Berlin 2024 – scientific programme

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QI: Fachverband Quanteninformation

QI 12: Poster I

QI 12.5: Poster

Tuesday, March 19, 2024, 11:00–14:30, Poster B

Coherence as a resource for phase estimation — •Felix Ahnefeld¹, Thomas Theurer², and Martin B. Plenio¹ — ¹Institut für Theoretische Physik, Universität Ulm — ²Department of Mathematics and Statistics, Institute for Quantum Science and Technology, University of Calgary

Quantum phase estimation is a vital subroutine for several quantum algorithms that promise super-polynomial speedups compared to the best-known classical algorithm. Given a fixed number of copies of a black box unitary, the goal is to estimate an eigenvalue of the unitary, i.e., a phase factor, as precisely as possible. Quantum mechanical strategies can outperform classical estimation strategies and the question arises which resources allow for such an advantage. We address this question by investigating a family of constrained phase estimation protocols whose performance is measured with respect to the average cost of a generic cost function that penalizes deviations of the phase estimates to the true value. We quantitatively link the performance of the protocol with so-called measures of quantum coherence that are rigorously defined within the framework of a quantum resource theory. We show that for every non-trivial cost function, which one can think of as the specific task phase estimation should solve, coherence grants an operational advantage compared to classical strategies. Lastly, we provide universal bounds on the average cost in terms of the number of the query size and the provided coherence.

Keywords: Quantum resource theories; Coherence theory; Quantum Computation; Quantum advantages