Superposing pure quantum states with partial prior information

Abstract

The principle of superposition is an intriguing feature of quantum mechanics, which is regularly exploited in many different circumstances. A recent work [M. Oszmaniec et al., Phys. Rev. Lett. 116, 110403 (2016)] shows that the fundamentals of quantum mechanics restrict the process of superimposing two unknown pure states, even though it is possible to superimpose two quantum states with partial prior knowledge. The prior knowledge imposes geometrical constraints on the choice of input states. We discuss an experimentally feasible protocol to superimpose multiple pure states of a $d$-dimensional quantum system and carry out an explicit experimental realization for two single-qubit pure states with partial prior information on a two-qubit NMR quantum information processor.