Darmstadt 2008 – scientific programme

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Q: Fachverband Quantenoptik und Photonik

Q 41: Quanteninformation (Konzepte und Methoden III)

Q 41.1: Talk

Thursday, March 13, 2008, 14:00–14:15, 1B

Channel Representation of Quantum Error-Correcting Codes — •Johannes Gütschow, Holger Vogts, and Reinhard Werner — Institut für Mathematische Physik, TU Braunschweig, www.imaph.tu-bs.de

Quantum error-correcting codes (qeccs) are essential for most of the proposed realizations of quantum computation to correct errors due to decoherence. Quantum convolutional codes (qccs) are a promising candidate for on line encoding and decoding of a flow of quantum information thus enabling the sending party to begin with the transmission of quantum information before the end of the flow (or a block) is reached. Analogously the decoding process can begin before the end of the transmission. Until now, only the noise and interaction with the environment were described in the channel formalism. We investigate qeccs and describe their encoders as channels. Block encoders are represented by memoryless channels, whereas convolutional encoders are described by memory channels. Convolutional encoders need to be "non-catastrophic", meaning an error on a single source qubit should only affect a finite number of target qubits. We investigate the relation between this condition and the "forgetfulness"-property of quantum memory channels.