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