in a significant number of investigations in quantum information, ranging from quantum simulation [16,17] to quantum computation [18][19][20][21][22] and communication [23,24].”
From Photonic quantum information processing: a review (2019) · cites this paper as [22]
Self-check
Percentages, sums and reported differences re-computed from the paper’s own numbers.
Each contradiction between two passages listed here was confirmed by an independent check.
Rated minor: it would not touch a result — a value no result rests on, a p-value that stays on the same side of the significance level, or a conflict that is clerical, resolved elsewhere in the paper, or outside its own findings.
In the paper
“The distribution of the triplet and singlet states |Ψ+〉 (φ = 0) and |Ψ−〉 (φ = π) emerging from the quantum walk was reconstructed”
“The measured bosonic and fermionic distributions compared with expected ones are reported in Fig. 4a-b for |Φ+〉 and |Ψ−〉.”
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Measurement of the refractive index profile of waveguides using defocusing microscopy
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Dynamical Triangulation Induced by Quantum Walk
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Anonymous communication scheme based on quantum walk on Cayley graph
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Metadata
- Authors
- Sansoni, L., Sciarrino, F., Vallone, G., Mataloni, P., Crespi, A., Ramponi, R., & Osellame, R.
- Affiliations
- Sapienza University of Rome (IT)
- National Institute of Optics (IT)
- University of Padua (IT)
- Istituto di Fotonica e Nanotecnologie (IT)
- ORCID
- Venue
- Physical Review Letters
- Publisher
- American Physical Society (APS)
- Published
- 2012-01-05
- Volume
- 108
- Issue
- 1
- Pages
- 010502-010502
- ISSN
- 0031-9007 (ISSN-L)
- 1079-7114
- OpenAlex
- W1990940849
- Semantic Scholar
- eb1d90c629963289aca81d1514051460022aa368
- Cited by
- 578
- References
- 32
- Citations by year
- 2026: 25 · 2025: 16 · 2024: 32 · 2023: 16 · 2022: 36 · 2021: 37 · 2020: 36 · 2019: 58 · 2018: 43 · 2017: 35 · 2016: 52 · 2015: 51 · 2014: 69 · 2013: 43 · 2012: 28
- FWCI
- 55.97
- Type
- journal article
- Language
- en
- Open access
- green
- arxiv.org
- Locations
- Physical Review Letters (publishedVersion)
- PubMed (publishedVersion)
- arXiv (Cornell University) (submittedVersion)
- INO Open Portal (submittedVersion)
- IRIS Research product catalog (Sapienza University of Rome) (submittedVersion)
- Virtual Community of Pathological Anatomy (University of Castilla La Mancha) (submittedVersion)
- Padua Research Archive (University of Padova) (submittedVersion, other-oa)
- arXiv (Cornell University)
- Topics
- Physical Sciences › Computer Science › Artificial Intelligence › Quantum Computing Algorithms and Architecture
- Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Quantum Information and Cryptography
- Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Quantum Mechanics and Applications
- Keywords
- quantum walks, two-particle quantum walk, fermionic statistics, polarization entanglement, integrated photonics, waveguide circuits, polarization insensitivity, discrete-time quantum walks
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