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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 ...
• 59.3k
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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 ...
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Are concurrence $C$ and purity of reduced state $p$ related by $C^2\le 4p(1-p)$?

The source is that it probably just made it up. Funnily enough, chatgpt3.5 also gives me the same relation if asked in general for an "inequality between concurrence and purity of reduced state&...
• 25.6k
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}{\...
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 ...