Skip to main content
7 votes
Accepted

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 ...
DaftWullie's user avatar
  • 59.3k
4 votes
Accepted

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 ...
DaftWullie's user avatar
  • 59.3k
4 votes
Accepted

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&...
glS's user avatar
  • 25.6k
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}{\...
David Bar Moshe's user avatar
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 ...
Niagara Falls's user avatar

Only top scored, non community-wiki answers of a minimum length are eligible