We investigate sampling procedures that certify that an arbitrary
\nquantum state on $n$ subsystems is close to an ideal mixed state
\n$\\varphi^{\\otimes n}$ for a given reference state $\\varphi$, up to
\nerrors on a few positions. This task makes no sense classically: it
\nwould correspond to certifying that a given bitstring was generated
\naccording to some desired probability distribution. However, in the
\nquantum case, this is possible if one has access to a prover who can
\nsupply a purification of the mixed state.<\/p>\n
In this work, we introduce the concept of mixed-state certification, and
\nwe show that a natural sampling protocol offers secure certification in
\nthe presence of a possibly dishonest prover: if the verifier accepts
\nthen he can be almost certain that the state in question has been
\ncorrectly prepared, up to a small number of errors.<\/p>\n
We then apply this result to two-party quantum coin-tossing. Given that
\nstrong coin tossing is impossible, it is natural to ask “how close can
\nwe get”. This question has been well studied and is nowadays well
\nunderstood from the perspective of the bias of individual coin tosses.
\nWe approach and answer this question from a different—and somewhat
\northogonal—perspective, where we do not look at individual coin tosses
\nbut at the global entropy instead. We show how two distrusting parties
\ncan produce a common high-entropy source, where the entropy is an
\narbitrarily small fraction below the maximum (except with negligible
\nprobability).<\/p>\n","protected":false},"excerpt":{"rendered":"
We investigate sampling procedures that certify that an arbitrary quantum state on $n$ subsystems is close to an ideal mixed state $\\varphi^{\\otimes n}$ for a given reference state $\\varphi$, up to errors on a few positions. This task makes no sense classically: it would correspond to certifying that a given bitstring was generated according to […]<\/p>\n","protected":false},"author":20,"featured_media":0,"template":"","class_list":["post-1132","seminar","type-seminar","status-publish","hentry"],"_links":{"self":[{"href":"https:\/\/webs.uab.cat\/giq\/wp-json\/wp\/v2\/seminar\/1132","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/webs.uab.cat\/giq\/wp-json\/wp\/v2\/seminar"}],"about":[{"href":"https:\/\/webs.uab.cat\/giq\/wp-json\/wp\/v2\/types\/seminar"}],"author":[{"embeddable":true,"href":"https:\/\/webs.uab.cat\/giq\/wp-json\/wp\/v2\/users\/20"}],"wp:attachment":[{"href":"https:\/\/webs.uab.cat\/giq\/wp-json\/wp\/v2\/media?parent=1132"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}