Concurrence (quantum computing)

In quantum computing, the concurrence is an entanglement monotone defined for a mixed state of two qubits as

${\mathcal {C}}(\rho )\equiv \max(0,{\sqrt {\lambda _{1}}}-{\sqrt {\lambda _{2}}}-{\sqrt {\lambda _{3}}}-{\sqrt {\lambda _{4}}})$

in which $\lambda _{1},...,\lambda _{4}$ are the eigenvalues of

${\sqrt {{\sqrt {\rho }}(\sigma _{y}\otimes \sigma _{y})\rho ^{*}(\sigma _{y}\otimes \sigma _{y}){\sqrt {\rho }}}}$

in decreasing order and $\sigma _{y}$ is a Pauli spin matrix.

From it one can calculate the entanglement of formation.

References

• Scott Hill and William K. Wootters, Entanglement of a Pair of Quantum Bits, 1997.
• William K. Wootters, Entanglement of Formation of an Arbitrary State of Two Qubits 1998.