Maximal Entanglement. Applications in Quantum Information and Particle Physics
[eng] The aim of this thesis is to study the quantum entanglement and, in particular, under which circumstances is maximum. In the first place, Bell's inequalities are analyzed from an operational point of view. In particular, we focus on those involving qutrits. The states that maximally viola...
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| Tipo de recurso: | tesis doctoral |
| Estado: | Versión publicada |
| Fecha de publicación: | 2019 |
| País: | España |
| Institución: | Universidad de Barcelona |
| Repositorio: | Dipòsit Digital de la UB |
| OAI Identifier: | oai:diposit.ub.edu:2445/140386 |
| Acceso en línea: | https://hdl.handle.net/2445/140386 http://hdl.handle.net/10803/667489 |
| Access Level: | acceso abierto |
| Palabra clave: | Física de partícules Entrellaçament quàntic Ordinadors quàntics Particle physics Quantum entanglement Quantum computers |
| Sumario: | [eng] The aim of this thesis is to study the quantum entanglement and, in particular, under which circumstances is maximum. In the first place, Bell's inequalities are analyzed from an operational point of view. In particular, we focus on those involving qutrits. The states that maximally violate these inequalities are of the GHZ type, for inequalities involving qubits, and little deformations of GHZ state, for those involving qutrits. This result shows that, although maximum entanglement and non-locality are very close concepts, they are not equivalent. In the second place, multipartite entanglement in spin chains is studied. We use as a figure of merit the hyperdeterminant and two polynomial invariants, S and T. These figures quantify a specific type of quadripartite entanglement, as demonstrated by an analysis of well-known quantum states such as the GHZ or W. In an Ising spin chain, we observe a pronounced peak near the quantum phase transition. Similar results are observed for the XXZ and Haldane- Shastry models for the case of the S and T invariants. For that reason, we conclude that these figures of merit are sensitive to quantum phase transitions. The second part of the thesis focuses on the field of quantum computing. This field has experienced a significant expansion in recent years. Due to this growth, several companies have started to develop prototypes of quantum computers. For this reason, one line of research in quantum computing is to propose methods to benchmark these machines. One of the methods presented in this thesis consists of the exact simulation of a XY spin chain. We propose a circuit that diagonalizes the XY Hamiltonian, which allows simulating time evolution and thermal states as well. Since this model is exactly solvable, the results obtained from a quantum computer can be compared with the theoretical solution. After running this circuit for four qubits on two IBM computers and one from Rigetti computing company, we obtain worse results than expected. With this, we conclude that there are error sources that, in general, are not being taken into account and that become relevant even in such small circuits. Moreover, we propose another method to test quantum computers performance: the simulation of absolutely maximally entangled states. The implementation of these circuits is a hard but necessary test for a quantum computer since the advantage of quantum algorithms lies in the generation of entanglement. Finally, we study the generation of entanglement at the most fundamental level: particle physics. We obtain that the QED interaction at tree-level is dictated by the imposition of maximal entanglement in outgoing particles. We apply the same philosophy in processes involving weak neutral currents obtaining that the weak mixing angle must be pi / 6, very close to the experimental value. |
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