these arise from a useful result in majorization theory. This work complements recent studies in quantum computation where the deviation of the Born Rule from the LTP is measured in terms of negativity of Wigner functions.'
author:
- 'John B. DeBrota$^\dag$'
- 'Christopher A. Fuchs$^\dag$'
- 'Blake C. Stacey'
date: 23 January 2020
title: Symmetric Informationally Complete Measurements Identify the Irreducible Difference between Classical and Quantum Systems
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Quantum information theory represents a change of perspective. Rather than regarding quantum physics as a limitation on our abilities—the typical sentiment of older texts—we have learned that it can augment them. In frustrating some ambitions, it enables more subtle ones. Deviation from classicality is a *resource,* and the idea that this resource can be quantified as a modification of the classical probability calculus dates to the beginning of the field [@Feynman:1981]. More recent inquiries have developed this notion precisely: The “negativity” in a Wigner-function representation of quantum states is now understood to be valuable in its own right [@Veitch:2014; @Howard:2014; @Delfosse:2015; @Pashayan:2015; @Stacey:2016; @Zhu:2016; @DeBrota:2017; @Howard:2017; @Raussendorf:2017; @Kocia:2017]. But what does this line of thinking say about quantum mechanics itself? Can one, following the lead of Carnot, take what might seem a 