Sphere-Packing Bound for Symmetric Classical-Quantum Channels

2017/01/11 by Cheng, Hao-Chung, Hsieh, Min-Hsiu, Tomamichel, Marco
#FOS: Computer and information sciences #FOS: Physical sciences #Information Theory (cs.IT) #Quantum Physics (quant-ph)

paper · doi:10.48550/arxiv.1701.02957

Abstract

We provide a sphere-packing lower bound for the optimal error probability in finite blocklengths when coding over a symmetric classical-quantum channel. Our result shows that the pre-factor can be significantly improved from the order of the subexponential to the polynomial. The established pre-factor is essentially optimal because it matches the best known random coding upper bound in the classical case. Our approaches rely on a sharp concentration inequality in strong large deviation theory and crucial properties of the error-exponent function.

Related

• Error Exponents for Quantum Packing Problems via An Operator Layer Cake Theorem
• Moderate Deviation Analysis for Classical-Quantum Channels and Quantum Hypothesis Testing
• Error exponent of activated non-signaling assisted classical-quantum channel coding
• Performances of Block Codes Attaining the Expurgated and Cutoff Rate Lower Bounds on the Error Exponent of Binary Classical-Quantum Channels
• A Minimax Converse for Quantum Channel Coding