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DTSTART:20240310T070000
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DTSTART:20231105T060000
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DTSTART;TZID=America/Toronto:20240328T130000
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URL:https://uwaterloo.ca/institute-for-quantum-computing/events/smooth-min-
 entropy-lower-bounds-approximation-chains
LOCATION:QNC - Quantum Nano Centre 200 University Avenue West 1201 Waterloo
  ON N2L 3G1 Canada
SUMMARY:Smooth min-entropy lower bounds for approximation chains
CLASS:PUBLIC
DESCRIPTION:IQC SEMINAR - ASHUTOSH MARWAH\, UNIVERSITY OF MONTREAL\n\nQuant
 um-Nano Centre\, 200 University Ave West\, Room QNC 1201\nWaterloo\, ON CA
  N2L 3G1\n\nFor a state $\\rho_{A_1^n B}$\, we call a sequence of states\n
 $(\\sigma_{A_1^k B}^{(k)})_{k=1}^n$ an approximation chain if for every\n$
 1 \\leq k \\leq n$\, $\\rho_{A_1^k B} \\approx_\\epsilon \\sigma_{A_1^k\nB
 }^{(k)}$. In general\, it is not possible to lower bound the smooth\nmin-e
 ntropy of such a $\\rho_{A_1^n B}$\, in terms of the entropies of\n$\\sigm
 a_{A_1^k B}^{(k)}$ without incurring very large penalty factors.\nIn this 
 paper\, we study such approximation chains under additional\nassumptions. 
 We begin by proving a simple entropic triangle\ninequality\, which allows 
 us to bound the smooth min-entropy of a state\nin terms of the R\\'enyi en
 tropy of an arbitrary auxiliary state while\ntaking into account the smoot
 h max-relative entropy between the two.\nUsing this triangle inequality\, 
 we create lower bounds for the smooth\nmin-entropy of a state in terms of 
 the entropies of its approximation\nchain in various scenarios. In particu
 lar\, utilising this approach\, we\nprove approximate versions of the asym
 ptotic equipartition property\nand entropy accumulation. In a companion pa
 per\, we show that the\ntechniques developed in this paper can be used to 
 prove the security\nof quantum key distribution in the presence of source 
 correlations.
DTSTAMP:20260420T001126Z
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