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Deutsche Physikalische Gessellschaft IOP Institute of Physics

Graph state generation with noisy mirror-inverting spin chains

Focus on Measurement-Based Quantum Information Processing

Stephen R Clark1, Alexander Klein, Martin Bruderer and Dieter Jaksch

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Part of Focus on Measurement-Based Quantum Information Processing

We investigate the influence of noise on a graph state generation scheme which exploits a mirror inverting spin chain. Within this scheme the spin chain is used repeatedly as an entanglement bus (EB) to create multi-partite entanglement. The noise model we consider comprises of each spin of this EB being exposed to independent local noise which degrades the capabilities of the EB. Here we concentrate on quantifying its performance as a single-qubit channel and as a mediator of a two-qubit entangling gate, since these are basic operations necessary for graph state generation using the EB. In particular, for the single-qubit case we numerically calculate the average channel fidelity and whether the channel becomes entanglement breaking, i.e. expunges any entanglement the transferred qubit may have with other external qubits. We find that neither local decay nor dephasing noise cause entanglement breaking. This is in contrast to local thermal and depolarizing noise where we determine a critical length and critical noise coupling, respectively, at which entanglement breaking occurs. The critical noise coupling for local depolarizing noise is found to exhibit a power-law dependence on the chain length. For two-qubits we similarly compute the average gate fidelity and whether the ability for this gate to create entanglement is maintained. The concatenation of these noisy gates for the construction of a five-qubit linear cluster state and a Greenberger–Horne–Zeilinger state indicates that the level of noise that can be tolerated for graph state generation is tightly constrained.


PACS

03.67.Mn Entanglement measures, witnesses, and other characterizations

03.65.Ud Entanglement and quantum nonlocality (e.g. EPR paradox, Bell's inequalities, GHZ states, etc.)

05.40.Ca Noise

Subjects

Computational physics

Statistical physics and nonlinear systems

Quantum information and quantum mechanics

Dates

Issue 6 (June 2007)

Received 16 February 2007

Published 29 June 2007



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