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SUMMARY:On Composite Quantum Hypothesis Testing - Mario Berta\, Imperial
DTSTART:20171027T110000Z
DTEND:20171027T120000Z
UID:TALK93973@talks.cam.ac.uk
CONTACT:Steve Brierley
DESCRIPTION:We extend quantum Stein's lemma in asymmetric quantum hypothes
 is testing to composite null and alternative hypotheses. As our main resul
 t\, we show that the asymptotic error exponent for testing convex combinat
 ions of quantum states rho^(otimes n) against convex combinations of quant
 um states sigma^(otimes n) is given by a regularized quantum relative entr
 opy distance formula. We prove that in general such a regularization is ne
 eded but also discuss various settings where our formula as well as extens
 ions thereof become single-letter. This includes a novel operational inter
 pretation of the relative entropy of coherence in terms of hypothesis test
 ing. For our proof\, we start from the composite Stein's lemma for classic
 al probability distributions and lift the result to the non-commutative se
 tting by only using elementary properties of quantum entropy. Finally\, ou
 r findings also imply an improved Markov type lower bound on the quantum c
 onditional mutual information in terms of the regularized quantum relative
  entropy - featuring an explicit and universal recovery map.
LOCATION:MR11\, Centre for Mathematical Sciences\, Wilberforce Road\, Camb
 ridge
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