Abstract
We review a general theory to describe the nonunitary evolution of quantum systems under measurement, which is the main subject of the first part of this Thesis. Quantum measurement theory provides us with a theoretical framework to discuss how a quantum system exhibits an unavoidable change due to a measurement process. In particular, theory of continuous measurements gives a unified description to study the nonunitary dynamics of quantum systems subject to weak and frequent repeated measurements. In Sect. 2.1, we formulate a quantum measurement process based on an indirect measurement model and review its mathematical property. In Sect. 2.2, we apply it to formulate a theory of continuous observations, in which measurements are performed continuously in time.
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Notes
- 1.
We remark that \(dN_{m}\) is not a simple Poisson process as its intensity depends on a stochastic vector \(|\psi \rangle _{S}\).
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Ashida, Y. (2020). Continuous Observation of Quantum Systems. In: Quantum Many-Body Physics in Open Systems: Measurement and Strong Correlations. Springer Theses. Springer, Singapore. https://doi.org/10.1007/978-981-15-2580-3_2
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DOI: https://doi.org/10.1007/978-981-15-2580-3_2
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