Measurements in quantum systems have an intrinsic probabilistic character that can not be explained the same way as the probabilistic behavior of classical systems. In particular, depending on the incompatibility relations among the measurements and the state of the quantum system being probed, it is impossible to describe the probabilities generated by an experiment using a single classical probability space. This impossibility has several consequences, and contextuality and non-locality are two intriguing characteristics of quantum system emerging from this observation. Quantum non-locality and quantum contextuality are necessary ingredients for the advantage of quantum systems over their classical counterpartsin a myriad of situations. Non-locality is an essential ingredient in several device-independent protocols involving multipartite systems; quantum contextuality is a necessary resource for universal computation in models based onmagic state distillation, in measurement-based quantum computation and also in computational models of qubits; the presence of contextuality in a given system lower bounds the classical memory needed to simulate the experiment and in some situations reproducing the results of sequential measurements on a quantum system exhibiting contextuality requires more memory than theinformation-carrying capacity of the system itself; non-locality and contextuality can be used to certify the generation of genuinely random numbers, a major problem in various areas, especially in cryptography; contextuality offersadvantages in the problems of discrimination of states and one-way communication protocols.Recently, quantum contextuality has also been identified as a resource for certifying quantum signatures in thermodynamics and metrology.Quantum thermodynamics is the field of research that investigates heat, work, temperature, and related concepts in quantum systems. Quantummetrology is the field of research that investigates how to develop strategiesto perform high-resolution and highly sensitive measurements of physical parameters using quantum systems.A fundamental difference between classical and quantum dynamics is that the latteris generally contextual. This implies the existence of quantum engines whosepower output scaling requires contextuality. Contextuality can also be used as a resource for local metrology.In this project our goal is to investigate the relation between quantum contextuality and quantum thermodynamics, as well as related problems, such asquantum metrology. Contextuality may be related to thermodynamics in twoways. In one hand, it can be used as resource to understand and engineerquantum advantages in thermodynamic tasks. On the other hand, since contextuality is related to the statistics of an experiment, contextuality is relatedto information, and information is an important concept in thermodynamics.This may help us understand the cost of producing contextual correlations interms of energy, heat, and other related quantities. Isso pode nos ajudar a entender o custo de produzir correlações contextuais emtermos de energia, calor e outras quantidades relacionadas.
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