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Questions tagged [concurrence]

A quantification of quantum entanglement that also serves as a separability criterion. Concurrence equal to zero indicates an unentangled/separable state. A non-zero concurrence "quantifies" how far the states in question are from achieving separability.

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The concurrence of a two-qubit state $\rho$ can be written as $$\mathcal C(\rho) = \max(0, \lambda_1-\lambda_2-\lambda_3-\lambda_4),$$ where $\lambda_i$ are the eigenvalues of $|\sqrt\rho\sqrt{\tilde\... • 18.3k 1 vote 0 answers 160 views What is the relation between fidelity and concurrence for a two qubit maximally mixed state? I am trying to understand the relation between Fidelity and Concurrence for a two qubit maximally mixed state. When I calculate the Fidelity and Concurrence, I observe that Concurrence is zero whereas ... • 105 4 votes 1 answer 277 views How to sample from the uniform distribution over the tensor product of two Bloch spheres? For some context, I am trying to assess the capacity that certain two qubit gates have to create entanglement. To do this I am using the idea of "entangling power", where one takes their ... • 441 6 votes 1 answer 320 views Why do we use complex-conjugate instead of complex-conjugate-transpose when calculating the concurrence? When we use the formula to calculate two-qubit entanglement, like these: $$C(\rho)=\max \left\{\sqrt{e_{1}}-\sqrt{e_{2}}-\sqrt{e_{3}}-\sqrt{e_{4}}, 0\right\}\tag{18}$$ with the quantities$...
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The concurrence for a state $\rho$ as defined here is $$C(\rho) = {\rm max}\{0, \lambda_1-\lambda_2-\lambda_3-\lambda_4\}.$$ Where $\lambda_i$ are the eigenvalues of matrix ...
Take two pure bi-partite states $\psi$ and $\phi$ that have the same amount of entanglement in them as quantified by concurrence (does the measure make a difference?). Can any such states be ...