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.
Questions tagged [concurrence]
13 questions
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votes
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Can two states with the same entanglement be transformed into each other using local unitaries?
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 transformed into each other using local unitaries?
user120404
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Connection between the definitions of concurrence for a two-qubit states
The concurrence for a state $\rho$ as defined here is
\begin{equation}
C(\rho) = {\rm max}\{0, \lambda_1-\lambda_2-\lambda_3-\lambda_4\}.
\end{equation}
Where $\lambda_i$ are the eigenvalues of matrix $ \sqrt{\sqrt{\rho} \tilde{\rho} \sqrt{\rho}}$,…
Tobias Fritzn
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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 $e_{i}\left(e_{1} \geq e_{2} \geq e_{3} \geq e_{4}\right)$…
karry
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How to get to the formula for the entanglement of formation of two-qubit states?
An explicit formula for the entanglement of formation $E(\rho)$ for an arbitrary two-qubit state $\rho$ was given by Wooters in Entanglement of Formation of an Arbitrary State of Two Qubits. The entanglement of formation is defined as the minimal…
glS
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Are concurrence $C$ and purity of reduced state $p$ related by $C^2\le 4p(1-p)$?
Asking this question to an AI, I got the result that the relation between concurrence and purity of a single qubit in a mixed bipartite state, as follows:
$$C^2 \le 4p(1-p)\,, $$
Where $C$ is concurrence, and $p$ is the purity of a single…
reza
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4
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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 favorite entanglement measure and takes some distribution over…
Jake Xuereb
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Does correcting a density matrix to be positive semi-definite affect its concurrence?
I am working on calculating the concurrence of a two-qubit system, and I encountered an issue where my density matrix occasionally has small negative eigenvalues due to numerical errors in my computations (e.g., constructing the density matrix from…
amirhoseyn Asghari
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Comparative Analysis of Entanglement Measures: Von Neumann Entropy vs. Concurrence
I am seeking clarification on the comparative aspects of two prominent measures of entanglement: Von Neumann entropy and concurrence. My goal is to understand the key differences in how these measures quantify entanglement and their appropriate…
amirhoseyn Asghari
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Why does $\sigma_y$ seem to have a special role in the two-qubit concurrence?
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 $|\sqrt\rho\sqrt{\tilde\rho}|$, using the notation…
glS
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Issue with Converting 2D Green's Function to 1D and Concurrence Behavior in Polar Coordinates
I am working on a model in superconductivity and have found the normal and anomalous Green's functions in real space. First, I computed the Green's functions in terms of the variables $ x $ and $ y $, then defined $ r = \sqrt{x^2 + y^2} $. After…
amirhoseyn Asghari
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What is the concurrence between A and BC?
I was studing about the monogamy.
Then I saw this phrase
$$C_{AB}^2 + C_{AC}^2 ≤ C_{A(BC)}^2$$
where $C_{AB}, C_{AC} $ are the concurrences between A and B and between A and C respectively, while $C_{A(BC)}$ is the concurrence between subsystems A…
reza
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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 Fidelity is one.
In some of the papers, I read…
Ganesh M
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How to calculate Minimum Residual Contangle for Entanglement
I used expectation values of Heisenberg Langevin equations to construct a 6 × 6 covariance matrix between three qubits.
Now, I am confused in the formula for minimum Residual contangle. I have understanding of logarithm negativity but I'm confused…
Syed Shahmir Kazmi
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