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 Letters %D 2016 %T Quantifying {Entanglement} of {Maximal} {Dimension} in {Bipartite} {Mixed} {States} %A Sentís, Gael %A Eltschka, Christopher %A Gühne, Otfried %A Huber, Marcus %A Siewert, Jens %X The Schmidt coefficients capture all entanglement properties of a pure bipartite state and therefore determine its usefulness for quantum information processing. While the quantification of the corresponding properties in mixed states is important both from a theoretical and a practical point of view, it is considerably more difficult, and methods beyond estimates for the concurrence are elusive. In particular this holds for a quantitative assessment of the most valuable resource, the forms of entanglement that can only exist in high-dimensional systems. We derive a framework for lower bounding the appropriate measure of entanglement, the so-called G-concurrence, through few local measurements. Moreover, we show that these bounds have relevant applications also for multipartite states. %B Physical Review Letters %V 117 %P 190502 %U https://link.aps.org/doi/10.1103/PhysRevLett.117.190502 %R 10.1103/PhysRevLett.117.190502 %0 Journal Article %J Physical Review Letters %D 2016 %T Quantum Change Point %A Sentís, Gael %A Bagan, Emilio %A Calsamiglia, John %A Chiribella, Giulio %A Muñoz-Tapia, Ramon %B Physical Review Letters %V 117 %8 Jan-10-2016 %U http://link.aps.org/doi/10.1103/PhysRevLett.117.150502http://link.aps.org/article/10.1103/PhysRevLett.117.150502 %! Phys. Rev. Lett. %R 10.1103/PhysRevLett.117.150502 %0 Thesis %D 2014 %T Dealing with ignorance: universal discrimination, learning and quantum correlations %A Sentís, Gael %X The problem of discriminating the state of a quantum system among a number of hypothetical states is usually addressed under the assumption that one has perfect knowledge of the possible states of the system. In this thesis, I analyze the role of the prior information available in facing such problems, and consider scenarios where the information regarding the possible states is incomplete. In front of a complete ignorance of the possible states' identity, I discuss a quantum "programmable" discrimination machine for qubit states that accepts this information as input programs using a quantum encoding, rather than as a classical description. The optimal performance of these machines is studied for general qubit states when several copies are provided, in the schemes of unambiguous, minimum-error, and error-margin discrimination. Then, this type of automation in discrimination tasks is taken further. By realizing a programmable machine as a device that is trained through quantum information to perform a specific task, I propose a quantum "learning" machine for classifying qubit states that does not require a quantum memory to store the qubit programs and, nevertheless, performs as good as quantum mechanics permits. Such learning machine thus allows for several optimal uses with no need for retraining. A similar learning scheme is also discussed for coherent states of light. I present it in the context of the readout of a classical memory by means of classically correlated coherent signals, when these are produced by an imperfect source. I show that, in this case, the retrieval of information stored in the memory can be carried out more accurately when fully general quantum measurements are used. Finally, as a transversal topic, I propose an efficient algorithmic way of decomposing any quantum measurement into convex combinations of simpler (extremal) measurements. %I Universitat Autònoma de Barcelona %8 06/2014 %U http://arxiv.org/abs/1407.4690 %0 Journal Article %J Scientific Reports (Nature Publishing Group) %D 2012 %T Quantum learning without quantum memory %A Sentís, Gael %A Calsamiglia, John %A Muñoz-Tapia, Ramon %A Bagan, Emilio %X A quantum learning machine for binary classification of qubit states that does not require quantum memory is introduced and shown to perform with the minimum error rate allowed by quantum mechanics for any size of the training set. This result is shown to be robust under (an arbitrary amount of) noise and under (statistical) variations in the composition of the training set, provided it is large enough. This machine can be used an arbitrary number of times without retraining. Its required classical memory grows only logarithmically with the number of training qubits, while its excess risk decreases as the inverse of this number, and twice as fast as the excess risk of an “estimate-and-discriminate” machine, which estimates the states of the training qubits and classifies the data qubit with a discrimination protocol tailored to the obtained estimates. %B Scientific Reports (Nature Publishing Group) %I Nature Publishing Group %V 2 %P 708 %8 10/2012 %U http://www.nature.com/srep/2012/121005/srep00708/full/srep00708.html %R 10.1038/srep00708 %0 Journal Article %J Physical Review A %D 2010 %T Multicopy programmable discrimination of general qubit states %A Sentís, Gael %A Bagan, Emili %A Calsamiglia, John %A Muñoz-Tapia, Ramon %X Quantum state discrimination is a fundamental primitive in quantum statistics where one has to correctly identify the state of a system that is in one of two possible known states. A programmable discrimination machine performs this task when the pair of possible states is not a priori known but instead the two possible states are provided through two respective program ports. We study optimal programmable discrimination machines for general qubit states when several copies of states are available in the data or program ports. Two scenarios are considered: One in which the purity of the possible states is a priori known, and the fully universal one where the machine operates over generic mixed states of unknown purity. We find analytical results for both the unambiguous and minimum error discrimination strategies. This allows us to calculate the asymptotic performance of programmable discrimination machines when a large number of copies are provided and to recover the standard state discrimination and state comparison values as different limiting cases. %B Physical Review A %V 82 %P 042312 %8 10/2010 %U http://link.aps.org/doi/10.1103/PhysRevA.82.042312 %R 10.1103/PhysRevA.82.042312