The Min-Entropy of Classical-Quantum Combs for Measurement-Based Applications

• URL: http://arxiv.org/abs/2212.00553v3
• Date: Wed, 6 Dec 2023 15:50:47 GMT
• Title: The Min-Entropy of Classical-Quantum Combs for Measurement-Based Applications
• Authors: Isaac D. Smith, Marius Krumm, Lukas J. Fiderer, Hendrik Poulsen Nautrup and Hans J. Briegel
• Abstract summary: We formalise multi-round learning processes using a generalisation of classical-quantum states, called classical-quantum combs. We focus attention on an array of problems derived from measurement-based quantum computation (MBQC) and related applications.
• Score: 0.5999777817331317
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: 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 (Chiribella and Ebler, NJP, 2016) 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. We also introduce a novel connection between MBQC and quantum causal models that arises in this context.

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