Multipartite entanglement in heterogeneous systems

Abstract

Heterogeneous bipartite quantum pure states, composed of two subsystems with a different number of levels, cannot have both reductions maximally mixed. In this work, we demonstrate existence of a wide range of highly entangled states of heterogeneous multipartite systems consisting of $N>2$ parties such that every reduction to one and two parties is maximally mixed. Two constructions of generating genuinely multipartite maximally entangled states of heterogeneous systems for an arbitrary number of subsystems are presented. Such states are related to quantum error correction codes over mixed alphabets and mixed orthogonal arrays. Additionally, we show the advantages of considering heterogeneous systems in practical implementations of multipartite steering.

12 pages, 1 figure. Comments are very welcome!

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• Efficient Toffoli Gates Using Qudits
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Cited by in corpus (18)

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• Bounds on absolutely maximally entangled states from shadow inequalities, and the quantum MacWilliams identity
• Quantum Experiments and Graphs II: Quantum Interference, Computation and State Generation
• Quantum Experiments and Graphs III: High-Dimensional and Multi-Particle Entanglement
• $k$-Uniform states and quantum information masking
• Entanglement robustness against particle loss in multiqubit systems
• How entangled can a multi-party system possibly be?
• Quantum k-uniform states for heterogeneous systems from irredundant mixed orthogonal arrays
• Existence of locally maximally entangled quantum states via geometric invariant theory
• Constructions of $k$-uniform states from mixed orthogonal arrays
• Phase diagram of bipartite entanglement
• Near MDS and near quantum MDS codes via orthogonal arrays
• Synchronize accelerated clock in a multipartite relativistic quantum system
• Purity and construction of arbitrary dimensional $k$-uniform mixed states
• Coarse-grained entanglement classification through orthogonal arrays
• Feynman graphs and the large dimensional limit of multipartite entanglement
• Absolutely maximally entangled pure states of multipartite quantum systems
• Iterative methods for computing U-eigenvalues of non-symmetric complex tensors with application in quantum entanglement