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

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.Comment: 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 ring

Graphical description of the action of Clifford operators on stabilizer states

We introduce a graphical representation of stabilizer states and translate the action of Clifford operators on stabilizer states into graph operations on the corresponding stabilizer-state graphs. Our stabilizer graphs are constructed of solid and hollow nodes, with (undirected) edges between nodes and with loops and signs attached to individual nodes. We find that local Clifford transformations are completely described in terms of local complementation on nodes and along edges, loop complementation, and change of node type or sign. Additionally, we show that a small set of equivalence rules generates all graphs corresponding to a given stabilizer state; we do this by constructing an efficient procedure for testing the equality of any two stabilizer graphs.Comment: 14 pages, 8 figures. Version 2 contains significant changes. Submitted to PR

Fault-Tolerant Thresholds for Encoded Ancillae with Homogeneous Errors

I describe a procedure for calculating thresholds for quantum computation as a function of error model given the availability of ancillae prepared in logical states with independent, identically distributed errors. The thresholds are determined via a simple counting argument performed on a single qubit of an infinitely large CSS code. I give concrete examples of thresholds thus achievable for both Steane and Knill style fault-tolerant implementations and investigate their relation to threshold estimates in the literature.Comment: 14 pages, 5 figures, 3 tables; v2 minor edits, v3 completely revised, submitted to PR