Constructs the operator computing the Rényi2 entanglement entropy of
a state \(| \Psi \rangle\) for a partition with partition A:
\[S_2 = -\log_2 \text{Tr}_A [\rho^2]\]
where \(\rho = | \Psi \rangle \langle \Psi |\) is the density
matrix of the system and \(\text{Tr}_A\) indicates the partial
trace over the partition A.
The Monte Carlo estimator of S_2 [Hastings et al., PRL 104, 157201 (2010)] is:
\[S_2 = - \log \langle \frac{\Psi(\sigma,\eta^{\prime}) \Psi(\sigma^{\prime},\eta)}{\Psi(\sigma,\eta) \Psi(\sigma^{\prime},\eta^{\prime})} \rangle\]
where the mean is taken over the distribution
\(\Pi(σ,η) \Pi(σ',η')\), \(\sigma \in A\),
\(\eta \in \bar{A}\) and
\(\Pi(\sigma, \eta) = |\Psi(\sigma,\eta)|^2 / \langle \Psi | \Psi \rangle\).
- Parameters:
hilbert (None) – hilbert space of the system.
partition (array) – list of the indices identifying the degrees of
freedom in one partition of the full system. All
indices should be integers between 0 and hilbert.size
- Returns:
Rényi2 operator for which computing the expected value.
