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.

}, issn = {0031-9007}, doi = {10.1103/PhysRevLett.119.140506}, author = {Sent{\'\i}s, Gael and Calsamiglia, John and Mu{\~n}oz-Tapia, Ramon} } @article {784, title = {Quantum Change Point}, journal = {Physical Review Letters}, volume = {117}, year = {2016}, month = {Jan-10-2016}, issn = {0031-9007}, doi = {10.1103/PhysRevLett.117.150502}, url = {http://link.aps.org/doi/10.1103/PhysRevLett.117.150502http://link.aps.org/article/10.1103/PhysRevLett.117.150502}, author = {Sent{\'\i}s, Gael and Bagan, Emilio and Calsamiglia, John and Chiribella, Giulio and Mu{\~n}oz-Tapia, Ramon} } @article {gendra_beating_2012, title = {Beating noise with abstention in state estimation}, journal = {New Journal of Physics}, volume = {14}, number = {10}, year = {2012}, pages = {105015}, issn = {1367-2630}, doi = {10.1088/1367-2630/14/10/105015}, url = {http://iopscience.iop.org/1367-2630/14/10/105015}, author = {Gendra, Bernat and Ronco-Bonvehi, Elio and Calsamiglia, John and Mu{\~n}oz-Tapia, Ramon and Bagan, Emilio} } @article {Sentis:2012uq, title = {Quantum learning without quantum memory}, journal = {Scientific Reports (Nature Publishing Group)}, volume = {2}, year = {2012}, month = {10/2012}, pages = {708}, publisher = {Nature Publishing Group}, abstract = {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 {\textquotedblleft}estimate-and-discriminate{\textquotedblright} machine, which estimates the states of the training qubits and classifies the data qubit with a discrimination protocol tailored to the obtained estimates.}, doi = {10.1038/srep00708}, url = {http://www.nature.com/srep/2012/121005/srep00708/full/srep00708.html}, author = {Sent{\'\i}s, Gael and Calsamiglia, John and Mu{\~n}oz-Tapia, Ramon and Bagan, Emilio} } @mastersthesis {392, title = {Quantum Accuracy Limits and Benchmarks in Continuos Variable Systems}, volume = {Doctorat en F{\'\i}sica}, year = {2011}, month = {10/2011}, school = {Universitat Aut{\`o}noma de Barcelona}, type = {PhD}, address = {Barcelona}, author = {Bracons, Mariona (formerly Mariona Aspachs)} } @mastersthesis {295, title = {Discriminaci{\'o} qu{\`a}ntica}, volume = {Grau en F{\'\i}sica}, year = {2010}, month = {07/2010}, school = {Universitat Aut{\`o}noma de Barcelona}, type = {BSc Thesis}, address = {Barcelona}, abstract = {S{\textquoteright}estudia la discriminaci{\'o} de diferents sistemes qu{\`a}ntics. S{\textquoteright}analitza el proc{\'e}s de discriminaci{\'o} entre q{\'u}bits, i es compara amb la discriminaci{\'o} de mesures projectives. Seguidament, es busquen les condicions en les quals la discriminaci{\'o} entre mesures projectives {\'e}s perfecta, i es realitza el mateix per a la discriminaci{\'o} de transformacions unit{\`a}ries, per tal de comparar ambd{\'o}s resultats.}, author = {Arnau Pujol} } @article {de_vicente_estimation_2010, title = {Estimation of quantum finite mixtures}, journal = {Physical Review A}, volume = {81}, number = {1}, year = {2010}, month = {1/2010}, pages = {012332}, abstract = {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.}, doi = {10.1103/PhysRevA.81.012332}, url = {http://link.aps.org/doi/10.1103/PhysRevA.81.012332}, author = {de Vicente, J. I. and Calsamiglia, John and Mu{\~n}oz-Tapia, Ramon and Bagan, Emilio} } @article {sentis_multicopy_2010, title = {Multicopy programmable discrimination of general qubit states}, journal = {Physical Review A}, volume = {82}, number = {4}, year = {2010}, month = {10/2010}, pages = {042312}, abstract = {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.