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.

VL - 119 ER - TY - JOUR T1 - Quantum Change Point JF - Physical Review Letters Y1 - 2016 A1 - Sentís, Gael A1 - Bagan, Emilio A1 - John Calsamiglia A1 - Chiribella, Giulio A1 - Muñoz-Tapia, Ramon VL - 117 UR - http://link.aps.org/doi/10.1103/PhysRevLett.117.150502http://link.aps.org/article/10.1103/PhysRevLett.117.150502 JO - Phys. Rev. Lett. ER - TY - JOUR T1 - Beating noise with abstention in state estimation JF - New Journal of Physics Y1 - 2012 A1 - Gendra, Bernat A1 - Ronco-Bonvehi, Elio A1 - John Calsamiglia A1 - Muñoz-Tapia, Ramon A1 - Bagan, Emilio VL - 14 UR - http://iopscience.iop.org/1367-2630/14/10/105015 ER - TY - JOUR T1 - Quantum learning without quantum memory JF - Scientific Reports (Nature Publishing Group) Y1 - 2012 A1 - Sentís, Gael A1 - John Calsamiglia A1 - Muñoz-Tapia, Ramon A1 - Bagan, Emilio AB - 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. PB - Nature Publishing Group VL - 2 UR - http://www.nature.com/srep/2012/121005/srep00708/full/srep00708.html ER - TY - JOUR T1 - Optimal signal states for quantum detectors JF - New Journal of Physics Y1 - 2011 A1 - Oreshkov, Ognyan A1 - Calsamiglia, John A1 - Muñoz-Tapia, Ramon A1 - Bagan, Emili VL - 13 UR - https://iopscience.iop.org/article/10.1088/1367-2630/13/7/073032 JO - New J. Phys. ER - TY - THES T1 - Quantum Accuracy Limits and Benchmarks in Continuos Variable Systems T2 - Departament de Físca, Grup de Física Teòria: Informació i fenòmens quàntics Y1 - 2011 A1 - Bracons, Mariona (formerly Mariona Aspachs) JF - Departament de Físca, Grup de Física Teòria: Informació i fenòmens quàntics PB - Universitat Autònoma de Barcelona CY - Barcelona VL - Doctorat en Física ER - TY - THES T1 - Discriminació quàntica T2 - Departament de Físca, Grup de Física Teòria: Informació i fenòmens quàntics Y1 - 2010 A1 - Arnau Pujol AB - S'estudia la discriminació de diferents sistemes quàntics. S'analitza el procés de discriminació entre qúbits, i es compara amb la discriminació de mesures projectives. Seguidament, es busquen les condicions en les quals la discriminació entre mesures projectives és perfecta, i es realitza el mateix per a la discriminació de transformacions unitàries, per tal de comparar ambdós resultats. JF - Departament de Físca, Grup de Física Teòria: Informació i fenòmens quàntics PB - Universitat Autònoma de Barcelona CY - Barcelona VL - Grau en Física ER - TY - JOUR T1 - Estimation of quantum finite mixtures JF - Physical Review A Y1 - 2010 A1 - de Vicente, J. I. A1 - John Calsamiglia A1 - Muñoz-Tapia, Ramon A1 - Bagan, Emilio AB - 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. VL - 81 UR - http://link.aps.org/doi/10.1103/PhysRevA.81.012332 ER - TY - JOUR T1 - Multicopy programmable discrimination of general qubit states JF - Physical Review A Y1 - 2010 A1 - Sentís, Gael A1 - Bagan, Emili A1 - John Calsamiglia A1 - Muñoz-Tapia, Ramon AB - 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. VL - 82 UR - http://link.aps.org/doi/10.1103/PhysRevA.82.042312 ER - TY - JOUR T1 - Recycling of qubits JF - Physica Scripta Y1 - 2010 A1 - P Rapcan A1 - John Calsamiglia A1 - Muñoz-Tapia, Ramon A1 - Bagan, Emilio A1 - V Buzek AB - 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. VL - T140 UR - http://iopscience.iop.org/1402-4896/2010/T140/014059?fromSearchPage=true ER - TY - JOUR T1 - Phase estimation for thermal Gaussian states JF - Physical Review A (Atomic, Molecular, and Optical Physics) Y1 - 2009 A1 - Aspachs, Mariona A1 - John Calsamiglia A1 - Muñoz-Tapia, Ramon A1 - Bagan, Emili KW - gaussian noise KW - gaussian states KW - optical losses KW - optical squeezing KW - phase estimation KW - quantum noise KW - thermal noise VL - 79 UR - http://link.aps.org/abstract/PRA/v79/e033834 ER - TY - JOUR T1 - Phase-covariant quantum benchmarks JF - Physical Review A (Atomic, Molecular, and Optical Physics) Y1 - 2009 A1 - John Calsamiglia A1 - Aspachs, Mariona A1 - Muñoz-Tapia, Ramon A1 - Bagan, Emili KW - quantum benchmarks VL - 79 UR - http://link.aps.org/doi/10.1103/PhysRevA.79.050301 ER - TY - JOUR T1 - Phase variance of squeezed vacuum states JF - Physical Review A (Atomic, Molecular, and Optical Physics) Y1 - 2008 A1 - Bagan, Emili A1 - Monras, Alex A1 - Muñoz-Tapia, Ramon KW - optical squeezing VL - 78 UR - http://link.aps.org/abstract/PRA/v78/e043829 ER - TY - JOUR T1 - Quantum Chernoff bound as a measure of distinguishability between density matrices: Application to qubit and Gaussian states JF - Physical Review A (Atomic, Molecular, and Optical Physics) Y1 - 2008 A1 - John Calsamiglia A1 - Muñoz-Tapia, Ramon A1 - Masanes, Lluís A1 - Acín, Antonio A1 - Bagan, Emili KW - Bayes methods KW - error statistics KW - quantum chernoff bound KW - quantum statistical mechanics KW - quantum theory VL - 77 UR - http://link.aps.org/abstract/PRA/v77/e032311 ER - TY - JOUR T1 - Discriminating States: The Quantum Chernoff Bound JF - Physical Review Letters Y1 - 2007 A1 - K. M. R. Audenaert A1 - John Calsamiglia A1 - Muñoz-Tapia, Ramon A1 - Bagan, Emili A1 - Masanes, Lluís A1 - Acín, Antonio A1 - Verstraete, Frank KW - quantum chernoff bound KW - state discrimination VL - 98 UR - http://scitation.aip.org/getabs/servlet/GetabsServlet?prog=normal&id=PRLTAO000098000016160501000001&idtype=cvips&gifs=yes ER - TY - JOUR T1 - How to hide a secret direction JF - New Journal of Physics Y1 - 2007 A1 - Bagan, Emili A1 - John Calsamiglia A1 - Demkowicz-Dobrzanski, R. A1 - Muñoz-Tapia, Ramon AB - 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. VL - 9 UR - http://iopscience.iop.org/1367-2630/9/8/244/pdf/1367-2630\_9\_8\_244.pdf ER - TY - JOUR T1 - Recycling of quantum information: Multiple observations of quantum systems JF - arXiv Y1 - 2007 A1 - Rapcan, Peter A1 - John Calsamiglia A1 - Muñoz-Tapia, Ramon A1 - Bagan, Emili A1 - Bużek, Vladimir AB - 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. UR - http://arxiv.org/abs/0708.1086 ER - TY - JOUR T1 - Aligning spatial frames through quantum channels JF - International Journal of Quantum Information Y1 - 2006 A1 - Bagan, Emili A1 - Muñoz-Tapia, Ramon VL - 4 ER - TY - JOUR T1 - Optimal full estimation of qubit mixed states JF - Physical Review A (Atomic, Molecular, and Optical Physics) Y1 - 2006 A1 - Bagan, Emili A1 - Ballester, M. A. A1 - Gill, R. D. A1 - Monras, Alex A1 - Muñoz-Tapia, Ramon KW - mixed states KW - probability KW - state estimation VL - 73 UR - http://scitation.aip.org/getabs/servlet/GetabsServlet?prog=normal&id=PLRAAN000073000003032301000001&idtype=cvips&gifs=yes ER - TY - JOUR T1 - Relative states, quantum axes, and quantum references JF - Physical Review A (Atomic, Molecular, and Optical Physics) Y1 - 2006 A1 - Bagan, Emili A1 - Iblisdir, Sofyan A1 - Muñoz-Tapia, Ramon KW - quantum theory VL - 73 UR - http://scitation.aip.org/getabs/servlet/GetabsServlet?prog=normal&id=PLRAAN000073000002022341000001&idtype=cvips&gifs=yes ER - TY - JOUR T1 - Secrecy properties of quantum channels JF - Physical Review A (Atomic, Molecular, and Optical Physics) Y1 - 2006 A1 - Acín, Antonio A1 - Bae, J. A1 - Bagan, Emili A1 - Baig, Marià A1 - Masanes, Lluís A1 - Muñoz-Tapia, Ramon KW - information theory KW - protocols KW - quantum cryptography VL - 73 UR - http://scitation.aip.org/getabs/servlet/GetabsServlet?prog=normal&id=PLRAAN000073000001012327000001&idtype=cvips&gifs=yes ER - TY - JOUR T1 - Separable Measurement Estimation of Density Matrices and its Fidelity Gap with Collective Protocols JF - Physical Review Letters Y1 - 2006 A1 - Bagan, Emili A1 - Ballester, M. A. A1 - Gill, R. D. A1 - Muñoz-Tapia, Ramon A1 - Romero-Isart, Oriol KW - mixed states KW - state estimation VL - 97 UR - http://scitation.aip.org/getabs/servlet/GetabsServlet?prog=normal&id=PRLTAO000097000013130501000001&idtype=cvips&gifs=yes ER - TY - JOUR T1 - Comprehensive analysis of quantum pure-state estimation for two-level systems JF - Physical Review A (Atomic, Molecular, and Optical Physics) Y1 - 2005 A1 - Bagan, Emili A1 - Monras, Alex A1 - Muñoz-Tapia, Ramon AB - 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) Cramér-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. PB - American Physical Society VL - 71 UR - http://link.aps.org/doi/10.1103/PhysRevA.71.062318 ER - TY - JOUR T1 - Multiple-copy two-state discrimination with individual measurements JF - Physical Review A (Atomic, Molecular, and Optical Physics) Y1 - 2005 A1 - Acín, Antonio A1 - Bagan, Emili A1 - Baig, Marià A1 - Masanes, Lluís A1 - Muñoz-Tapia, Ramon KW - state discrimination VL - 71 UR - http://link.aps.org/abstract/PRA/v71/e032338 ER - TY - JOUR T1 - Purity Estimation with Separable Measurements JF - Physical Review Letters Y1 - 2005 A1 - Bagan, Emili A1 - Ballester, M. A. A1 - Muñoz-Tapia, Ramon A1 - Romero-Isart, Oriol AB - 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 Cramér-Rao bound is discussed. PB - American Physical Society VL - 95 UR - http://link.aps.org/doi/10.1103/PhysRevLett.95.110504 ER - TY - JOUR T1 - Collective versus local measurements in a qubit mixed-state estimation JF - Physical Review A (Atomic, Molecular, and Optical Physics) Y1 - 2004 A1 - Bagan, Emili A1 - Baig, Marià A1 - Muñoz-Tapia, Ramon A1 - Rodriguez, A. AB - 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. PB - American Physical Society VL - 69 UR - http://link.aps.org/doi/10.1103/PhysRevA.69.010304 ER - TY - JOUR T1 - Entanglement-assisted alignment of reference frames using a dense covariant coding JF - Physical Review A (Atomic, Molecular, and Optical Physics) Y1 - 2004 A1 - Bagan, Emili A1 - Baig, Marià A1 - Muñoz-Tapia, Ramon AB - 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. PB - American Physical Society VL - 69 UR - http://link.aps.org/doi/10.1103/PhysRevA.69.050303 ER - TY - JOUR T1 - Quantum reverse engineering and reference-frame alignment without nonlocal correlations JF - Physical Review A (Atomic, Molecular, and Optical Physics) Y1 - 2004 A1 - Bagan, Emili A1 - Baig, Marià A1 - Muñoz-Tapia, Ramon AB - 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. PB - American Physical Society VL - 70 UR - http://link.aps.org/doi/10.1103/PhysRevA.70.030301 ER - TY - CONF T1 - Optimal reconstruction of a pure qubit state with local measurements T2 - Proceedings of the 8th ICSSUR Y1 - 2003 A1 - Bagan, Emili A1 - Baig, Marià A1 - Monras, Alex A1 - Muñoz-Tapia, Ramon JF - Proceedings of the 8th ICSSUR PB - Rinton Press (2003) ER - TY - JOUR T1 - Aligning Reference Frames with Quantum States JF - arXiv Y1 - 2001 A1 - Bagan, Emili A1 - Baig, Marià A1 - Muñoz-Tapia, Ramon UR - http://arxiv.org/abs/quant-ph/0106155 ER -