qiskit.quantum_info.concurrence¶
-
concurrence(state)[source]¶ Calculate the concurrence of a quantum state.
The concurrence of a bipartite
Statevector\(|\psi\rangle\) is given by\[C(|\psi\rangle) = \sqrt{2(1 - Tr[\rho_0^2])}\]where \(\rho_0 = Tr_1[|\psi\rangle\!\langle\psi|]\) is the reduced state from by taking the \(~qiskit.quantum_info.partial_trace\) of the input state.
For density matrices the concurrence is only defined for 2-qubit states, it is given by:
\[C(\rho) = \max(0, \lambda_1 - \lambda_2 - \lamda_3 - \lambda_4)\]where \(\lambda _1 \ge \lambda _2 \ge \lambda _3 \ge \lambda _4\) are the ordered eigenvalues of the matrix \(R=\sqrt{\sqrt{\rho }(Y\otimes Y)\overline{\rho}(Y\otimes Y)\sqrt{\rho}}\).
- Parameters
state (Statevector or DensityMatrix) – a 2-qubit quantum state.
- Returns
The concurrence.
- Return type
float
- Raises
QiskitError – if the input state is not a valid QuantumState.
QiskitError – if input is not a bipartite QuantumState.
QiskitError – if density matrix input is not a 2-qubit state.