Experimentally superposing two pure states with partial prior knowledge

TL;DR

This paper experimentally demonstrates a probabilistic quantum superposition protocol for two pure states with partial prior knowledge, achieving high fidelity and highlighting its limitations when overlaps approach zero.

Contribution

First experimental realization of a probabilistic superposition protocol for pure states with partial prior knowledge in a three-qubit NMR system.

Findings

Average fidelity over 99% for prepared superpositions

Protocol fails or yields low fidelity when overlaps approach zero

Feasibility demonstrated across a range of input states

Abstract

Superposition, arguably the most fundamental property of quantum mechanics, lies at the heart of quantum information science. However, how to create the superposition of any two unknown pure states remains as a daunting challenge. Recently, it is proved that such a quantum protocol does not exist if the two input states are completely unknown, whereas a probabilistic protocol is still available with some prior knowledge about the input states [M. Oszmaniec \emph{et al.}, Phys. Rev. Lett. 116, 110403 (2016)]. The knowledge is that both of the two input states have nonzero overlaps with some given referential state. In this work, we experimentally realize the probabilistic protocol of superposing two pure states in a three-qubit nuclear magnetic resonance system. We demonstrate the feasibility of the protocol by preparing a families of input states, and the average fidelity between the prepared state and expected superposition state is over 99%. Moreover, we experimentally illustrate the limitation of the protocol that it is likely to fail or yields very low fidelity, if the nonzero overlaps are approaching zero. Our experimental implementation can be extended to more complex situations and other quantum systems.