Entanglement in Graph States and its Applications

By M. Hein, Wolfgang Dür, Jens Eisert, Robert Raussendorf, Maarten Van den Nest, Hans J. Briegel. 2006

555 citations recorded by the source corpus.

Graph states form a rich class of entangled states that exhibit important aspects of multi-partite entanglement. At the same time, they can be described by a number of parameters that grows only moderately with the system size. They have a variety of applications in quantum information theory, most prominently as algorithmic resources in the context of the one-way quantum computer, but also in other fields such as quantum error correction and multi-partite quantum communication, as well as in the study of foundational issues such as non-locality and decoherence. In this review, we give a tutorial introduction into the theory of graph states. We introduce various equivalent ways how to define graph states, and discuss the basic notions and properties of these states. The focus of this review is on their entanglement properties. These include aspects of non-locality, bi-partite and multi-partite entanglement and its classification in terms of the Schmidt measure, the distillability properties of mixed entangled states close to a pure graph state, as well as the robustness of their entanglement under decoherence. We review some of the known applications of graph states, as well as proposals for their experimental implementation.

Subfields: Artificial Intelligence

View Paper: https://www.semanticscholar.org/paper/a0095ea6b13b95073088f2afb6e33e4d7761b04e

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Citations in the corpus

Many-Body Quantum Magic (2020, background): “Conversely, it is known that every stabilizer state is equivalent to a graph state, up to a tensor product of local Clifford unitaries [83, 84].”
Graphical calculus for Gaussian pure states (2010, background): “3 Weighted graph states for qubits have been deﬁned [40] but they are not stabilizer states.”
Flux-controlled quantum computation with Majorana fermions (2013, background): “The cluster state may be prepared in several ways [41, 43].”
A quantum processor based on coherent transport of entangled atom arrays (2021, unknown): “tivity between qubit arrays in parallel, we carry out preparation of entangled graph states: a large class of useful quantum information states, with examples ranging from GHZ states and cluster states to quantum error correction codes [30].”
Quantifying entanglement resources (2014, background): “Similarly, the N-qubit cluster state is locally inequivalent to any N-qubit GHZ state (or W state) [192, 193].”
Entanglement certification from theory to experiment (2018, methodology): “Apart from this generically applicable method, most available GME witnesses are tailored towards detecting specific states, such as graph states [270] or stabilizer states [186–188], Dicke states [271], or generally symmetric states [272].”
Emergent Quantum State Designs from Individual Many-Body Wave Functions (2021, background): “When the initial state is evolved under Ising interactions without on-site field terms for duration τ , the resultant state is equivalent to the graph state [49] associated with the graph in Fig.”