}, doi = {10.1103/PhysRevA.82.042312}, url = {http://link.aps.org/doi/10.1103/PhysRevA.82.042312}, author = {Sent{\'\i}s, Gael and Bagan, Emili and Calsamiglia, John and Mu{\~n}oz-Tapia, Ramon} } @article {rapcan_recycling_2010, title = {Recycling of qubits}, journal = {Physica Scripta}, volume = {T140}, year = {2010}, pages = {014059}, abstract = {We consider a finite number, N, of qubits that encode a pure single qubit state SU(2) covariantly. Given the N-qubit state has already been measured optimally to estimate the single-qubit state, we analyse the maximum information obtainable by a second, and subsequent observers ignorant of important details of the previous measurements. We quantify the information acquired by each observer as a function of N and of the number of independent observers that in succession have independently measured the same ensemble of qubits before him.}, issn = {0031-8949}, doi = {10.1088/0031-8949/2010/T140/014059}, url = {http://iopscience.iop.org/1402-4896/2010/T140/014059?fromSearchPage=true}, author = {P Rapcan and Calsamiglia, John and Mu{\~n}oz-Tapia, Ramon and Bagan, Emilio and V Buzek} } @article {Aspachs2009, title = {Phase estimation for thermal Gaussian states}, journal = {Physical Review A (Atomic, Molecular, and Optical Physics)}, volume = {79}, number = {3}, year = {2009}, month = {03/2009}, pages = {033834{\textendash}12}, keywords = {gaussian noise, gaussian states, optical losses, optical squeezing, phase estimation, quantum noise, thermal noise}, doi = {10.1103/PhysRevA.79.033834}, url = {http://link.aps.org/abstract/PRA/v79/e033834}, author = {Aspachs, Mariona and Calsamiglia, John and Mu{\~n}oz-Tapia, Ramon and Bagan, Emili} } @article {Calsamiglia2009, title = {Phase-covariant quantum benchmarks}, journal = {Physical Review A (Atomic, Molecular, and Optical Physics)}, volume = {79}, number = {5}, year = {2009}, pages = {050301{\textendash}4}, keywords = {quantum benchmarks}, issn = {1050-2947}, doi = {10.1103/PhysRevA.79.050301}, url = {http://link.aps.org/doi/10.1103/PhysRevA.79.050301}, author = {Calsamiglia, John and Aspachs, Mariona and Mu{\~n}oz-Tapia, Ramon and Bagan, Emili} } @article {Bagan2008, title = {Phase variance of squeezed vacuum states}, journal = {Physical Review A (Atomic, Molecular, and Optical Physics)}, volume = {78}, number = {4}, year = {2008}, month = {10/2008}, pages = {043829{\textendash}7}, keywords = {optical squeezing}, doi = {10.1103/PhysRevA.78.043829}, url = {http://link.aps.org/abstract/PRA/v78/e043829}, author = {Bagan, Emili and Monras, Alex and Mu{\~n}oz-Tapia, Ramon} } @article {Calsamiglia2008, title = {Quantum Chernoff bound as a measure of distinguishability between density matrices: Application to qubit and Gaussian states}, journal = {Physical Review A (Atomic, Molecular, and Optical Physics)}, volume = {77}, number = {3}, year = {2008}, month = {03/2008}, pages = {032311{\textendash}15}, keywords = {Bayes methods, error statistics, quantum chernoff bound, quantum statistical mechanics, quantum theory}, doi = {10.1103/PhysRevA.77.032311}, url = {http://link.aps.org/abstract/PRA/v77/e032311}, author = {Calsamiglia, John and Mu{\~n}oz-Tapia, Ramon and Masanes, Llu{\'\i}s and Ac{\'\i}n, Antonio and Bagan, Emili} } @article {Audenaert2007, title = {Discriminating States: The Quantum Chernoff Bound}, journal = {Physical Review Letters}, volume = {98}, number = {16}, year = {2007}, month = {04/2007}, pages = {160501{\textendash}4}, keywords = {quantum chernoff bound, state discrimination}, doi = {10.1103/PhysRevLett.98.160501}, url = {http://scitation.aip.org/getabs/servlet/GetabsServlet?prog=normal\&id=PRLTAO000098000016160501000001\&idtype=cvips\&gifs=yes}, author = {K. M. R. Audenaert and Calsamiglia, John and