Superposing pure quantum states with partial prior information

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.

9 pages, 4 figures

References in corpus (7)

• Quantum Computing
• Creation of superposition of unknown quantum states
• Approximate Quantum Adders with Genetic Algorithms: An IBM Quantum Experience
• The Forbidden Quantum Adder
• Experimental creation of superposition of unknown photonic quantum states
• Experimentally superposing two pure states with partial prior knowledge
• Universal superposition of arbitrary orthogonal states

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• Quantum Algorithm for a Convergent Series of Approximations towards the Exact Solution of the Lowest Eigenstates of a Hamiltonian