qiskit.quantum_info.concurrence

concurrence(state)

Calculate the concurrence of a quantum state.

The concurrence of a bipartite Statevector $|\psi\rangle$ is given by

where $\rho_0 = Tr_1[|\psi\rangle\!\langle\psi|]$ is the reduced state from by taking the partial_trace() of the input state.

For density matrices the concurrence is only defined for 2-qubit states, it is given by:

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 orDensityMatrix) – 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.