Clauser–Horne–Shimony–Holt inequality
E463604
The Clauser–Horne–Shimony–Holt inequality is a key formulation of Bell's inequality used in quantum mechanics to test the incompatibility of local hidden variable theories with the predictions of quantum entanglement.
All labels observed (8)
| Label | Occurrences |
|---|---|
| CHSH inequality | 5 |
| Clauser–Horne–Shimony–Holt inequality canonical | 4 |
| Bell inequalities | 3 |
| CHSH Bell inequality | 1 |
| CHSH Bell test experiment | 1 |
| CHSH experiment | 1 |
| CHSH-type Bell inequality | 1 |
| Clauser–Horne–Shimony–Holt experiment | 1 |
How this entity was disambiguated
This entity first appeared as the object of triple T4706891 — resolving that mention is where its identity was fixed. The disambiguator weighed these candidate entities and picked the highlighted one (or “None”, minting a new entity). This is how homonymy is resolved: the same surface form can point to different entities.
NED1
Entity disambiguation (via context triple)
gpt-5-mini-2025-08-07
Target entity: Clauser–Horne–Shimony–Holt inequality Context triple: [John F. Clauser, notableWork, Clauser–Horne–Shimony–Holt inequality]
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A.
Aspect experiment on Bell inequality tests (1982)
The Aspect experiment on Bell inequality tests (1982) was a landmark series of quantum physics experiments that provided strong evidence for quantum entanglement and the violation of Bell's inequalities, challenging local hidden-variable theories.
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B.
Einstein–Podolsky–Rosen paradox
The Einstein–Podolsky–Rosen paradox is a thought experiment that challenges the completeness of quantum mechanics by highlighting the strange, nonlocal correlations predicted for entangled particles.
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C.
Frauchiger–Renner paradox
The Frauchiger–Renner paradox is a thought experiment in quantum foundations that extends Wigner’s friend scenario to argue that standard quantum theory cannot consistently describe its own use by multiple observers.
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D.
Wigner’s friend thought experiment
Wigner’s friend thought experiment is a foundational quantum mechanics scenario that explores the role of observers and consciousness in measurement by considering how different observers can assign conflicting quantum states to the same system.
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E.
Bennett–Brassard 1984 protocol
The Bennett–Brassard 1984 protocol is the first quantum key distribution scheme, using quantum properties of photons to enable two parties to establish a shared secret key with security guaranteed by the laws of quantum mechanics.
- F. None of above. chosen
- G. Unsure - the case is ambiguous/there is not enough information to decide.
NED2
Entity disambiguation (via description)
gpt-5-mini-2025-08-07
Target entity: Clauser–Horne–Shimony–Holt inequality Target entity description: The Clauser–Horne–Shimony–Holt inequality is a key formulation of Bell's inequality used in quantum mechanics to test the incompatibility of local hidden variable theories with the predictions of quantum entanglement.
-
A.
Aspect experiment on Bell inequality tests (1982)
The Aspect experiment on Bell inequality tests (1982) was a landmark series of quantum physics experiments that provided strong evidence for quantum entanglement and the violation of Bell's inequalities, challenging local hidden-variable theories.
-
B.
Einstein–Podolsky–Rosen paradox
The Einstein–Podolsky–Rosen paradox is a thought experiment that challenges the completeness of quantum mechanics by highlighting the strange, nonlocal correlations predicted for entangled particles.
-
C.
Frauchiger–Renner paradox
The Frauchiger–Renner paradox is a thought experiment in quantum foundations that extends Wigner’s friend scenario to argue that standard quantum theory cannot consistently describe its own use by multiple observers.
-
D.
Wigner’s friend thought experiment
Wigner’s friend thought experiment is a foundational quantum mechanics scenario that explores the role of observers and consciousness in measurement by considering how different observers can assign conflicting quantum states to the same system.
-
E.
Bennett–Brassard 1984 protocol
The Bennett–Brassard 1984 protocol is the first quantum key distribution scheme, using quantum properties of photons to enable two parties to establish a shared secret key with security guaranteed by the laws of quantum mechanics.
