Authors : Debopam Ghosh

Volume/Issue : Volume 8 - 2023, Issue 12 - December

Google Scholar : http://tinyurl.com/u9hmebej

Scribd : http://tinyurl.com/4963bu4x

DOI : https://doi.org/10.5281/zenodo.10374569

Abstract : The research article presents a mathematical framework for calculation of arithmetic mean and associated standard deviation of a set of replicate measurements, based on assignment of data point weightage as diagonal entries of the Density matrix descriptions generated from the set of data points under consideration. The framework presented provides flexibility in choice of the assigned weightage distributions by allowing for evolution of these weightage contributions under the effect of completely positive trace preserving transformations implemented through Unitary Quantum de-coherence channels [1, 8, 10, 11, 12, 14, 15, 17]. The presented formulation contains the conventional calculation procedure as a special case which involve the tuning parameter ‘θ’ being set equal to zero. Numerical case studies presented in the paper provide appropriate illustration of the mathematical constructs and terminology introduced.

Keywords : Arithmetic mean and Standard deviation of a set of measurements, Density Matrix description associated with mathematical constructs, Completely Positive Trace Preserving transformations, Kraus operators, Quantum Channels and Quantum de-coherence, Obliqueness factor associated with mean-variance partitioning of a set of measurements.