01519nas a2200169 4500008003900000245004200039210004200081260001100123300001100134490000700145520106100152100001701213700002201230700002401252700001801276856005501294 2010 d00aEstimation of quantum finite mixtures0 aEstimation of quantum finite mixtures c1/2010 a0123320 v813 aWe consider the problem of determining the weights of a quantum ensemble. That is to say, given a quantum system that is in a set of possible known states according to an unknown probability law, we give strategies to estimate the individual probabilities, weights, or mixing proportions. Such strategies can be used to estimate the frequencies at which different independent signals are emitted by a source. They can also be used to estimate the weights of particular terms in a canonical decomposition of a quantum channel. The quality of these strategies is quantified by a covariance-type error matrix. According with this cost function, we give optimal strategies in both the single-shot and multiple-copy scenarios. The latter is also analyzed in the asymptotic limit of large number of copies. We give closed expressions of the error matrix for two-component quantum mixtures of qubit systems. The Fisher information plays an unusual role in the problem at hand, providing exact expressions of the minimum covariance matrix for any number of copies.1 aVicente, J I1 aCalsamiglia, John1 aMuĂ±oz-Tapia, Ramon1 aBagan, Emilio uhttp://link.aps.org/doi/10.1103/PhysRevA.81.012332