Quantum Inequalities Comparison
Explore the fundamental differences between Bell inequalities (testing spatial correlations) and Leggett-Garg inequalities (testing temporal correlations) in quantum mechanics.
This interactive table compares two key concepts in quantum foundations: Bell inequalities (spatial nonlocality) and Leggett-Garg inequalities (temporal macrorealism). Click on rows to highlight them, or use the buttons below to explore specific aspects.
| Dimension | Bell Inequalities | Leggett–Garg Inequalities (LGI) |
|---|---|---|
| What they test | Local realism in spatially separated systems | Macrorealism and noninvasive measurability in a single system over time |
| Type of correlations | Spatial correlations between two or more distinct subsystems | Temporal correlations of one system measured at different times |
| Underlying classical assumptions | Locality and realism | Macrorealism per se and noninvasive measurability |
| Quantum violation implies | Nonlocality or contextuality | Failure of macrorealism or impossibility of noninvasive measurement |
| Typical experimental platforms | Entangled photons, trapped ions, superconducting qubits | Superconducting qubits, nuclear spins, mesoscopic systems |
| Mathematical structure | Inequalities involving joint probabilities of outcomes from separated detectors | Inequalities involving time-separated correlation functions Cij = ⟨Q(ti) Q(tj)⟩ |
| Canonical inequality form | CHSH: |S| ≤ 2 | LGI: K = C12 + C23 - C13 ≤ 1 |
| Interpretational target | Limits of classical locality | Limits of classical realism in time (macrorealism) |
| Historical motivation | Einstein–Podolsky–Rosen paradox and nonlocality | Determining whether macroscopic systems can behave quantum-mechanically |
| Conceptual analogue | Spatial entanglement tests | "Entanglement in time" or temporal coherence tests |
Quantum Concepts Explained
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