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SUMMARY:On Composite Quantum Hypothesis Testing - Mario Berta (Imperial)
DTSTART:20180503T131500Z
DTEND:20180503T141500Z
UID:TALK105586@talks.cam.ac.uk
CONTACT:Johannes Bausch
DESCRIPTION:We extend quantum Stein’s lemma in asymmetric quantum hypoth
 esis testing to composite null and alternative hypotheses. As our main res
 ult\, we show that the asymptotic error exponent for testing convex combin
 ations of quantum states rho against convex combinations of quantum states
  sigma(otimes n) is given by a regularized quantum relative entropy distan
 ce formula. We prove that in general such a regularization is needed but a
 lso discuss various settings where our formula as well as extensions there
 of become single-letter. This includes a novel operational interpretation 
 of the relative entropy of coherence in terms of hypothesis testing. For o
 ur proof\, we start from the composite Stein’s lemma for classical proba
 bility distributions and lift the result to the non-commutative setting by
  only using elementary properties of quantum entropy. Finally\, our findin
 gs also imply an improved Markov type lower bound on the quantum condition
 al mutual information in terms of the regularized quantum relative entropy
  – featuring an explicit and universal recovery map.
LOCATION:MR21\, Centre for Mathematical Sciences\, Wilberforce Road\, Camb
 ridge
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