Abstract
We introduce on physical grounds a natural metric structure for the space of states \(\hat{D}\) in quantum mechanics, in order to estimate, for instance, the quality of an approximation through the distance between a state and one of its approximations. This metric is issued naturally from quantum information theory. Its construction relies on an analysis of the mathematical foundations of quantum mechanics and on von Neumann’s entropy S=-Tr \(\hat{D}\) ln \(\hat{D}\). Its form, ds 2=-d2 S(\(\hat{D}\)) deserves mathematical study.
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Balian, R. (2013). A Metric for Quantum States Issued from von Neumann’s Entropy. In: Nielsen, F., Barbaresco, F. (eds) Geometric Science of Information. GSI 2013. Lecture Notes in Computer Science, vol 8085. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-40020-9_56
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DOI: https://doi.org/10.1007/978-3-642-40020-9_56
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-40019-3
Online ISBN: 978-3-642-40020-9
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