We have decided to discontinue the publication of preprints on our preprint server as of 1 March 2024. The publication culture within mathematics has changed so much due to the rise of repositories such as ArXiV (www.arxiv.org) that we are encouraging all institute members to make their preprints available there. An institute's repository in its previous form is, therefore, unnecessary. The preprints published to date will remain available here, but we will not add any new preprints here.
MiS Preprint
4/2024
Characterizing the superposition of arbitrary random quantum states and a known quantum state
Bo Li, Xiao-Bin Liang and Shao-Ming Fei
Abstract
The superposition of states is one of the most fundamental issues in the quantum world. Generally there do not exist physical operations to superpose two unknown random states with nonzero probability. We investigate the superposition problem of unknown qubit states with respect to a fixed qubit state. It is shown that under trace-nonincreasing completely positive operations the superposable state sets are located in circles on the Bloch sphere. Meanwhile, we prove that the quantum states in a circle on the Bloch sphere are superposable with respect to a fixed state. Finally, for the high-dimensional case we illustrate that any superposition transformation protocols will violate the no-cloning principle for almost all the states. Our results also promote the understanding and applications of the superposition principle in view of quantum no-go theorems.
