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.

1 aSentís, Gael1 aCalsamiglia, John1 aMuñoz-Tapia, Ramon uhttps://grupsderecerca.uab.cat/giq/node/84101346nas a2200169 4500008003900000245008800039210006900127300001100196490000800207520080100215100001801016700002601034700002001060700001801080700001801098856006001116 2016 d00aQuantifying {Entanglement} of {Maximal} {Dimension} in {Bipartite} {Mixed} {States}0 aQuantifying Entanglement of Maximal Dimension in Bipartite Mixed a1905020 v1173 aThe 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.1 aSentís, Gael1 aEltschka, Christopher1 aGühne, Otfried1 aHuber, Marcus1 aSiewert, Jens uhttps://link.aps.org/doi/10.1103/PhysRevLett.117.19050200519nas a2200169 4500008003900000022001400039245002500053210002500078260001600103490000800119100001800127700001800145700002200163700002300185700002400208856011700232 2016 d a0031-900700aQuantum Change Point0 aQuantum Change Point cJan-10-20160 v1171 aSentís, Gael1 aBagan, Emilio1 aCalsamiglia, John1 aChiribella, Giulio1 aMuñoz-Tapia, Ramon uhttp://link.aps.org/doi/10.1103/PhysRevLett.117.150502http://link.aps.org/article/10.1103/PhysRevLett.117.15050202307nas a2200109 4500008003900000245008800039210006900127260004800196520190000244100001802144856003502162 2014 d00aDealing with ignorance: universal discrimination, learning and quantum correlations0 aDealing with ignorance universal discrimination learning and qua bUniversitat Autònoma de Barcelonac06/20143 aThe 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.1 aSentís, Gael uhttp://arxiv.org/abs/1407.469001375nas a2200169 4500008003900000245004400039210004400083260003700127300000800164490000600172520087200178100001801050700002201068700002401090700001801114856007301132 2012 d00aQuantum learning without quantum memory0 aQuantum learning without quantum memory bNature Publishing Groupc10/2012 a7080 v23 aA 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.1 aSentís, Gael1 aCalsamiglia, John1 aMuñoz-Tapia, Ramon1 aBagan, Emilio uhttp://www.nature.com/srep/2012/121005/srep00708/full/srep00708.html01581nas a2200169 4500008003900000245006600039210006600105260001200171300001100183490000700194520107400201100001801275700001701293700002201310700002401332856005501356 2010 d00aMulticopy programmable discrimination of general qubit states0 aMulticopy programmable discrimination of general qubit states c10/2010 a0423120 v823 aQuantum 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.1 aSentís, Gael1 aBagan, Emili1 aCalsamiglia, John1 aMuñoz-Tapia, Ramon uhttp://link.aps.org/doi/10.1103/PhysRevA.82.042312