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# Tag Info

## New answers tagged density-matrix

• 6,462
1 vote

### Can different density matrices have 100% fidelity with a given pure state?

If $|\psi\rangle$ is a pure state and $\rho$ is a density matrix, then $F(|\psi\rangle\!\langle\psi|,\rho)=\langle\psi|\rho|\psi\rangle=1$ iff $\rho=|\psi\rangle\!\langle\psi|$. Or more generally, ...
• 25.4k
Accepted

### Exponential Quantum Speedup for the Traveling Salesman Problem - where is the catch?

The catch is the parameter $\kappa$, the condition number of the embedding matrix. I can't comment on the correctness of the whole work. This will require a thorough examination of the content. But ...
• 657

### What's the Schmidt decomposition of $|\psi\rangle = 1/ \sqrt{3}( |0\rangle| 0\rangle + |0\rangle |1\rangle + |1\rangle |1\rangle)$?

One way of computing the decomposition is through density matrices, but then you will have to diagonalize those density matrices. This requires the eigenvalue decomposition of each density matrix. ...
• 2,646
Accepted

• 1,624