Concurrence (quantum computing)

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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 $λ 1,...,λ 4$ are the eigenvalues of

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

in decreasing order and $σ y$ 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.

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Categories: Theoretical computer science | Quantum information science

Concurrence (quantum computing)

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