Estimating Quantum Entropy

摘要: The entropy of a quantum system is measure its randomness, and has applications in measuring entanglement. We study the problem estimating von Neumann entropy, $S(\rho)$ , Renyi $S_{\alpha }(\rho)$ an unknown mixed state $\rho $ $d$ dimensions, given access to independent copies . provide algorithms with copy complexity $O(d^{2/\alpha })$ for $\alpha $O(d^{2})$ non-integral >1$ These bounds are at least quadratic which order dependence on number required entire For integral other hand, we algorithm sub-quadratic $O(d^{2-2/\alpha show optimality by providing matching lower bound.