BEGIN:VCALENDAR
VERSION:2.0
PRODID:-//Talks.cam//talks.cam.ac.uk//
X-WR-CALNAME:Talks.cam
BEGIN:VEVENT
SUMMARY:Moderate and Large Deviation Analysis for C-Q Channels - Min-Hsiu 
 Hsieh
DTSTART:20170608T130000Z
DTEND:20170608T140000Z
UID:TALK73002@talks.cam.ac.uk
CONTACT:Sergii Strelchuk
DESCRIPTION:This talk will combine two recent results of mine. \n1. arXiv:
 1704.05703: We study lower bounds on the optimal error probability in clas
 sical coding over classical-quantum channels at rates below the capacity\,
  commonly termed quantum sphere-packing bounds. Winter and Dalai have deri
 ved such bounds for classical-quantum channels\; however\, the exponents i
 n their bounds only coincide when the channel is classical. In this paper\
 , we show that these two exponents admit a variational representation and 
 are related by the Golden-Thompson inequality\, reaffirming that Dalai's e
 xpression is stronger in general classical-quantum channels. Second\, we e
 stablish a sphere-packing bound for classical-quantum channels\, which sig
 nificantly improves Dalai's 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 expo
 nent vanishes in the order of o(logn/n)\, indicating our sphere-packing bo
 und is almost exact in the high rate regime. Finally\, for a special class
  of symmetric classical-quantum channels\, we can completely characterize 
 its optimal error probability without the constant composition code assump
 tion. The main technical contributions are two converse Hoeffding bounds f
 or quantum hypothesis testing and the saddle-point properties of error exp
 onent functions.\n2.  arXiv:1701.03195: In this work\, we study the optima
 l decay of error probability when the transmission rate approaches channel
  capacity slowly\, a research area known as moderate deviation analysis. O
 ur result shows that the reliable communication through a classical-quantu
 m channel with positive channel dispersion is possible when the transmissi
 on rate approaches the channel capacity a rate slower than 1/sqrt(n). The 
 proof employs a refined sphere-packing bound in strong large deviation the
 ory\, and the asymptotic expansions of the error-exponent functions. Moder
 ate deviation analysis for quantum hypothesis testing is also established.
  The converse directly follows from our channel coding result. The achieva
 bility can be proved by using a recent noncommutative concentration inequa
 lity.
LOCATION:MR11\, Centre for Mathematical Sciences\, Wilberforce Road\, Camb
 ridge
END:VEVENT
END:VCALENDAR