# Superposing pure quantum states with partial prior information

## TL;DR

This paper explores the superposition of pure quantum states with partial prior information, proposing a feasible protocol for superposing multiple states and demonstrating it experimentally on a two-qubit NMR system.

## Contribution

It introduces a practical protocol for superposing multiple pure states with partial prior knowledge and provides an experimental realization for two-qubit states.

## Key findings

- Superposition of multiple states is feasible with partial prior info.
- Experimental demonstration on a two-qubit NMR system.
- Protocol respects quantum mechanical constraints.

## Abstract

The principle of superposition is an intriguing feature of Quantum Mechanics, which is regularly exploited at various instances. A recent work [PRL \textbf{116}, 110403 (2016)] shows that the fundamentals of Quantum Mechanics restrict the superposition of two arbitrary pure states of a quantum system, even though it is possible to superpose two quantum states with partial prior knowledge. The prior knowledge imposes geometrical constraints on the choice of input pure states. We discuss an experimentally feasible protocol to superpose multiple pure states of a $d$ dimensional quantum system and carry out an explicit experimental realization to superpose two single-qubit pure states on a two-qubit NMR quantum information processor.