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SUMMARY:Computable entanglement cost - Ludovico Lami\, University of Amste
 rdan and QuSoft
DTSTART:20240613T131500Z
DTEND:20240613T141500Z
UID:TALK217909@talks.cam.ac.uk
CONTACT:Laurens Lootens
DESCRIPTION:Quantum information theory is plagued by the problem of regula
 risations\, which require the evaluation of formidable asymptotic quantiti
 es. This makes it computationally intractable to gain a precise quantitati
 ve understanding of the ultimate efficiency of key operational tasks such 
 as entanglement manipulation. Here we consider the problem of computing th
 e asymptotic entanglement cost of preparing noisy quantum states under qua
 ntum operations with positive partial transpose (PPT). A previously claime
 d solution to this problem [Wang/Wilde\, PRL 125(4):040502 (2020)] is show
 n to be incorrect. We construct instead an alternative solution in the for
 m of two hierarchies of semi-definite programs that converge to the true a
 symptotic value of the entanglement cost from above and from below. Our ma
 in result establishes that this convergence happens exponentially fast\, t
 hus yielding an efficient algorithm that approximates the cost up to an ad
 ditive error ε in time poly(D\,log(1/ε))\, where D is the underlying Hil
 bert space dimension. To our knowledge\, this is the first time that an as
 ymptotic entanglement measure is shown to be efficiently computable despit
 e no closed-form formula being available. I will conclude the talk by pres
 enting some intriguing open questions suggested by our work.
LOCATION:MR2
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