Quantum Experiments and Graphs: Multiparty States as coherent superpositions of Perfect Matchings
arXiv:1705.06646 · doi:10.1103/PhysRevLett.119.240403
Abstract
We show a surprising link between experimental setups to realize high-dimensional multipartite quantum states and Graph Theory. In these setups, the paths of photons are identified such that the photon-source information is never created. We find that each of these setups corresponds to an undirected graph, and every undirected graph corresponds to an experimental setup. Every term in the emerging quantum superposition corresponds to a perfect matching in the graph. Calculating the final quantum state is in the complexity class #P-complete, thus cannot be done efficiently. To strengthen the link further, theorems from Graph Theory -- such as Hall's marriage problem -- are rephrased in the language of pair creation in quantum experiments. We show explicitly how this link allows to answer questions about quantum experiments (such as which classes of entangled states can be created) with graph theoretical methods, and potentially simulate properties of Graphs and Networks with quantum experiments (such as critical exponents and phase transitions).
arXiv comment6+5 pages, 4+7 figures
References in corpus (25)
- Quantum Computing
- Ultra-bright source of polarization-entangled photons
- Quantum Imaging with Undetected Photons
- A Multiparticle Generalization of Entanglement Swapping
- On-chip quantum interference between silicon photon-pair sources
- Witnessing multipartite entanglement
- Gaussian Boson Sampling
- Infrared Spectroscopy with Visible Light
- Multi-photon entanglement in high dimensions
- Detection of high-dimensional genuine multi-partite entanglement of mixed states
- Entanglement Percolation in Quantum Networks
- Automated Search for new Quantum Experiments
- The structure of multidimensional entanglement in multipartite systems
- Direct generation of photon triplets using cascaded photon-pair sources
- Direct generation of three-photon polarization entanglement
- Orbital angular momentum of photons and the entanglement of Laguerre-Gaussian modes
- Entanglement by Path Identity
- Quantum complex networks
- Entanglement percolation in quantum complex networks
- Coherence and multimode correlations from vacuum fluctuations in a microwave superconducting cavity
- Induced Coherence, Vacuum Fields, and Complementarity in Biphoton Generation
- Quantifying the Momentum Correlation between Two Light Beams by Detecting One
- Multipartite entanglement percolation
- On-chip generation of photon-triplet states
- Rotational covariance and GHZ contradictions for three or more particles of any dimension
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- A novel approach to perturbative calculations for a large class of interacting boson theories
- Questions on the Structure of Perfect Matchings inspired by Quantum Physics
- Experimental Solutions to the High-Dimensional Mean King's Problem
- Digital Discovery of a Scientific Concept at the Core of Experimental Quantum Optics
- Deep Quantum Graph Dreaming: Deciphering Neural Network Insights into Quantum Experiments
- Experimental study of the distributions of off-diagonal scattering-matrix elements of quantum graphs with symplectic symmetry
- Graph-theoretic insights on the constructability of complex entangled states
- Nonlinear-linear duality for multipath quantum interference
- Quantum interference with time-frequency modes and multiple-photons generated by a silicon nitride microresonator
- Automated Discovery of Non-local Photonic Gates