The Leggett–Garg inequalities are theoretical tools designed to test whether macroscopic systems—like large objects or complex quantum states—can behave according to classical realism or whether they exhibit quantum effects.
Proposed by Anthony Leggett and Anupam Garg in 1985, these inequalities test two key assumptions:
- Macroscopic realism: A system exists in a definite state at all times, independent of observation.
- Non-invasive measurability: It is possible to observe the system without altering its future dynamics.
Using a sequence of measurements at different times, the Leggett–Garg inequalities set statistical limits that any classical system (obeying the two assumptions) should satisfy.
However, quantum systems can violate these inequalities, showing that:
- The system does not have definite properties until measured,
- Or that measurements inherently disturb the system,
- Or both—implying a breakdown of classical realism even at macroscopic scales.
These inequalities have been tested in experiments with:
- Superconducting circuits,
- Spin systems,
- Optical setups,
- And biological molecules.
Violations of the Leggett–Garg inequalities support the idea that quantum coherence and superposition may persist in larger systems than once believed, blurring the line between the quantum and classical worlds.