Johnston, NathanielSikora, Jamie2023-05-092023-05-092022-11http://hdl.handle.net/10919/114996In this work we examine quantum states which have non -negative amplitudes (in a fixed basis) and the channels which preserve them. These states include the ground states of stoquastic Hamiltonians and they are of interest since they avoid the Sign Problem and can thus be efficiently simulated. In optimization theory, the convex cone generated by such states is called the set of completely positive (CP) matrices (not be confused with completely positive superoperators). We introduce quantum channels which preserve these states and call them completely positive completely positive. To study these states and channels, we use the framework of resource theories and investigate how to measure and quantify this resource.(c) 2022 The Author(s). Published by Elsevier Inc.application/pdfenCreative Commons Attribution-NonCommercial-NoDerivatives 4.0 InternationalCompletely positive matricesCompletely positive mapsQuantum resource theoriesArticle - Refereedhttps://doi.org/10.1016/j.laa.2022.08.0166531873-1856