Mu{\~n}oz-Tapia, Ramon and Bagan, Emili and Masanes, Llu{\'\i}s and Ac{\'\i}n, Antonio and Verstraete, Frank} } @article {Bagan2007, title = {How to hide a secret direction}, journal = {New Journal of Physics}, volume = {9}, year = {2007}, pages = {244}, abstract = {We present a procedure to share a secret spatial direction in the absence of a common reference frame using a multipartite quantum state. The procedure guarantees that the parties can determine the direction if they perform joint measurements on the state, but fail to do so if they restrict themselves to local operations and classical communication (LOCC). We calculate the fidelity for joint measurements, give bounds on the fidelity achievable by LOCC, and prove that there is a non-vanishing gap between the two of them, even in the limit of infinitely many copies. The robustness of the procedure under particle loss is also studied. As a by-product we find bounds on the probability of discriminating by LOCC between the invariant subspaces of total angular momentum N/2 and N/2-1 in a system of N elementary spins.}, doi = {doi:10.1088/1367-2630/9/8/244}, url = {http://iopscience.iop.org/1367-2630/9/8/244/pdf/1367-2630\_9\_8\_244.pdf}, author = {Bagan, Emili and Calsamiglia, John and Demkowicz-Dobrzanski, R. and Mu{\~n}oz-Tapia, Ramon} } @article {Rapcan2007, title = {Recycling of quantum information: Multiple observations of quantum systems}, journal = {arXiv}, year = {2007}, month = {08/2007}, abstract = {Given a finite number of copies of an unknown qubit state that have already been measured optimally, can one still extract any information about the original unknown state? We give a positive answer to this question and quantify the information obtainable by a given observer as a function of the number of copies in the ensemble, and of the number of independent observers that, one after the other, have independently measured the same ensemble of qubits before him. The optimality of the protocol is proven and extensions to other states and encodings are also studied. According to the general lore, the state after a measurement has no information about the state before the measurement. Our results manifestly show that this statement has to be taken with a grain of salt, specially in situations where the quantum states encode confidential information.}, url = {http://arxiv.org/abs/0708.1086}, author = {Rapcan, Peter and Calsamiglia, John and Mu{\~n}oz-Tapia, Ramon and Bagan, Emili and Bu{\.z}ek, Vladimir} } @article {Bagan2006c, title = {Aligning spatial frames through quantum channels}, journal = {International Journal of Quantum Information}, volume = {4}, year = {2006}, pages = {5}, author = {Bagan, Emili and Mu{\~n}oz-Tapia, Ramon} } @article {Bagan2006, title = {Optimal full estimation of qubit mixed states}, journal = {Physical Review A (Atomic, Molecular, and Optical Physics)}, volume = {73}, number = {3}, year = {2006}, month = {03/2006}, pages = {032301{\textendash}18}, keywords = {mixed states, probability, state estimation}, doi = {10.1103/PhysRevA.73.032301}, url = {http://scitation.aip.org/getabs/servlet/GetabsServlet?prog=normal\&id=PLRAAN000073000003032301000001\&idtype=cvips\&gifs=yes}, author = {Bagan, Emili and Ballester, M. A. and Gill, R. D. and Monras, Alex and Mu{\~n}oz-Tapia, Ramon} } @article {Bagan2006b, title = {Relative states, quantum axes, and quantum references}, journal = {Physical Review A (Atomic, Molecular, and Optical Physics)}, volume = {73}, number = {2}, year = {2006}, month = {02/2006}, pages = {022341{\textendash}6}, keywords = {quantum theory}, doi = {10.1103/PhysRevA.73.022341}, url = {http://scitation.aip.org/getabs/servlet/GetabsServlet?prog=normal\&id=PLRAAN000073000002022341000001\&idtype=cvips\&gifs=yes}, author = {Bagan, Emili and Iblisdir, Sofyan and Mu{\~n}oz-Tapia, Ramon} } @article {Acin2006, title = {Secrecy properties of quantum channels}, journal = {Physical Review A (Atomic, Molecular, and Optical Physics)}, volume = {73}, number = {1}, year = {2006}, month = {01/2006}, pages = {012327{\textendash}5}, keywords = {information theory, protocols, quantum cryptography}, doi = {10.1103/PhysRevA.73.012327}, url = {http://scitation.aip.org/getabs/servlet/GetabsServlet?prog=normal\&id=PLRAAN000073000001012327000001\&idtype=cvips\&gifs=yes}, author = {Ac{\'\i}n, Antonio and Bae, J. and Bagan, Emili and Baig, Mari{\`a} and Masanes, Llu{\'\i}s and Mu{\~n}oz-Tapia, Ramon} } @article {Bagan2006a, title = {Separable Measurement Estimation of Density Matrices and its Fidelity Gap with Collective Protocols}, journal = {Physical Review Letters}, volume = {97}, number = {13}, year = {2006}, pages = {130501{\textendash}4}, keywords = {mixed states, state estimation}, doi = {10.1103/PhysRevLett.97.130501}, url = {http://scitation.aip.org/getabs/servlet/GetabsServlet?prog=normal\&id=PRLTAO000097000013130501000001\&idtype=cvips\&gifs=yes}, author = {Bagan, Emili and Ballester, M. A. and Gill, R. D. and Mu{\~n}oz-Tapia, Ramon and Romero-Isart, Oriol} } @article {Bagan2005a, title = {Comprehensive analysis of quantum pure-state estimation for two-level systems}, journal = {Physical Review A (Atomic, Molecular, and Optical Physics)}, volume = {71}, number = {6}, year = {2005}, month = {06/2005}, pages = {062318}, publisher = {American Physical Society}, abstract = {Given N identical copies of the state of a quantum two-level system, we analyze its optimal estimation. We consider two situations: general pure states and (pure) states restricted to lie on the equator of the Bloch sphere. We perform a complete and comprehensive analysis of the optimal schemes based on local measurements, and give results (optimal measurements, maximum fidelity, etc.) for arbitrary N, not necessarily large, within the Bayesian framework. We also make a comparative analysis of the asymptotic limit of these results with those derived from a (pointwise) Cram{\'e}r-Rao type of approach. We give explicit schemes based on local measurements and no classical communication that saturate the fidelity bounds of the most general collective schemes.}, issn = {1050-2947}, doi = {10.1103/PhysRevA.71.062318}, url = {http://link.aps.org/doi/10.1103/PhysRevA.71.062318}, author = {Bagan, Emili and Monras, Alex and Mu{\~n}oz-Tapia, Ramon} } @article {Acin2005, title = {Multiple-copy two-state discrimination with individual measurements}, journal = {Physical Review A (Atomic, Molecular, and Optical Physics)}, volume = {71}, number = {3}, year = {2005}, pages = {032338}, keywords = {state discrimination}, doi = {10.1103/PhysRevA.71.032338}, url = {http://link.aps.org/abstract/PRA/v71/e032338}, author = {Ac{\'\i}n, Antonio and Bagan, Emili and Baig, Mari{\`a} and Masanes, Llu{\'\i}s and Mu{\~n}oz-Tapia, Ramon} } @article {Bagan2005, title = {Purity Estimation with Separable Measurements}, journal = {Physical Review Letters}, volume = {95}, number = {11}, year = {2005}, month = {09/2005}, pages = {110504}, publisher = {American Physical Society}, abstract = {Given a large number N of copies of a qubit state of which we wish to estimate its purity, we prove that separable-measurement protocols can be as efficient as the optimal joint-measurement one if classical communication is used. This shows that the optimal estimation of the entanglement of a two-qubit state can also be achieved asymptotically with fully separable measurements. Thus, quantum memories provide no advantage in this situation. The relationship between our global Bayesian approach and the quantum Cram{\'e}r-Rao bound is discussed.