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DTSTART;TZID=America/Toronto:20240213T150000
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URL:https://uwaterloo.ca/institute-for-quantum-computing/events/entanglemen
 t-cost-infinite-dimensional-physical-systems
LOCATION:QNC - Quantum Nano Centre 200 University Avenue West 1201 Waterloo
  ON N2L 3G1 Canada
SUMMARY:Entanglement cost for infinite-dimensional physical systems
CLASS:PUBLIC
DESCRIPTION:CS/MATH SEMINAR - KOHDAI KUROIWA\, PERIMETER INSTITUTE\n\nUnive
 rsity of Waterloo\, 200 University Ave. W. Waterloo\, ON. QNC 1201\n+ ZOOM
 \n\nIn this work\, we prove that the entanglement cost equals the\nregular
 ized entanglement of formation for any infinite-dimensional\nquantum state
  with finite quantum entropy on at least one of the\nsubsystems. This gene
 ralizes a foundational result in quantum\ninformation theory that was prev
 iously formulated only for operations\nand states on finite-dimensional sy
 stems. The extension to infinite\ndimensions is nontrivial because the con
 ventional tools for\nestablishing both the direct and converse bounds\, i.
 e.\, strong\ntypically\, monotonicity\, and asymptotic continuity\, are no
  longer\ndirectly applicable. To address this problem\, we construct a new
 \nentanglement dilution protocol for infinite-dimensional states\nimplemen
 table by local operations and a finite amount of one-way\nclassical commun
 ication (one-way LOCC)\, using weak and strong\ntypicality multiple times.
  We also prove the optimality of this\nprotocol among all protocols even u
 nder infinite-dimensional separable\noperations by developing an argument 
 based on alternative forms of\nmonotonicity and asymptotic continuity of t
 he entanglement of\nformation for infinite-dimensional states. Along the w
 ay\, we derive a\nnew integral representation for the quantum entropy of\n
 infinite-dimensional states\, which we believe to be of independent\ninter
 est. Our results allow us to fully characterize an important\noperational 
 entanglement measure -- the entanglement cost -- for all\ninfinite-dimensi
 onal physical systems. This talk is based\non arXiv:2401.09554 [https://a
 rxiv.org/abs/2401.09554]. 
DTSTAMP:20260430T014333Z
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