QLunch: The spectrum of asymptotic LOCC conversion – University of Copenhagen

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QLunch: The spectrum of asymptotic LOCC conversion

Speaker: Asger Kjærulff Jensen from QMATH

The spectrum of asymptotic LOCC conversion

The objects of study are finite dimensional k-partite pure quantum states, and convertability between these states via Local Operations and Classical Communication (LOCC). These states form a semiring under direct sum and tensor product, and ordering this semiring by LOCC convertability yields an ordered semiring. We apply Strassen’s spectral theorem, which you may remember from Peter Vrana’s last quantum lunch. The asymptotic extraction rate between states with converse error exponent, r, is the rate at which one can extract one state from another with probability of success decaying as 2^{-nr}. The spectrum immediately yields a formula for this extraction rate. As with the SLOCC case, we can only determine the full spectrum in the case k=2, where we get a concrete formula extending a result by Winter et al. from 2002.