The Min-Entropy of Classical-Quantum Combs for Measurement-Based Applications
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 encod...
| Main Authors: | , , , , |
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| Format: | Article |
| Language: | English |
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Verein zur Förderung des Open Access Publizierens in den Quantenwissenschaften
2023-12-01
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| Series: | Quantum |
| Online Access: | https://quantum-journal.org/papers/q-2023-12-12-1206/pdf/ |
| _version_ | 1827586557784096768 |
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| author | Isaac D. Smith Marius Krumm Lukas J. Fiderer Hendrik Poulsen Nautrup Hans J. Briegel |
| author_facet | Isaac D. Smith Marius Krumm Lukas J. Fiderer Hendrik Poulsen Nautrup Hans J. Briegel |
| author_sort | Isaac D. Smith |
| collection | DOAJ |
| description | 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. |
| first_indexed | 2024-03-09T00:03:19Z |
| format | Article |
| id | doaj.art-bfa2c36ca8a94c268c4651b58cae2b76 |
| institution | Directory Open Access Journal |
| issn | 2521-327X |
| language | English |
| last_indexed | 2024-03-09T00:03:19Z |
| publishDate | 2023-12-01 |
| publisher | Verein zur Förderung des Open Access Publizierens in den Quantenwissenschaften |
| record_format | Article |
| series | Quantum |
| spelling | doaj.art-bfa2c36ca8a94c268c4651b58cae2b762023-12-12T14:54:31ZengVerein zur Förderung des Open Access Publizierens in den QuantenwissenschaftenQuantum2521-327X2023-12-017120610.22331/q-2023-12-12-120610.22331/q-2023-12-12-1206The Min-Entropy of Classical-Quantum Combs for Measurement-Based ApplicationsIsaac D. SmithMarius KrummLukas J. FidererHendrik Poulsen NautrupHans J. BriegelLearning 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.https://quantum-journal.org/papers/q-2023-12-12-1206/pdf/ |
| spellingShingle | Isaac D. Smith Marius Krumm Lukas J. Fiderer Hendrik Poulsen Nautrup Hans J. Briegel The Min-Entropy of Classical-Quantum Combs for Measurement-Based Applications Quantum |
| title | The Min-Entropy of Classical-Quantum Combs for Measurement-Based Applications |
| title_full | The Min-Entropy of Classical-Quantum Combs for Measurement-Based Applications |
| title_fullStr | The Min-Entropy of Classical-Quantum Combs for Measurement-Based Applications |
| title_full_unstemmed | The Min-Entropy of Classical-Quantum Combs for Measurement-Based Applications |
| title_short | The Min-Entropy of Classical-Quantum Combs for Measurement-Based Applications |
| title_sort | min entropy of classical quantum combs for measurement based applications |
| url | https://quantum-journal.org/papers/q-2023-12-12-1206/pdf/ |
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