The detection of change points is a pivotal task in statistical analysis. In the quantum realm, it is a new primitive where one aims at identifying the point where a source that supposedly prepares a sequence of particles in identical quantum states starts preparing a mutated one. We obtain the optimal procedure to identify the change point with certainty-naturally at the price of having a certain probability of getting an inconclusive answer. We obtain the analytical form of the optimal probability of successful identification for any length of the particle sequence. We show that the conditional success probabilities of identifying each possible change point show an unexpected oscillatory behavior. We also discuss local (online) protocols and compare them with the optimal procedure.

%B PHYSICAL REVIEW LETTERS %V 119 %R 10.1103/PhysRevLett.119.140506 %0 Journal Article %J Physical Review A %D 2010 %T Estimation of quantum finite mixtures %A de Vicente, J. I. %A John Calsamiglia %A Muñoz-Tapia, Ramon %A Bagan, Emilio %X We 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. %B Physical Review A %V 81 %P 012332 %8 1/2010 %U http://link.aps.org/doi/10.1103/PhysRevA.81.012332 %R 10.1103/PhysRevA.81.012332 %0 Journal Article %J Physical Review A (Atomic, Molecular, and Optical Physics) %D 2004 %T Entanglement-assisted alignment of reference frames using a dense covariant coding %A Bagan, Emili %A Baig, Marià %A Muñoz-Tapia, Ramon %X We present a procedure inspired by dense coding, which enables a highly efficient transmission of information of a continuous nature. The procedure requires the sender and the recipient to share a maximally entangled state. We deal with the concrete problem of aligning reference frames or trihedra by means of a quantum system. We find the optimal covariant measurement and compute the corresponding average error, which has a remarkably simple close form. The connection of this procedure with that of estimating unitary transformations on qubits is briefly discussed. %B Physical Review A (Atomic, Molecular, and Optical Physics) %I American Physical Society %V 69 %P 050303 %8 05/2004 %G eng %U http://link.aps.org/doi/10.1103/PhysRevA.69.050303 %R 10.1103/PhysRevA.69.050303