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quant-ph2025
Approximating quantum states by states of low rank
Nathaniel Johnston, Chi-Kwong Li
Given a positive integer k, it is natural to ask for a formula for the distance between a given density matrix (i.e., mixed quantum state) and the set of density matrices of rank a…
math.FA2025
Generalizing the Cauchy-Schwarz inequality: Hadamard powers and tensor products
Nathaniel Johnston, Sarah Plosker, Charles Torrance +1
We explore and generalize a Cauchy-Schwarz-type inequality originally proved in [Electronic Journal of Linear Algebra 35, 156-180 (2019)]: $\|\mathbf{v}^2\|\|\mathbf{w}^2\| - \lang…