Certifying measurement incompatibility in prepare-and-measure and Bell scenarios
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arXiv
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| Hauptverfasser: | , , , |
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| Format: | Preprint |
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2024
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| _version_ | 1866914046498832384 |
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| author | Egelhaaf, Sophie Pauwels, Jef Quintino, Marco Túlio Uola, Roope |
| author_facet | Egelhaaf, Sophie Pauwels, Jef Quintino, Marco Túlio Uola, Roope |
| contents | We consider the problem of certifying measurement incompatibility in a prepare-and-measure (PM) scenario. We present different families of sets of qubit measurements which are incompatible, but cannot lead to any quantum over classical advantage in PM scenarios. Our examples are obtained via a general theorem which proves a set of qubit dichotomic measurements can have their incompatibility certified in a PM scenario if and only if their incompatibility can be certified in a bipartite Bell scenario where the parties share a maximally entangled state. Our framework naturally suggests a hierarchy of increasingly stronger notions of incompatibility, in which more power is given to the classical simulation by increasing its dimensionality. For qubits, we give an example of measurements whose incompatibility can be certified against trit simulations, which we show is the strongest possible notion for qubits in this framework. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_06787 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Certifying measurement incompatibility in prepare-and-measure and Bell scenarios Egelhaaf, Sophie Pauwels, Jef Quintino, Marco Túlio Uola, Roope Quantum Physics We consider the problem of certifying measurement incompatibility in a prepare-and-measure (PM) scenario. We present different families of sets of qubit measurements which are incompatible, but cannot lead to any quantum over classical advantage in PM scenarios. Our examples are obtained via a general theorem which proves a set of qubit dichotomic measurements can have their incompatibility certified in a PM scenario if and only if their incompatibility can be certified in a bipartite Bell scenario where the parties share a maximally entangled state. Our framework naturally suggests a hierarchy of increasingly stronger notions of incompatibility, in which more power is given to the classical simulation by increasing its dimensionality. For qubits, we give an example of measurements whose incompatibility can be certified against trit simulations, which we show is the strongest possible notion for qubits in this framework. |
| title | Certifying measurement incompatibility in prepare-and-measure and Bell scenarios |
| topic | Quantum Physics |
| url | https://arxiv.org/abs/2407.06787 |