# Quantum Correlations

**Quantum correlations** describe how measurements on different parts of a system are correlated. Beyond entanglement, correlations include classical correlations (knowable information) and quantum discord (information that's quantum-mechanical only).

## Second-Order Correlations

$g^{(2)}(\tau) = \langle a^\dagger a^\dagger a a \rangle(t) / (\langle a^\dagger a \rangle^2)$ measures photon bunching (coherent light, $g^{(2)} \approx 1$) vs antibunching (single photons, $g^{(2)} < 1$).

```python
from qutip import *
import numpy as np

# Cavity with decay
H = 1.0 * a.dag() * a  # Resonator energy
c_ops = [0.1 * a]       # Photon loss

times = np.linspace(0, 10, 100)
n0 = 5  # Initial photon number
rho0 = fock_dm(10, n0)

# Solve for expectation values
e_ops = [a.dag() * a, a.dag() * a.dag() * a * a]
result = mesolve(H, rho0, times, c_ops, e_ops)

n = result.expect[0]        # ⟨n⟩
n2 = result.expect[1]       # ⟨n²⟩
g2 = n2 / (n**2)            # g^(2)
```

Correlations reveal quantum dynamics. A decaying resonator shows bunching as photons leave; a driven system shows different correlations.

## Higher-Order Correlations

QuTiP can compute arbitrarily high-order correlations ($g^{(3)}$, $g^{(4)}$, etc.) by passing operators like $a^\dagger a^\dagger a a$ to expectation value lists.

Correlations are measurable—they correspond to real experiments (intensity correlations in optics, spin correlations in spins). Use them to verify simulations against experiments.