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CATEGORIES:CQIF Seminar
SUMMARY:Computable entanglement cost - Ludovico Lami\, Uni
versity of Amsterdan and QuSoft
DTSTART;TZID=Europe/London:20240613T141500
DTEND;TZID=Europe/London:20240613T151500
UID:TALK217909AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/217909
DESCRIPTION:Quantum information theory is plagued by the probl
em of regularisations\, which require the evaluati
on of formidable asymptotic quantities. This makes
it computationally intractable to gain a precise
quantitative understanding of the ultimate efficie
ncy of key operational tasks such as entanglement
manipulation. Here we consider the problem of comp
uting the asymptotic entanglement cost of preparin
g noisy quantum states under quantum operations wi
th positive partial transpose (PPT). A previously
claimed solution to this problem [Wang/Wilde\, PRL
125(4):040502 (2020)] is shown to be incorrect. W
e construct instead an alternative solution in the
form of two hierarchies of semi-definite programs
that converge to the true asymptotic value of the
entanglement cost from above and from below. Our
main result establishes that this convergence happ
ens exponentially fast\, thus yielding an efficien
t algorithm that approximates the cost up to an ad
ditive error ε in time poly(D\,log(1/ε))\, where D
is the underlying Hilbert space dimension. To our
knowledge\, this is the first time that an asympt
otic entanglement measure is shown to be efficient
ly computable despite no closed-form formula being
available. I will conclude the talk by presenting
some intriguing open questions suggested by our w
ork.
LOCATION:MR2
CONTACT:Laurens Lootens
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