Multipartite entanglement and quantum algorithms

[eng] Quantum information science has grown from being a very small subfield in the 70s until being one of the most dynamic fields in physics, both in fundamentals and applications. In the theoretical section, perhaps the feature that has attracted most interest is the notion of entanglement, the ghostly relation between particles that dazzled Einstein and has provided fabulous challenges to build a coherent interpretation of quantum mechanics. While not completely solved, we have today learned enough to feel less uneasy with this fundamental problem, and the focus has shifted towards its potential powerful applications. Entanglement is now being studied from different perspectives as a resource for performing information processing tasks. With bipartite entanglement being largely understood nowadays, many questions remain unanswered in the multipartite case. The first part of this thesis deals with multipartite entanglement in different contexts. In the first chapters it is studied within the whole corresponding Hilbert space, and we investigate several entanglement measures searching for states that maximize them, including violations of Bell inequalities. Later, focus is shifted towards hamiltonians that have entangled ground states, and we investigate entanglement as a way to establish a distance between theories and we study frustration and methods to efficiently solve hamiltonians that exhibit it. In the practical section, the most promised upcoming technological advance is the advent of quantum computers. In the 90s some quantum algorithms improving the performance of all known classical algorithms for certain problems started to appear, while in the 2000s the first universal computers of few atoms began to be built, allowing implementation of those algorithms in small scales. The D-Wave machine already performs quantum annealing in thousands of qubits, although some controversy over the true quantumness of its internal workings surrounds it. Many countries in the planet are devoting large amounts of money to this field, with the recent European flagship and the involvement of the largest US technological companies giving reasons for optimism. The second part of this thesis deals with some aspects of quantum computation, starting with the creation of the field of cloud quantum computation with the appearance of the first computer available to the general public through internet, which we have used and analysed extensively. Also small incursions in quantum adiabatic computation and quantum thermodynamics are present in this second part.[cat] La informació quàntica ha crescut des d'un petit subcamp als anys setanta fins a esdevenir un dels camps més dinàmics de la física actualment, tant en aspectes fonamentals com en les seves aplicacions. En la secció teòrica, potser la propietat que ha atret més interès és la noció d'entrellaçament, la relació fantasmagòrica entre partícules que va deixar estupefacte Einstein i que ha suposat un enorme desafiament per a construir una interpretació coherent de la mecànica quàntica. Sense estar totalment solucionat, hem après prou per sentir-nos menys incòmodes amb aquest problema fonamental i el focus s'ha desplaçat a les seves aplicacions potencials. L'entrellaçament s'estudia avui en dia des de diferents perspectives com a recurs per realitzar tasques de processament de la informació. L'entrellaçament bipartit està ja molt ben comprès, però en el cas multipartit queden moltes qüestions obertes. La primera part d'aquesta tesi tracta de l'entrellaçament multipartit en diferents contextos. Estudiem l'hiperdeterminant com a mesura d'entrellaçament el cas de 4 qubits, analitzem l'existència i les propietats matemàtiques dels estats absolutament màximament entrellaçats, trobem noves desigualtats de Bell, estudiem l'espectre d'entrellaçament com a mesura de distància entre teories i estudiem xarxes tensorials per tractar eficientment sistemes frustrats. En l'apartat pràctic, el més prometedor avenç tecnològic del camp és l'adveniment dels ordinadors quàntics. La segona part de la tesi tracta d'alguns aspectes de computació quàntica, començant per la creació del camp de la computació quàntica al núvol, amb l'aparició del primer ordinador disponible per al públic general, que hem usat extensament. També fem petites incursions a la computació quàntica adiabàtica i a la termodinàmica quàntica en aquesta segona par

Absolutely Maximally Entangled states, combinatorial designs and multi-unitary matrices

Absolutely Maximally Entangled (AME) states are those multipartite quantum states that carry absolute maximum entanglement in all possible partitions. AME states are known to play a relevant role in multipartite teleportation, in quantum secret sharing and they provide the basis novel tensor networks related to holography. We present alternative constructions of AME states and show their link with combinatorial designs. We also analyze a key property of AME, namely their relation to tensors that can be understood as unitary transformations in every of its bi-partitions. We call this property multi-unitarity.Comment: 18 pages, 2 figures. Comments are very welcom

Operational approach to Bell inequalities: applications to qutrits

Bell inequalities can be studied both as constraints in the space of probability distributions and as expectation values of multipartite operators. The latter approach is particularly useful when considering outcomes as eigenvalues of unitary operators. This brings the possibility of exploiting the complex structure of the coefficients in the Bell operators. We investigate this avenue of though in the known case of two outcomes, and find new Bell inequalities for the cases of three outcomes and $n=3,4,5$ and $6$ parties. We find their corresponding classical bounds and their maximum violation in the case of qutrits. We further propose a novel way to generate Bell inequalities based on a mapping from maximally entangled states to Bell operators and produce examples for different outcomes and number of parties.Comment: 10 pages, no figures. A sign error in Eq.(10), appearing in the published version, has been correcte

