Sampling mixed quantum states
Seminar author:Frederic Dupuis
Event date and time:05/11/2018 02:00:pm
Event location:GIQ Seminar Room (C5/262)
Event contact:frederic.dupuis@loria.fr
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 some desired probability distribution. However, in the
quantum case, this is possible if one has access to a prover who can
supply a purification of the mixed state.
In this work, we introduce the concept of mixed-state certification, and
we show that a natural sampling protocol offers secure certification in
the presence of a possibly dishonest prover: if the verifier accepts
then he can be almost certain that the state in question has been
correctly prepared, up to a small number of errors.
We then apply this result to two-party quantum coin-tossing. Given that
strong coin tossing is impossible, it is natural to ask “how close can
we get”. This question has been well studied and is nowadays well
understood from the perspective of the bias of individual coin tosses.
We approach and answer this question from a different—and somewhat
orthogonal—perspective, where we do not look at individual coin tosses
but at the global entropy instead. We show how two distrusting parties
can produce a common high-entropy source, where the entropy is an
arbitrarily small fraction below the maximum (except with negligible
probability).