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Is there a concentration inequality for the quantum gate fidelity $F(C,U)$ for a channel $C$ such that $\int dU F(C,U)=X$?

The function described in the question is 1-Lipschitz. To argue this, we'll get an inequality in place before we start writing integrals. If $\vert \gamma\rangle$ and $\vert\delta\rangle$ are unit ...
John Watrous's user avatar
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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, ...
glS's user avatar
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