Modeling Pauli measurements on graph states with nearest-neighbor classical communication

Abstract

We propose a communication-assisted local-hidden-variable model that yields the correct outcome for the measurement of any product of Pauli operators on an arbitrary graph state, i.e., that yields the correct global correlation among the individual measurements in the Pauli product. Within this model, communication is restricted to a single round of message passing between adjacent nodes of the graph. We show that any model sharing some general properties with our own is incapable, for at least some graph states, of reproducing the expected correlations among all subsets of the individual measurements. The ability to reproduce all such correlations is found to depend on both the communication distance and the symmetries of the communication protocol.

9 pages, 2 figures. Version 2 significantly revised. Now includes a site-invariant protocol for linear chains and a proof that no limited communication protocol can correctly predict all quantum correlations for rings

References in corpus (7)

• Persistent entanglement in arrays of interacting particles
• Graphical description of the action of local Clifford transformations on graph states
• Universal resources for measurement-based quantum computation
• Bell Inequalities for Graph States
• Nonlocality of cluster states of qubits
• Fast simulation of stabilizer circuits using a graph state representation
• Optimal classical-communication-assisted local model of n-qubit Greenberger-Horne-Zeilinger correlations

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• Experimental Test of Bell inequalities with Six-Qubit Graph States
• Simulation of equatorial von Neumann measurements on GHZ states using nonlocal resources
• Playing nonlocal games with phases of quantum matter
• A multi-player, multi-team nonlocal game for the toric code
• Unconditional quantum magic advantage in shallow circuit computation
• Possibilistic simulation of quantum circuits by classical circuits
• Stabilizer states and local realism
• Error Channels and the Threshold for Fault-tolerant Quantum Computation
• The genuinely multipartite nonlocality of graph states is model-dependent
• Investigation of quantum entanglement simulation by random variables theories augmented by either classical communication or nonlocal effects
• Self-Testing Graph States Permitting Bounded Classical Communication