A Simple Comparative Analysis of Exact and Approximate Quantum Error Correction

Cafaro, Carlo; van Loock, Peter

doi:10.1142/S1230161214500024

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A Simple Comparative Analysis of Exact and Approximate Quantum Error Correction

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Cafaro, Carlo
van Loock Research Group, Research Groups, Max Planck Institute for the Science of Light, Max Planck Society;

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van Loock, Peter
van Loock Research Group, Research Groups, Max Planck Institute for the Science of Light, Max Planck Society;

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Citation

Cafaro, C., & van Loock, P. (2014). A Simple Comparative Analysis of Exact and Approximate Quantum Error Correction. OPEN SYSTEMS & INFORMATION DYNAMICS, 21(3): 1450002. doi:10.1142/S1230161214500024.

Cite as: https://hdl.handle.net/11858/00-001M-0000-002D-65B3-7

Abstract

We present a comparative analysis of exact and approximate quantum error correction by means of simple unabridged analytical computations. For the sake of clarity, using primitive quantum codes, we study the exact and approximate error correction of the two simplest unital (Pauli errors) and nonunital (non-Pauli errors) noise models, respectively. The similarities and differences between the two scenarios are stressed. In addition, the performances of quantum codes quantified by means of the entanglement fidelity for different recovery schemes are taken into consideration in the approximate case. Finally, the role of self-complementarity in approximate quantum error correction is briefly addressed.