Asymptotic majorization of probability distributions and LOCC transformations

2018. 10. 17. 16:00
Asger Kjærulff Jensen

Given two pure bipartite quantum states $|ψ\rangle$ and $|φ\rangle$, Nielsen’s theorem states that $|ψ\rangle$ can be exactly transformed into $|φ\rangle$ via local quantum operations and classical communication (LOCC), if and only if  $P\preceq Q$ (P is majorized by Q). Here P and Q are the squared Schmidt coefficients of $|ψ\rangle$ and $|φ\rangle$, respectively. From a quantum resource theory perspective, this motivates determining for which P and Q the relation $P^{\otimes N}\preceq Q^{\otimes N}$ holds for large N, as this relates to asymptotic extraction rates between quantum states. This talk explores and provides a solution to this problem, yielding an expression for the exact asymptotic extraction rate between pure bipartite states: $\min_{\alpha\in [0,\infty]}\frac{H_\alpha(P)}{H_\alpha(Q)}$.