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Q: Fachverband Quantenoptik und Photonik

Q 3: Quantum Information (Concepts and Methods) I

Q 3.6: Vortrag

Montag, 9. März 2020, 12:30–12:45, e001

Proving uncertainty relations with semi-definite programming — •Timo Simnacher, Xiao-Dong Yu, and Otfried Gühne — Naturwissenschaftlich-Technische Fakultät, Universität Siegen, Walter-Flex-Straße 3, 57068 Siegen

Heisenberg's uncertainty principle conveys a major distinction between quantum and classical physics. Since its formulation, uncertainty relations have become one of the exceptional trademarks of quantum mechanics. Beside being of fundamental importance, current experiments are indeed able to approach these universal limitations. Although extensive research has been conducted in particular in the field of quantum information theory, there is still no general understanding of uncertainty relations, especially when it comes to more than two measurement settings.

One serious obstacle hindering further advances in the theory of uncertainty relations is the non-linearity common to both, variance- and entropy-based formulations. We present a general method to linearize such relations utilizing multiple copies of the same quantum state. Using semi-definite programming techniques, we provide effective relaxations to obtain non-trivial bounds for relevant state-independent uncertainty relations. Furthermore, we formulate uncertainty relations in terms of moment matrices to achieve results independent of the explicit measurement settings. Semi-definite programs have the advantage of providing a certificate, proving the obtained bounds up to numerical precision.