Entanglement and non local correlations: quantum resources for information processing
Quantum Information Theory (QIT) studies how information can be processed and transmitted when encoded on quantum states. Practically, it can be understood as the effort to generalize Classical Information Theory to the quantum world. Interestingly, the fact that very-small scale Physics differs con...
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| Format: | doctoral thesis |
| Publication Date: | 2013 |
| Country: | España |
| Institution: | Universitat Politècnica de Catalunya (UPC) |
| Repository: | UPCommons. Portal del coneixement obert de la UPC |
| Language: | English |
| OAI Identifier: | oai:upcommons.upc.edu:2117/94882 |
| Online Access: | https://hdl.handle.net/2117/94882 https://dx.doi.org/10.5821/dissertation-2117-94882 |
| Access Level: | Open access |
| Keyword: | Quàntums, Teoria dels Fotònica Àrees temàtiques de la UPC::Enginyeria de la telecomunicació |
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Entanglement and non local correlations: quantum resources for information processing |
| title |
Entanglement and non local correlations: quantum resources for information processing |
| spellingShingle |
Entanglement and non local correlations: quantum resources for information processing Prettico, Giuseppe Quàntums, Teoria dels Fotònica Àrees temàtiques de la UPC::Enginyeria de la telecomunicació |
| title_short |
Entanglement and non local correlations: quantum resources for information processing |
| title_full |
Entanglement and non local correlations: quantum resources for information processing |
| title_fullStr |
Entanglement and non local correlations: quantum resources for information processing |
| title_full_unstemmed |
Entanglement and non local correlations: quantum resources for information processing |
| title_sort |
Entanglement and non local correlations: quantum resources for information processing |
| dc.creator.none.fl_str_mv |
Prettico, Giuseppe |
| author |
Prettico, Giuseppe |
| author_facet |
Prettico, Giuseppe |
| author_role |
author |
| dc.contributor.none.fl_str_mv |
Acín dal Maschio, Antonio |
| dc.subject.none.fl_str_mv |
Quàntums, Teoria dels Fotònica Àrees temàtiques de la UPC::Enginyeria de la telecomunicació |
| topic |
Quàntums, Teoria dels Fotònica Àrees temàtiques de la UPC::Enginyeria de la telecomunicació |
| description |
Quantum Information Theory (QIT) studies how information can be processed and transmitted when encoded on quantum states. Practically, it can be understood as the effort to generalize Classical Information Theory to the quantum world. Interestingly, the fact that very-small scale Physics differs considerably from that of macroscopic objects offers a richer structure to the new theory. Among other phenomena, entanglement is at the heart of many quantum information protocols. It is the most spectacular and counter-intuitive manifestation of quantum mechanics: it signifies the existence of non-local correlations. Although intrinsically non-intuitive, these strange effects have been shown to lead to intriguing applications with no classical analogue. The main scope of this thesis is to establish qualitative and quantitative connections among the different quantum and classical information resources. Among the many weird effects that quantum systems present, the non-additivity concept plays an important role. In the quantum realm, the joint processing of two quantum resources is often better than the sum of the two resources. Activation is the strongest manifestation of non-additivity. It can be understood as the capability of two objects to achieve a given task that is impossible for each of them when considered individually. From a classical point of view, it is unknown whether such a process can hold. Here we focus on the classical secret-key rate. We provide two probability distributions conjectured to have bound information, hence from which it is conjectured that no secret key can be extracted when taken individually, but that lead to a positive secret-key rate when combined. For that, we exploit the close connection between the information-theoretic key agreement and the quantum entanglement scenario. Successively, we move to the multipartite scenario showing a one-to-one correspondence between bound information and bound entanglement. We provide an example of multipartite bound information which shares the same features of its quantum analogue, the Smolin state. Later, we move to prove a deep connection between privacy and non-locality. We do it by showing that all private states violate the Bell-CHSH inequality. Private states are those entangled states from which a perfectly secure cryptographic key can be extracted. An example of those is the maximally entangled state. But still, there are other private states that are not maximally entangled. While a maximally entangled state violates a Bell's inequality, this is not known a priori for the whole set. We give a general proof valid for any dimension and any number of parties. Private states, then, not only represent the unit of quantum privacy, but also allow two distant parties to establish a different quantum resource, namely non-local correlations. Lastly, we tackle the connection between