Activación de metrología cuántica de estados en escenarios con ruido.
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Date
2026
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Universidad de Concepción
Abstract
La metrología cuántica promete superar los límites clásicos de precisión en la estimación de parámetros, sin embargo, la presencia de ruido ambiental suele degradar esta ventaja, forzando al sistema a obedecer el límite clásico estándar. En esta tesis, se aborda el problema de la estimación de parámetros, con el uso del Steering Temporal como recurso metrologíco principal, en canales cuánticos afectados por ruido de amortiguamiento de amplitud (Amplitude Damping Channel). Para combatir esta incapacidad de estimación se utilizó operaciones de prey post-filtración. La implementación consiste en un arreglo experimental óptico utilizando una fuente de fotones anunciados (heralded photons) generados por conversión paramétrica descendente espontánea (SPDC), con el objetivo de trabajar en un régimen cuántico de fotones individuales. En el contexto del uso de steering temporal con motivos de metrología el escenario a implementar es uno de preparación y medida, específicamente una única partícula es enviada al laboratorio de Alice para aplicar un set de operaciones incompatibles en un tiempo t1. Y así luego implementar una fase θ. Finalmente el estado que recibe Bob en un tiempo t2 dependerá de lo realizado por Alice y la fase aplicada. La tarea de Bob es, a través de mediciones incompatibles, saber si el ensamble de estados violan alguna desigualdad de steering, para saber si existe algún tipo de correlación temporal entre las mediciones de preparación y el ensamble de estados. Por el tipo de desigualdad de steering que utilizamos podemos concluir de igual manera si es posible o no realizar la estimación del parámetro θ. El objetivo planteado fue estudiar esta estimación de parámetro en un escenario realista, ya que las operaciones no son perfectas, agregamos un canal cuántico asociado a un error en la implementación de la operación unitaria. El amplitude damping channel representa la pérdida del estado hacia el ambiente. Para combatirlo se implementaron filtros estocásticos locales, parametrizados por el valor f, que nos permiten mitigar el efecto negativo del canal ruidoso asociado a la estimación de parámetro. La mejora se analizó a través de la violación de la desigualdad de steering V en función del nivel de ruido aplicado γ para distintos valores de filtros.
Los resultados demuestran que, sin ningún tipo de filtro (f = 0), la violación de la desigualdad de steering desaparece para valores de ruido γ ≥ 0,5, mitigando la ventaja cuántica dada por el steering. Sin embargo, mediante la implementación de filtros estocásticos locales (implementados por Alice y Bob), se logra recuperar la violación de la desigualdad (V > 0) en regímenes de alto ruido donde antes era imposible. Específicamente, con un filtro de f = 0,7, se evidencia una recuperación significativa de la capacidad de steering, validando que las operaciones estocásticas locales permiten activar la metrología cuántica en escenarios ruidosos a costa de una pérdida probabilística de fotones.
Quantum metrology promises to surpass classical precision limits in parameter estimation; however, the presence of environmental noise typically degrades this advantage, forcing the system to obey the standard classical limit. In this thesis, we address the problem of parameter estimation using Temporal Steering as the main metrological resource in quantum channels affected by amplitude damping noise (Amplitude Damping Channel). To combat this inability to estimate, preand post-filtering operations were used. The implementation consists of an optical experimental setup using a heralded photon source generated by spontaneous parametric down-conversion (SPDC), aiming to work in a single-photon quantum regime. In the context of using temporal steering for metrological purposes, the scenario to be implemented is a prepareand- measure setup; specifically, a single particle is sent to Alice’s laboratory to apply a set of incompatible operations at a time t1. Then, a phase θ is applied. Finally, the state that Bob receives at a time t2 will depend on the operations performed by Alice and the applied phase. Bob’s task is, through incompatible measurements, to determine if the ensemble of states violates a steering inequality in order to verify if there is any type of temporal correlation between the preparation measurements and the ensemble of states. Due to the type of steering inequality we use, we can similarly conclude whether or not it is possible to perform the estimation of the parameter θ. The proposed objective was to study this parameter estimation in a realistic scenario. Since operations are not perfect, we added a quantum channel associated with an error in the implementation of the unitary operation. The amplitude damping channel represents the loss of the state to the environment. To combat this, local stochastic filters, parameterized by the value f, were implemented, allowing us to mitigate the negative effect of the noisy channel associated with the parameter estimation. The improvement was analyzed through the violation of the steering inequality V as a function of the applied noise level γ for different filter values. The results demonstrate that, without any type of filter (f = 0), the violation of the steering inequality disappears for noise values γ ≥ 0,5, nullifying the quantum advantage provided by steering. However, by implementing local stochastic filters (applied by Alice and Bob), it is possible to recover the inequality violation (V > 0) in high-noise regimes where it was previously impossible. Specifically, with a filter of f = 0,7, a significant recovery of the steering capability is observed, validating that local stochastic operations allow quantum metrology to be activated in noisy scenarios at the cost of probabilistic photon loss.
Quantum metrology promises to surpass classical precision limits in parameter estimation; however, the presence of environmental noise typically degrades this advantage, forcing the system to obey the standard classical limit. In this thesis, we address the problem of parameter estimation using Temporal Steering as the main metrological resource in quantum channels affected by amplitude damping noise (Amplitude Damping Channel). To combat this inability to estimate, preand post-filtering operations were used. The implementation consists of an optical experimental setup using a heralded photon source generated by spontaneous parametric down-conversion (SPDC), aiming to work in a single-photon quantum regime. In the context of using temporal steering for metrological purposes, the scenario to be implemented is a prepareand- measure setup; specifically, a single particle is sent to Alice’s laboratory to apply a set of incompatible operations at a time t1. Then, a phase θ is applied. Finally, the state that Bob receives at a time t2 will depend on the operations performed by Alice and the applied phase. Bob’s task is, through incompatible measurements, to determine if the ensemble of states violates a steering inequality in order to verify if there is any type of temporal correlation between the preparation measurements and the ensemble of states. Due to the type of steering inequality we use, we can similarly conclude whether or not it is possible to perform the estimation of the parameter θ. The proposed objective was to study this parameter estimation in a realistic scenario. Since operations are not perfect, we added a quantum channel associated with an error in the implementation of the unitary operation. The amplitude damping channel represents the loss of the state to the environment. To combat this, local stochastic filters, parameterized by the value f, were implemented, allowing us to mitigate the negative effect of the noisy channel associated with the parameter estimation. The improvement was analyzed through the violation of the steering inequality V as a function of the applied noise level γ for different filter values. The results demonstrate that, without any type of filter (f = 0), the violation of the steering inequality disappears for noise values γ ≥ 0,5, nullifying the quantum advantage provided by steering. However, by implementing local stochastic filters (applied by Alice and Bob), it is possible to recover the inequality violation (V > 0) in high-noise regimes where it was previously impossible. Specifically, with a filter of f = 0,7, a significant recovery of the steering capability is observed, validating that local stochastic operations allow quantum metrology to be activated in noisy scenarios at the cost of probabilistic photon loss.
Description
Tesis presentada para optar al grado de Magíster en Ciencias con mención en Física.
Keywords
Metrología, Teoría cuántica, Ruido, Fotónica