Characterising and bounding the set of quantum behaviours in contextuality scenarios
The predictions of quantum theory resist generalised noncontextual explanations. In addition to the foundational relevance of this fact, the particular extent to which quantum theory violates noncontextuality limits available quantum advantage in communication and information processing. In the firs...
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| Format: | Article |
| Language: | English |
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Verein zur Förderung des Open Access Publizierens in den Quantenwissenschaften
2021-06-01
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| Series: | Quantum |
| Online Access: | https://quantum-journal.org/papers/q-2021-06-29-484/pdf/ |
| _version_ | 1818742467464265728 |
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| author | Anubhav Chaturvedi Máté Farkas Victoria J Wright |
| author_facet | Anubhav Chaturvedi Máté Farkas Victoria J Wright |
| author_sort | Anubhav Chaturvedi |
| collection | DOAJ |
| description | The predictions of quantum theory resist generalised noncontextual explanations. In addition to the foundational relevance of this fact, the particular extent to which quantum theory violates noncontextuality limits available quantum advantage in communication and information processing. In the first part of this work, we formally define contextuality scenarios via prepare-and-measure experiments, along with the polytope of general contextual behaviours containing the set of quantum contextual behaviours. This framework allows us to recover several properties of set of quantum behaviours in these scenarios, including contextuality scenarios and associated noncontextuality inequalities that require for their violation the individual quantum preparation and measurement procedures to be mixed states and unsharp measurements. With the framework in place, we formulate novel semidefinite programming relaxations for bounding these sets of quantum contextual behaviours. Most significantly, to circumvent the inadequacy of pure states and projective measurements in contextuality scenarios, we present a novel unitary operator based semidefinite relaxation technique. We demonstrate the efficacy of these relaxations by obtaining tight upper bounds on the quantum violation of several noncontextuality inequalities and identifying novel maximally contextual quantum strategies. To further illustrate the versatility of these relaxations, we demonstrate $\textit{monogamy of preparation contextuality}$ in a tripartite setting, and present a secure semi-device independent quantum key distribution scheme powered by quantum advantage in parity oblivious random access codes. |
| first_indexed | 2024-12-18T02:12:59Z |
| format | Article |
| id | doaj.art-3fba931484614ccbb62ef402ff87df32 |
| institution | Directory Open Access Journal |
| issn | 2521-327X |
| language | English |
| last_indexed | 2024-12-18T02:12:59Z |
| publishDate | 2021-06-01 |
| publisher | Verein zur Förderung des Open Access Publizierens in den Quantenwissenschaften |
| record_format | Article |
| series | Quantum |
| spelling | doaj.art-3fba931484614ccbb62ef402ff87df322022-12-21T21:24:27ZengVerein zur Förderung des Open Access Publizierens in den QuantenwissenschaftenQuantum2521-327X2021-06-01548410.22331/q-2021-06-29-48410.22331/q-2021-06-29-484Characterising and bounding the set of quantum behaviours in contextuality scenariosAnubhav ChaturvediMáté FarkasVictoria J WrightThe predictions of quantum theory resist generalised noncontextual explanations. In addition to the foundational relevance of this fact, the particular extent to which quantum theory violates noncontextuality limits available quantum advantage in communication and information processing. In the first part of this work, we formally define contextuality scenarios via prepare-and-measure experiments, along with the polytope of general contextual behaviours containing the set of quantum contextual behaviours. This framework allows us to recover several properties of set of quantum behaviours in these scenarios, including contextuality scenarios and associated noncontextuality inequalities that require for their violation the individual quantum preparation and measurement procedures to be mixed states and unsharp measurements. With the framework in place, we formulate novel semidefinite programming relaxations for bounding these sets of quantum contextual behaviours. Most significantly, to circumvent the inadequacy of pure states and projective measurements in contextuality scenarios, we present a novel unitary operator based semidefinite relaxation technique. We demonstrate the efficacy of these relaxations by obtaining tight upper bounds on the quantum violation of several noncontextuality inequalities and identifying novel maximally contextual quantum strategies. To further illustrate the versatility of these relaxations, we demonstrate $\textit{monogamy of preparation contextuality}$ in a tripartite setting, and present a secure semi-device independent quantum key distribution scheme powered by quantum advantage in parity oblivious random access codes.https://quantum-journal.org/papers/q-2021-06-29-484/pdf/ |
| spellingShingle | Anubhav Chaturvedi Máté Farkas Victoria J Wright Characterising and bounding the set of quantum behaviours in contextuality scenarios Quantum |
| title | Characterising and bounding the set of quantum behaviours in contextuality scenarios |
| title_full | Characterising and bounding the set of quantum behaviours in contextuality scenarios |
| title_fullStr | Characterising and bounding the set of quantum behaviours in contextuality scenarios |
| title_full_unstemmed | Characterising and bounding the set of quantum behaviours in contextuality scenarios |
| title_short | Characterising and bounding the set of quantum behaviours in contextuality scenarios |
| title_sort | characterising and bounding the set of quantum behaviours in contextuality scenarios |
| url | https://quantum-journal.org/papers/q-2021-06-29-484/pdf/ |
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