non-locality and genuine randomness. Non-locality and genuine intrinsic randomness have been the subject of active interest since the early days of quantum physics. Initially, this interest was mainly derived from their foundational and fundamental implications but recently it also has acquired a practical aspect. Recent development in device independent scenario have heightened the need to quantify both the randomness and non-locality inherent in quantum systems. While some works try to deepen this relation, we provide a simple method to detect Bell tests that allow the certification of maximal randomness. These arguments exploit the symmetries of Bell inequalities and assume the uniqueness of the quantum probability distribution maximally violating it. We show how these arguments can be applied to intuit the randomness intrinsic in a probability distribution without resorting to numerical calculations. |
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2013 |
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2013 2013-01-18 2013 2013-06-19 |
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doctoral thesis http://purl.org/coar/resource_type/c_db06 VoR http://purl.org/coar/version/c_970fb48d4fbd8a85 |
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info:eu-repo/semantics/doctoralThesis |
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https://hdl.handle.net/2117/94882 https://dx.doi.org/10.5821/dissertation-2117-94882 |
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https://hdl.handle.net/2117/94882 https://dx.doi.org/10.5821/dissertation-2117-94882 |
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Inglés eng |
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eng |
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Universitat Politècnica de Catalunya |
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Universitat Politècnica de Catalunya |
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Entanglement and non local correlations: quantum resources for information processingPrettico, GiuseppeQuàntums, Teoria delsFotònicaÀrees temàtiques de la UPC::Enginyeria de la telecomunicacióQuantum Information Theory (QIT) studies how information can be processed and transmitted when encoded on quantum states. Practically, it can be understood as the effort to generalize Classical Information Theory to the quantum world. Interestingly, the fact that very-small scale Physics differs considerably from that of macroscopic objects offers a richer structure to the new theory. Among other phenomena, entanglement is at the heart of many quantum information protocols. It is the most spectacular and counter-intuitive manifestation of quantum mechanics: it signifies the existence of non-local correlations. Although intrinsically non-intuitive, these strange effects have been shown to lead to intriguing applications with no classical analogue. The main scope of this thesis is to establish qualitative and quantitative connections among the different quantum and classical information resources. Among the many weird effects that quantum systems present, the non-additivity concept plays an important role. In the quantum realm, the joint processing of two quantum resources is often better than the sum of the two resources. Activation is the strongest manifestation of non-additivity. It can be understood as the capability of two objects to achieve a given task that is impossible for each of them when considered individually. From a classical point of view, it is unknown whether such a process can hold. Here we focus on the classical secret-key rate. We provide two probability distributions conjectured to have bound information, hence from which it is conjectured that no secret key can be extracted when taken individually, but that lead to a positive secret-key rate when combined. For that, we exploit the close connection between the information-theoretic key agreement and the quantum entanglement scenario. Successively, we move to the multipartite scenario showing a one-to-one correspondence between bound information and bound entanglement. We provide an example of multipartite bound information which shares the same features of its quantum analogue, the Smolin state. Later, we move to prove a deep connection between privacy and non-locality. We do it by showing that all private states violate the Bell-CHSH inequality. Private states are those entangled states from which a perfectly secure cryptographic key can be extracted. An example of those is the maximally entangled state. But still, there are other private states that are not maximally entangled. While a maximally entangled state violates a Bell's inequality, this is not known a priori for the whole set. We give a general proof valid for any dimension and any number of parties. Private states, then, not only represent the unit of quantum privacy, but also allow two distant parties to establish a different quantum resource, namely non-local correlations. Lastly, we tackle the connection between non-locality and genuine randomness. Non-locality and genuine intrinsic randomness have been the subject of active interest since the early days of quantum physics. Initially, this interest was mainly derived from their foundational and fundamental