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The accuracy of quantum information processing (QIP) protocols using qubit cluster states is known to be af- fected significantly by sources of environmental decoher- ence and imperfections (13) and removing all but only the most essential qubits in the cluster state is key to effective simulations (14). The central aim of this work is the study of the behavior of QIP carried out when an environment affects single-mode d-dimensional systems that comprise the qudit cluster states. We find that dis- advantages appear, in terms of robustness of QIP pro- tocols, when moving to higher dimensions; the accuracy of simulations decreases as the dimension increases. In addition, entangled pairs of qubit linear clusters appear to be more resilient to environmental effects in compari- son to qudit clusters. Our study questions the worthiness of efforts made toward the extension of one-way QC to higher-dimensional systems, where global properties of the entangled resources are crucial for the performance of a given QIP protocol.

physical review. a, atomic, molecular, and optical physics/physical review, a, atomic, molecular, and optical physics

Decoherence-based exploration of<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>d</mml:mi></mml:math>-dimensional one-way quantum computation: Information transfer and basic gates

Decoherence-based exploration ofd-dimensional one-way quantum computation: Information transfer and basic gates