- F. None of above. chosen
Statements (47)
| Predicate | Object |
|---|---|
| instanceOf |
Bell inequality
ⓘ
mathematical inequality ⓘ physical law ⓘ |
| alsoKnownAs |
CHSH inequality
ⓘ
linked to:
Clauser–Horne–Shimony–Holt inequality
|
| appliesTo |
bipartite systems
ⓘ
two spatially separated observers ⓘ two-qubit systems ⓘ |
| assumes |
locality
ⓘ
measurement independence ⓘ realism ⓘ |
| describes | constraints on correlations in local hidden variable theories ⓘ |
| field |
philosophy of physics
ⓘ
quantum foundations ⓘ quantum information theory ⓘ quantum mechanics ⓘ |
| generalizationOf | Bell inequality for two settings and two outcomes ⓘ |
| hasComponent | CHSH operator ⓘ |
| hasConsequence | demonstration of incompatibility between local realism and quantum mechanics ⓘ |
| hasDomain | correlation functions of measurement outcomes ⓘ |
| hasForm | |S| ≤ 2 for local hidden variable theories ⓘ |
| implies | no local hidden variable model can reproduce all quantum predictions ⓘ |
| inspired | numerous experimental tests of Bell inequalities ⓘ |
| mathematicalStructure | linear inequality in expectation values ⓘ |
| measurementScenario | two parties with two dichotomic observables each ⓘ |
| namedAfter |
Abner Shimony
ⓘ
John F. Clauser ⓘ Michael A. Horne ⓘ Richard A. Holt ⓘ |
| partOf | foundations of quantum theory ⓘ |
| publicationYear | 1969 ⓘ |
| quantumMechanicalBound | 2√2 ⓘ |
| relatedTo |
Bell theorem
ⓘ
linked to:
Bell’s theorem
Clauser–Horne inequality ⓘ EPR paradox ⓘ
linked to:
Einstein–Podolsky–Rosen paradox
Tsirelson bound ⓘ local realism ⓘ quantum nonlocality ⓘ |
| usedFor |
experimental tests of quantum entanglement
ⓘ
ruling out local hidden variable theories ⓘ testing Bell nonlocality ⓘ testing local realism ⓘ |
| usedIn |
device-independent quantum cryptography
ⓘ
loophole-free Bell tests ⓘ randomness certification ⓘ |
| violatedBy |
entangled quantum states
ⓘ
maximally entangled two-qubit states ⓘ singlet state of two spin-1/2 particles ⓘ |
How these facts were elicited
The pipeline generated the facts above by prompting gpt-5.1 with this entity's name + description and the instruction below.
Instruction
You are a knowledge base construction expert. Given a subject entity and a description of it, return factual statements that you know for the subject as a JSON list of dictionaries(triples), where keys must be "subject", "predicate" and "object". The number of facts may be very high, between 25 to 50 or more, for very popular subjects. For less popular subjects, the number of facts can be very low, like 5 or 10. # Requirements - If you don't know the subject at all, return an empty list. - If the subject is not a named entity, return an empty list. - Include at least one triple where predicate is "instanceOf". - Do not get too wordy. - Separate several objects into multiple triples with one object.
Input
Subject: Clauser–Horne–Shimony–Holt inequality Description of subject: The Clauser–Horne–Shimony–Holt inequality is a key formulation of Bell's inequality used in quantum mechanics to test the incompatibility of local hidden variable theories with the predictions of quantum entanglement.
Referenced by (17)
Full triples — surface form annotated when it differs from this entity's canonical label.
linked to: Clauser–Horne–Shimony–Holt inequality
linked to: Clauser–Horne–Shimony–Holt inequality
linked to: Clauser–Horne–Shimony–Holt inequality
Teleporting an unknown quantum state via dual classical and Einstein–Podolsky–Rosen channels
→
relatesTo
→
Bell inequalities
ⓘ
linked to: Clauser–Horne–Shimony–Holt inequality
subject linked to:
Clauser
linked to: Clauser–Horne–Shimony–Holt inequality
subject linked to:
Clauser
linked to: Clauser–Horne–Shimony–Holt inequality
linked to: Clauser–Horne–Shimony–Holt inequality
subject linked to:
John
linked to: Clauser–Horne–Shimony–Holt inequality
subject linked to:
John
linked to: Clauser–Horne–Shimony–Holt inequality
linked to: Clauser–Horne–Shimony–Holt inequality
subject linked to:
Bell’s theorem
linked to: Clauser–Horne–Shimony–Holt inequality
subject linked to:
Bell’s theorem
linked to: Clauser–Horne–Shimony–Holt inequality
linked to: Clauser–Horne–Shimony–Holt inequality