7 votes

Can two states with the same entanglement be transformed into each other using local unitaries?

Any two bipartite pure states $\psi$ and $\phi$ can be transformed into each other with local unitaries if and only if they have the same Schmidt coefficients. (To prove the 'only if' part, note that ...
  • 49.3k
3 votes

Connection between the definitions of concurrence for a two-qubit states

The Bell states $|\beta_k\rangle$ all satisfy $Y\otimes Y|\beta_k\rangle=\pm|\beta_k\rangle$. Hence, $\tilde\rho=\rho$. Thus, the matrix $\sqrt{\sqrt{\rho}\tilde\rho\sqrt{\rho}}=\rho$, given that all ...
  • 49.3k
2 votes

How to sample from the uniform distribution over the tensor product of two Bloch spheres?

The Hilbert space of a two-qubit system is $4$-dimensional complex vector space. An arbitrary normalized vector in this space can be written as: $$|\psi\rangle= \frac{[w_0 \, w_1 \, w_2 \, w_3]^t}{\...
1 vote

Why do we use complex-conjugate instead of complex-conjugate-transpose when calculating the concurrence?

I believe the question is: "why does Eq. 19 use $\rho^*$ instead of $\rho^\dagger$?" I believe this is because $\rho^* = \rho^\dagger$ for Hermitian matrices such as $\rho$, so it can be written ...

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