Spatial variations of the SrI 4607\AA scattering polarization signals at subgranular scale observed with ZIMPOL at GREGOR telescope

Sr I 4607\AA spectral line shows one of the strongest scattering polarization signals in the visible solar spectrum. The amplitudes of these signals are expected to vary at granular spatial scales. This variation can be due to changes in the magnetic field intensity and orientation (Hanle effect) as well as due to spatial and temporal variations in the plasma properties. Measuring the spatial variation of such polarization signal would allow us to study the properties of the magnetic fields at subgranular region. But, the observations are challenging since both high spatial resolution and high spectropolarimetric sensitivity are required at the same time. To the aim of measuring these spatial variations at granular scale, we carried out a spectro-polarimetric measurement with the Zurich IMaging POLarimeter (ZIMPOL), at the GREGOR solar telescope at different limb distances on solar disk. Our results show a spatial variation of scattering linear polarization signals in Sr I 4607\AA line at the granular scale at every $\mu$, starting from 0.2 to 0.8. The correlation between the polarization signal amplitude and the continuum intensity imply statistically that the scattering polarization is higher at the granular regions than in the intergranular lanes.Comment: 4 pages, 3 figures, Proceeding of Third Meeting of the Italian Solar and Heliospheric Community, OCTOBER 28-31, 2018 - TURI

Aspect prediction of the knitted fabrics from the yarn properties

The textile technologist knows that the prediction of the aspect of a finished knitted fabric, by the parameters of yarn evenness, does not agree, often, with the reality. There are fabrics, in the market, with irregular aspect, made with yarns in which we have detected few faults. The conventional criteria that are considered in the evenness measuring equipments for the faults detection in the yarns are very limited.In this paper a new evenness of mass index is proposed, denominated deviation rate DR, that, according to it is demonstrated in the experimental stage, it follows an excellent statistical correlation with the aspect of the knitted fabrics.Peer ReviewedPostprint (published version

Consideraciones para una interpretación histórica de la partita para flauta sola en La menor BWV 1013 de J. S. Bach

Siendo la partita en La menor de J. S. Bach una de las obras más importantes para instrumento solo del siglo XVIII, éste trabajo pretende, a partir de un análisis teórico e histórico, dar un concepto más allá de lo consignado en la partitura para poder interpretar la obra de manera informada y tomar las mejores decisiones en cuanto a elementos musicales de libre elección para el intérprete.Being the partita in A minor of J. S. Bach one of the most important works for unaccompanied instrument of the XVIII century, this project search, from a theoretical and historical analysis, to give a concept beyond the consigned in the score to be able to perform the piece in an informed manner and make the best decisions regarding musical elements of free choice for the performer.Maestro (a) en MúsicaPregrad

Experimental test of Mermin inequalities on a five-qubit quantum computer

Violation of Mermin inequalities is tested on the five-qubit IBM quantum computer. For three, four, and five parties, quantum states that violate the corresponding Mermin inequalities are constructed using quantum circuits on superconducting qubits. Measurements on different bases are included as additional final gates in the circuits. The experimental results obtained using the quantum computer show violation of all Mermin inequalities, with a clear degradation of the results in the five-qubit case. Though this quantum computer is not competitive to test Mermin inequalities as compared to other techniques when applied to a few qubits, it does offer the opportunity to explore multipartite entanglement for four and five qubits beyond the reach of other alternative technologies

Relation entre la solubilité alcaline et les paramètres de traction d'un filé de laine peignée soumis à des traitements acides et oxydants

Un hilado de lana peinada ha sido sometido a tratamientos ácidos y con peróxido de hidrógeno a efectos de preparar sustratos que presentan un amplio intervalo de solubilidades alcalinas. Se han relacionado los parámetros de tracción con la solubilidad alcalina de los correspondientes sustratos. Este estudio ha permitido ampliar la información sobre el motivo del aumento de la solubilidad en álcali producido por el blanqueo con peróxido de hidrógeno. Se ha relacionado la solubilidad alcalina de la lana con la tenacidad, elongación, módulo y trabajo de rotura.A worsted yarn has been subjected to acidic and hydrogen peroxide treatments in order to prepare substrates having a wide range of alkali solubilities. The tensile parameters of the resulting substrates have been related with their corresponding alkali solubilities. This study has allowed to obtain more information on the cause of the increase in alkali solubility produced during wool bleaching with hydrogen peroxide. It has also been possible to know how the alkali solubility of wool is related with other parameters (breaking elongation, modulus and work of rupture) of the studied yarns.Un filé de laine peignée a été soumis à des traitements acides et au peroxyde d’hydrogène pour préparer des substrats présentant une grande fourchette de solubilités alcalines. Les paramètres de traction ont été associés à la solubilité alcaline des substrats correspondants. L’étude a permis de compléter l’information sur les raisons de l’augmentation de la solubilité alcaline produite par le blanchiment au peroxyde d’hydrogène. La solubilité alcaline de la laine a été associée à la ténacité, à l’élongation, au module et au travail de rupture