Encoding graphs into quantum states: an axiomatic approach

Abstract

A fundamental problem in quantum information is to describe efficiently multipartite quantum states. An efficient representation in terms of graphs exists for several families of quantum states (graph, cluster, stabilizer states), motivating us to extend this construction to other classes. We introduce an axiomatic framework for mapping graphs to quantum states of a suitable physical system. Starting from three general axioms we derived a rich structure which includes and generalizes several classes of multipartite entangled state, like graph/stabilizer states, Gaussian cluster states, quantum random networks and projected entangled pair states (PEPS). Due to its flexibility we can extend the present formalism to include directed and weighted graphs.

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Cited by in corpus (12)

• Encoding Hypergraphs into Quantum States
• Thermodynamic formalism for dissipative quantum walks
• Bipartite separability and non-local quantum operations on graphs
• Relationship among locally maximally entanglable states, W states and hypergraph states under local unitary transformations
• Qudit hypergraph states and their properties
• Multipartite Entanglement and Hypergraph states of three qubits
• Thermal state entanglement entropy on a quantum graph
• Controlled remote implementation of operations via graph states
• Entropic measure and hypergraph states
• Laplacian matrices of weighted digraphs represented as quantum states
• Symmetric and Antisymmetric Quantum States from Graph Structure and Orientation
• Renormalization and small-world model of fractal quantum repeater networks