Contextuality, Complementarity, Signaling, and Bell Tests
This is a review devoted to the complementarity–contextuality interplay with connection to the Bell inequalities. Starting the discussion with complementarity, I point to contextuality as its seed. <i>Bohr contextuality</i> is the dependence of an observable’s outcome on the experimental...
| Main Author: | |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
MDPI AG
2022-09-01
|
| Series: | Entropy |
| Subjects: | |
| Online Access: | https://www.mdpi.com/1099-4300/24/10/1380 |
| _version_ | 1797473427316015104 |
|---|---|
| author | Andrei Khrennikov |
| author_facet | Andrei Khrennikov |
| author_sort | Andrei Khrennikov |
| collection | DOAJ |
| description | This is a review devoted to the complementarity–contextuality interplay with connection to the Bell inequalities. Starting the discussion with complementarity, I point to contextuality as its seed. <i>Bohr contextuality</i> is the dependence of an observable’s outcome on the experimental context; on the system–apparatus interaction. Probabilistically, complementarity means that the <i>joint probability distribution</i> (JPD) does not exist. Instead of the JPD, one has to operate with contextual probabilities. The Bell inequalities are interpreted as the statistical tests of contextuality, and hence, incompatibility. For context-dependent probabilities, these inequalities may be violated. I stress that contextuality tested by the Bell inequalities is the so-called <i>joint measurement contextuality</i> (JMC), the special case of Bohr’s contextuality. Then, I examine the role of signaling (marginal inconsistency). In QM, signaling can be considered as an experimental artifact. However, often, experimental data have signaling patterns. I discuss possible sources of signaling—for example, dependence of the state preparation on measurement settings. In principle, one can extract the measure of “pure contextuality” from data shadowed by signaling. This theory is known as <i>contextuality by default</i> (CbD). It leads to inequalities with an additional term quantifying signaling: Bell–Dzhafarov–Kujala inequalities. |
| first_indexed | 2024-03-09T20:14:22Z |
| format | Article |
| id | doaj.art-3e1524b868564ea0a7b781a02c349407 |
| institution | Directory Open Access Journal |
| issn | 1099-4300 |
| language | English |
| last_indexed | 2024-03-09T20:14:22Z |
| publishDate | 2022-09-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Entropy |
| spelling | doaj.art-3e1524b868564ea0a7b781a02c3494072023-11-24T00:02:40ZengMDPI AGEntropy1099-43002022-09-012410138010.3390/e24101380Contextuality, Complementarity, Signaling, and Bell TestsAndrei Khrennikov0International Center for Mathematical Modeling in Physics and Cognitive Sciences, Linnaeus University, SE-351 95 Växjö, SwedenThis is a review devoted to the complementarity–contextuality interplay with connection to the Bell inequalities. Starting the discussion with complementarity, I point to contextuality as its seed. <i>Bohr contextuality</i> is the dependence of an observable’s outcome on the experimental context; on the system–apparatus interaction. Probabilistically, complementarity means that the <i>joint probability distribution</i> (JPD) does not exist. Instead of the JPD, one has to operate with contextual probabilities. The Bell inequalities are interpreted as the statistical tests of contextuality, and hence, incompatibility. For context-dependent probabilities, these inequalities may be violated. I stress that contextuality tested by the Bell inequalities is the so-called <i>joint measurement contextuality</i> (JMC), the special case of Bohr’s contextuality. Then, I examine the role of signaling (marginal inconsistency). In QM, signaling can be considered as an experimental artifact. However, often, experimental data have signaling patterns. I discuss possible sources of signaling—for example, dependence of the state preparation on measurement settings. In principle, one can extract the measure of “pure contextuality” from data shadowed by signaling. This theory is known as <i>contextuality by default</i> (CbD). It leads to inequalities with an additional term quantifying signaling: Bell–Dzhafarov–Kujala inequalities.https://www.mdpi.com/1099-4300/24/10/1380contextualitycomplementarityBell inequalitiesquantum nonlocalityjoint probability distributionVäxjö model for contextual probability |
| spellingShingle | Andrei Khrennikov Contextuality, Complementarity, Signaling, and Bell Tests Entropy contextuality complementarity Bell inequalities quantum nonlocality joint probability distribution Växjö model for contextual probability |
| title | Contextuality, Complementarity, Signaling, and Bell Tests |
| title_full | Contextuality, Complementarity, Signaling, and Bell Tests |
| title_fullStr | Contextuality, Complementarity, Signaling, and Bell Tests |
| title_full_unstemmed | Contextuality, Complementarity, Signaling, and Bell Tests |
| title_short | Contextuality, Complementarity, Signaling, and Bell Tests |
| title_sort | contextuality complementarity signaling and bell tests |
| topic | contextuality complementarity Bell inequalities quantum nonlocality joint probability distribution Växjö model for contextual probability |
| url | https://www.mdpi.com/1099-4300/24/10/1380 |
| work_keys_str_mv | AT andreikhrennikov contextualitycomplementaritysignalingandbelltests |