}, issn = {0031-9007}, doi = {10.1103/PhysRevLett.95.110504}, url = {http://link.aps.org/doi/10.1103/PhysRevLett.95.110504}, author = {Bagan, Emili and Ballester, M. A. and Mu{\~n}oz-Tapia, Ramon and Romero-Isart, Oriol} } @article {Bagan2004, title = {Collective versus local measurements in a qubit mixed-state estimation}, journal = {Physical Review A (Atomic, Molecular, and Optical Physics)}, volume = {69}, number = {1}, year = {2004}, month = {01/2004}, pages = {010304}, publisher = {American Physical Society}, abstract = {We discuss the problem of estimating a qubit mixed state. We give the optimal estimation that can be inferred from any given set of measurements. For collective measurements and for a large number N of copies, we show that the error in the estimation varies as 1/N. For local measurements, we focus on the simpler case of states lying on the equatorial plane of the Bloch sphere. We show that the error using plain tomography varies as 1/N1/4, while our approach leads to an error proportional to 1/N3/4.}, issn = {1050-2947}, doi = {10.1103/PhysRevA.69.010304}, url = {http://link.aps.org/doi/10.1103/PhysRevA.69.010304}, author = {Bagan, Emili and Baig, Mari{\`a} and Mu{\~n}oz-Tapia, Ramon and Rodriguez, A.} } @article {Bagan2004a, title = {Entanglement-assisted alignment of reference frames using a dense covariant coding}, journal = {Physical Review A (Atomic, Molecular, and Optical Physics)}, volume = {69}, number = {5}, year = {2004}, month = {05/2004}, pages = {050303}, publisher = {American Physical Society}, abstract = {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.}, issn = {1050-2947}, doi = {10.1103/PhysRevA.69.050303}, url = {http://link.aps.org/doi/10.1103/PhysRevA.69.050303}, author = {Bagan, Emili and Baig, Mari{\`a} and Mu{\~n}oz-Tapia, Ramon} } @article {Bagan2004b, title = {Quantum reverse engineering and reference-frame alignment without nonlocal correlations}, journal = {Physical Review A (Atomic, Molecular, and Optical Physics)}, volume = {70}, number = {3}, year = {2004}, month = {09/2004}, pages = {030301}, publisher = {American Physical Society}, abstract = {The estimation of unknown qubit elementary gates and the alignment of reference frames are formally the same problem. Using quantum states made out of N qubits, we show that the theoretical precision limit for both problems, which behaves as 1/N2, can be asymptotically attained with a covariant protocol that exploits the quantum correlation of internal degrees of freedom instead of the more fragile entanglement between distant parties. This cuts by half the number of qubits needed to achieve the precision of the dense covariant coding protocol.}, issn = {1050-2947}, doi = {10.1103/PhysRevA.70.030301}, url = {http://link.aps.org/doi/10.1103/PhysRevA.70.030301}, author = {Bagan, Emili and Baig, Mari{\`a} and Mu{\~n}oz-Tapia, Ramon} } @conference {Bagan2003a, title = {Optimal reconstruction of a pure qubit state with local measurements}, booktitle = {Proceedings of the 8th ICSSUR}, year = {2003}, publisher = {Rinton Press (2003)}, organization = {Rinton Press (2003)}, author = {Bagan, Emili and Baig, Mari{\`a} and Monras, Alex and Mu{\~n}oz-Tapia, Ramon} } @article {Bagan2001b, title = {Aligning Reference Frames with Quantum States}, journal = {arXiv}, year = {2001}, url = {http://arxiv.org/abs/quant-ph/0106155}, author = {Bagan, Emili and Baig, Mari{\`a} and Mu{\~n}oz-Tapia, Ramon} }