# Entanglement Measures

**Entanglement** quantifies quantum correlations—whether a state is separable (product of individual states) or genuinely multi-body. QuTiP provides entanglement entropy, concurrence, and related measures.

## Entanglement Entropy

Entanglement entropy measures how much entropy is in a [[qutip-partial-trace|reduced state]]: $S_A = -\text{Tr}(\rho_A \log_2 \rho_A)$. For a pure state, if subsystem A is maximally entangled with the rest, $S_A = \log_2(d_A)$ (maximal).

```python
from qutip import *

# Bell state: maximally entangled
psi = (tensor(basis(2, 0), basis(2, 0)) + 
       tensor(basis(2, 1), basis(2, 1))).unit()
rho = psi * psi.dag()

# Entanglement entropy of qubit 0
rho_0 = ptrace(rho, 0)
ent = entropy_vn(rho_0)
print(ent)  # 1.0 bit (maximal for 2-level)

# Separable state (product): zero entanglement
psi_sep = tensor(basis(2, 0), basis(2, 0))
rho_sep = psi_sep * psi_sep.dag()
rho_0_sep = ptrace(rho_sep, 0)
print(entropy_vn(rho_0_sep))  # 0.0 (no entanglement)
```

## Concurrence

Concurrence measures entanglement of two-qubit states: $C \in [0, 1]$. For a Bell state, $C = 1$ (maximally entangled); for separable states, $C = 0$.

```python
C = concurrence(rho)
print(C)  # 1.0 for Bell state, 0 for product state
```

Entanglement is a resource for quantum advantage. Quantifying it is essential for understanding quantum simulations.