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Entropy as a bound for expectation values and variances of a general quantum mechanical observable

Shubhayan Sarkar

School of Physical Sciences, National Institute of Science Education and Research, HBNI, Jatni 752050, India

https://doi.org/10.1142/S0219749918500363Cited by:2 (Source: Crossref)

Abstract

Quantum information-theoretic approach had been identified as a way to understand the foundations of quantum mechanics as early as 1950 due to Shannon. However, there hasn’t been enough advancement or rigorous development of the subject. In the following paper we try to find the relationship between a general quantum mechanical observable and von Neumann entropy. We find that the expectation values and the uncertainties of the observables have bounds which depend on the entropy. The results also show that von Neumann entropy is not just the uncertainty of the state but also encompasses the information about expectation values and uncertainties of any observable which depend on the observers choice for a particular measurement. Also a reverse uncertainty relation is derived for $n$ quantum mechanical observables.

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