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qiskit.quantum_info.concurrence

concurrence(state)[Quellcode]

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 partial_trace() of the input state.

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

\[C(\rho) = \max(0, \lambda_1 - \lambda_2 - \lambda_3 - \lambda_4)\]

where \(\lambda _1 \ge \lambda _2 \ge \lambda _3 \ge \lambda _4\) are the ordered eigenvalues of the matrix \(R=\sqrt{\sqrt{\rho }(Y\otimes Y)\overline{\rho}(Y\otimes Y)\sqrt{\rho}}\).

Parameter

state (Statevector or DensityMatrix) – a 2-qubit quantum state.

Rückgabe

The concurrence.

Rückgabetyp

float

Verursacht
  • 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.