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QI: Fachverband Quanteninformation

QI 29: Quantum Information: Concept and Methods II

QI 29.8: Vortrag

Donnerstag, 21. März 2024, 17:00–17:15, HFT-TA 441

The Min-Entropy of Classical-Quantum Combs for Measurement-Based Applications — •Isaac D. Smith, Marius Krumm, Lukas J. Fiderer, Hendrik Poulsen Nautrup, and Hans J. Briegel — Institute for Theoretical Physics, UIBK, 6020 Innsbruck, Austria

Learning a hidden property of a quantum system typically requires a series of interactions. In this work, we formalise such multi-round learning processes using a generalisation of classical-quantum states, called classical-quantum combs. Here, 'classical' refers to a random variable encoding the hidden property to be learnt, and 'quantum' refers to the quantum comb describing the behaviour of the system. The optimal strategy for learning the hidden property can be quantified by applying the comb min-entropy to classical-quantum combs. To demonstrate the power of this approach, we focus attention on an array of problems derived from measurement-based quantum computation (MBQC) and related applications. Specifically, we describe a known blind quantum computation (BQC) protocol using the combs formalism and thereby leverage the min-entropy to provide a proof of single-shot security for multiple rounds of the protocol, extending the existing result in the literature. Furthermore, we consider a range of operationally motivated examples related to the verification of a partially unknown MBQC device. These examples involve learning the features of the device necessary for its correct use, including learning its internal reference frame for measurement calibration.

Keywords: Measurement-based quantum computation; Quantum combs; Min-entropy; Blind quantum computation