Sphere-packing bound for classical-quantum channels

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Conference Proceeding
IEEE International Symposium on Information Theory - Proceedings, 2018, 2018-January pp. 479 - 483
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© 2017 IEEE. We study lower bounds on the optimal error probability in channel coding at rates below capacity, commonly termed sphere-packing bounds. In this work, we establish a sphere-packing bound for classical-quantum channels, which significantly improves previous prefactor from the order of subexponential to polynomial. Furthermore, the gap between the obtained error exponent for constant composition codes and the best known classical random coding exponent vanishes in the order of o(log n/n), indicating our sphere-packing bound is almost exact in the high rate regime. The main technical contributions are two converse Hoeffding bounds for quantum hypothesis testing and the saddle-point properties of error exponent functions.
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