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Many-body quantum interference on hypercubes
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By choosing the waveguide spacing such that κ = Δ, the resulting square lattice constitutes a 2D hypercube for which the unitary transfer matrix after a coupling length L = π/(4Δ) is U = (1/√2)(1 i; i 1)⊗2.
“By choosing the waveguide spacing such that κ = Δ, the resulting square lattice constitutes a 2D HC (34) for which the unitary transfer matrix after a coupling length L = π/(4Δ) readsU=(12(1ii1))⊗2(3)where (…)⊗2 denotes the tensor square applied to the transfer matrix of a two-site coupler with equal output amplitudes for a single-site excitation, also designated as HC symmetry factor.”
From Exploring complex graphs using three-dimensional quantum walks of correlated photons (2021) · cites this paper as [34]
In 2011, Ma et al. used two polarization entangled photon pairs to study frustration in a tetramer, observing the transition between localized and resonating-valence-bond states at varying Heisenberg interaction strength.
“In 2011, Ma et al. used two polarization entangled photon pairs to study the process of frustration in a tetramer, a system with four spin-1/2 particles, observing the transition between localized and resonating-valence-bond states at varying Heisenberg interaction strength [632,633]”
From Photonic quantum information processing: a review (2019) · cites this paper as [633]
The Abstract discusses many-body interference on hypercubes, and section 4.2 discusses bosonic transformations on generalized hypercube graphs; neither addresses Ma et al.’s tetramer experiment. Searches for Ma et al., polarization-entangled photon pairs, frustration, and the localized-to-resonating-valence-bond transition found no passage about the claimed study. Page numbers were not available in our copy. (LLM, conf=0.76)
Experimental — accuracy not yet measuredPhase bookkeeping of all two-photon trajectories for the Σ1-Σ2, Σ2-Σ1, Σ2-Σ3, and Σ3-Σ2 input-output combinations reveals pairwise occurring paths with a phase difference of π, and therefore fully destructive quantum interference emerges.
“As predicted by the HC suppression laws (see section S3), phase bookkeeping of all two-photon trajectories for the Σ1-Σ2, Σ2-Σ1, Σ2-Σ3, and Σ3-Σ2 input-output combinations reveals pairwise occurring paths with a phase difference of π, and therefore, fully destructive quantum interference emerges (34).”
From Exploring complex graphs using three-dimensional quantum walks of correlated photons (2021) · cites this paper as [34]
Following this strategy to implement higher-dimensional graphs naturally gives rise to hypercube symmetries that have been predicted to leave their distinct signature on the evolution of correlated photon pairs.
“Notably, following this strategy to implement higher-dimensional graphs naturally gives rise to hypercube (HC) symmetries that have recently been predicted to leave their distinct signature on the evolution of correlated photon pairs (34).”
From Exploring complex graphs using three-dimensional quantum walks of correlated photons (2021) · cites this paper as [34]
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Cited by
Sorted by citations
Photonic quantum information processing: a review
Flamini, F., Spagnolo, N., & Sciarrino, F. (2019) · Reports on Progress in Physics · doi:10.1088/1361-6633/aad5b2 · Cited by 770
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Exploring complex graphs using three-dimensional quantum walks of correlated photons
Ehrhardt, M., Keil, R., Maczewsky, L. J., Dittel, C., Heinrich, M., & Szameit, A. (2021) · Science Advances · doi:10.1126/sciadv.abc5266 · Cited by 42
Self-citation
Metadata
- Authors
- Dittel, C., Keil, R., & Weihs, G.
- Venue
- Quantum Science and Technology
- Publisher
- IOP Publishing
- Published
- 2017-02-06
- Volume
- 2
- Issue
- 1
- Pages
- 015003
- ISSN
- 2058-9565
- Cited by
- 27
- References
- 14
- Licence
- Funders
- Canadian Institute for Advanced Research (Quantum Information Science Program)
- Austrian Science Fund (I 2562-N27, ; Austrian Science Fund: M 1849)
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