implications but recently it also has acquired a practical aspect. Recent development in device independent scenario have heightened the need to quantify both the randomness and non-locality inherent in quantum systems. While some works try to deepen this relation, we provide a simple method to detect Bell tests that allow the certification of maximal randomness. These arguments exploit the symmetries of Bell inequalities and assume the uniqueness of the quantum probability distribution maximally violating it. We show how these arguments can be applied to intuit the randomness intrinsic in a probability distribution without resorting to numerical calculations.La Teoría de la Información Cuántica (QIT) estudia como la información puede ser procesada y transmitida al codificarse en estados cuánticos. Prácticamente, se puede pensar como la generalización de la Teoría de Información Clásica al mundo cuántico. El hecho que la física a esta escala difiera considerablemente de aquella de los objetos macroscópicos ofrece una mayor riqueza a la estructura de la nueva teoría. Entre otros fenómenos, el entrelazamiento está a la base de muchos protocolos cuánticos. Es la más espectacular y anti-intuitiva manifestación de la mecánica cuántica observada en sistemas cuánticos compuestos: implica la existencia de correlaciones no-locales. No obstante la extrañeza de estos efectos, se han demostrado distintas aplicaciones sin ningún análogo clásico. El objetivo de esta tesis es establecer conexiones cualitativas y cuantitativas entre los diferentes recursos descritos por la teoría cuántica y clásica. Entre los efectos raros que los sistemas cuánticos muestran, la no-aditividad desempeña un papel muy importante. En el mundo cuántico, el uso de dos recursos cuánticos puede ser más ventajoso que la suma de los dos, considerados individualmente. La activación es la mas fuerte manifestación del fenómeno de no-aditividad. Este proceso se puede entender como la capacidad de dos objetos juntos de lograr una tarea que sería imposible por cada uno de ellos singularmente. Desde un punto de vista clásico, es desconocido si existen procesos o cantidades que no respetan la aditividad. Aquí, nos centramos en la tasa de clave secreta. Presentamos aquí dos distribuciones de probabilidad que conjeturamos contener bound information, o sea a partir de la cuales es imposible destilar bits secretos que dan bits secretos cuando utilizadas conjuntamente. Para probar este resultado, utilizamos la conexión existente entre entrelazamiento y el proceso de establecimiento de seguridad. Sucesivamente desplazándonos al caso multipartito, probamos una correspondencia uno a uno entre la bound information y el entrelazamiento no-destilable. Presentamos un ejemplo de bound information multipartita que comparte las mismas propiedades de su análogo cuántico, el estado de Smolin. Luego profundizamos la relación entre privacidad y no-localidad. Probamos que todos los estados que pertenecen al conjunto de estados privados violan una desigualdad de Bell, conocida como CHSH. Los estados privados son aquellos estados entrelazados de los cuales es posible extraer una clave secreta. Un ejemplo de estos estados es el estado máximamente entrelazado, pero hay otros que son privados aunque no máximamente entrelazados. Es conocido que un estado máximamente entrelazado puede violar una desigualdad de Bell, pero lo que se desconoce es si esto pasa para todos los estados privados. Nuestro resultado es general ya que nuestra prueba es válida para cualquier número de partes y cualquier dimensión del espacio local de cada una. Los estados privados, entonces, no solo permiten destilar una clave de forma segura sino que también presentan una propiedad tan fuerte como la no-localidad. Finalmente, investigamos la relación entre los conceptos de no-localidad y de aleatoriedad. Desde los orígenes de la teoría cuántica, los conceptos de no-localidad y de aleatoriedad fueron objeto de gran interés. A principio este interés se debía más a razones relacionadas con los fundamentos de la teoría, pero recientes resultados han empujado la comunidad científica a investigar ulteriormente y sobre todo a cuantificar la no-localidad y la aleatoriedad presente en los estados cuánticos. Aunque algunos autores se hayan movido en esta direccion, muchas preguntas han quedado sin respuestas. Aquí presentamos un simple método que permite detectar aquellas desigualdades de Bell que pueden certificar la presencia de máxima aleatoriedad. Nuestros resultados prueban como simples argumentos pueden dar complejas respuestas sin la necesidad de recorrer a computaciones numéricas.Universitat Politècnica de CatalunyaAcín dal Maschio, Antonio20132013-01-1820132013-06-19doctoral thesishttp://purl.org/coar/resource_type/c_db06VoRhttp://purl.org/coar/version/c_970fb48d4fbd8a85info:eu-repo/semantics/doctoralThesisapplication/pdfhttps://hdl.handle.net/2117/94882https://dx.doi.org/10.5821/dissertation-2117-94882reponame:UPCommons. Portal del coneixement obert de la UPCinstname:Universitat Politècnica de Catalunya (UPC)Inglésengopen accesshttp://purl.org/coar/access_right/c_abf2http://creativecommons.org/licenses/by-nc-sa/3.0/es/info:eu-repo/semantics/openAccessoai:upcommons.upc.edu:2117/948822026-05-27T15:37:01Z |
| score |
15,301603 |