Multipartite entanglement classes of a multiport beam-splitter

Abstract

The states generated by a multiport beam-splitter usually display genuine multipartite entanglement between the many spatial modes. Here we investigate the different classes of multipartite entangled states that arise in this practical situation, working within the paradigm of Stochastic Local Operations with Classical Communication. We highlight three scenarios, one where the multipartite entanglement classes follow a total number hierarchy, another where the various classes follow a nonclassicality degree hierarchy and a third one that is a combination of the previous two. Moreover, the multipartite entanglement of higher-dimensional versions of Dicke states relate naturally to our results.

arXiv comment10 pages, addition of 2 figures, 2 sections in the Appendix. Updated references, modified labeling of submatrices in the proof of Observation 3, minor corrections in the proof of Observation 5. Connections to higher-dimensional versions of Dicke states. Comments welcome!

References in corpus (36)

• Quantum entanglement
• Three qubits can be entangled in two inequivalent ways
• Entanglement detection
• Classification of mixed three-qubit states
• A Schmidt number for density matrices
• Entanglement of pure states for a single copy
• A computable measure of nonclassicality for light
• Normal forms and entanglement measures for multipartite quantum states
• Classification of multipartite entangled states by multidimensional determinants
• Schmidt number witnesses and bound entanglement
• Bell's theorem with and without inequalities for the three-qubit Greenberger-Horne-Zeilinger and W states
• Converting Nonclassicality into Entanglement
• Classification of multipartite entanglement in all dimensions
• Inductive classification of multipartite entanglement under SLOCC
• Genuinely multipartite entangled quantum states with fully local hidden variable models and hidden multipartite nonlocality
• Quantum scissors - finite-dimensional states engineering
• Classification of general n-qubit states under stochastic local operations and classical communication in terms of the rank of coefficient matrix
• Converting multilevel nonclassicality into genuine multipartite entanglement
• Characterizing multipartite entanglement classes via higher-dimensional embeddings
• Entanglement and nonclassicality for multi-mode radiation field states
• Verification of phased Dicke states
• Ideal Quantum Tele-amplification up to a Selected Energy Cut-off using Linear Optics
• Range criterion and classification of true entanglement in $2\times M\times N$ system
• Classification of multipartite entanglement containing infinitely many kinds of states
• Entanglement classification with matrix product states
• Analyzing quantum entanglement with the Schmidt decomposition in operator space
• Entanglement convertibility for infinite dimensional pure bipartite states
• Classification of arbitrary-dimensional multipartite pure states under stochastic local operations and classical communication using the rank of coefficient matrix
• Experimental entanglement generation using multiport beam splitters
• Limits to multipartite entanglement generation with bosons and fermions
• Generating Greenberger-Horne-Zeilinger states using multiport splitters
• No-go theorems for photon state transformations in quantum linear optics
• Nonclassical states that generate zero entanglement with a beam splitter
• Bipartite bound entanglement in continuous variables through deGaussification
• Criteria for SLOCC and LU Equivalence of Generic Multi-qudit States
• Multipartite States under Elementary Local Operations

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