# Tag Info

## Hot answers tagged state-discrimination

• 48.1k

### How to distinguish between two very similar pure quantum states?

The claim does not specify what protocols for distinguishing quantum states are acceptable. In particular, it does not state whether we are allowed to err or reserve judgment. Below, we note success ...
• 14.7k
Accepted

### How to find the POVM that optimally distinguishes between two given states?

The optimal probability of guessing correctly is $$\frac12 + \frac12 \Big\|\frac23 \rho_0 - \frac13 \rho_1 \Big\|_1$$ where $\| X \|_1 = \mathrm{Tr}[\sqrt{X^* X}]$ is the Schatten 1-norm. This ...
• 4,252
Accepted

### Is the quantum state discrimination success probability always $\lambda_0\langle\mu(0),\rho_0\rangle+\lambda_1\langle\mu(1),\rho_1\rangle$?

Yes. Expression (X) is in principle more general, but it boils down to doing classical post-processing of the outcomes, and this can always be included in the POVM. So as long as you do optimize over ...
• 1,727
Accepted

### Are projective measurements the only optimal measurements to discriminate between two states?

Suppose you are given either $\rho_1$ or $\rho_2$, and you also know that the probabilities you got one or the other are $p_1$ and $p_2$, respectively. If you have no prior knowledge of the ...
• 19.5k
Accepted

1 vote

### In classical state discrimination, why does the trace distance quantify the probability of success?

Upon some additional reflection, I found a way to see that the expressions are equivalent. I'm not sure whether this is the way that was intended in the text though, there might be better/more direct ...
• 19.5k
1 vote
Accepted

### Finding the optimal projective measurement to distinguish between two pure states

$\newcommand{\ket}{\lvert #1\rangle}\newcommand{\PP}{\mathbb{P}}$Given an arbitrary state $\ket a$, let us write the corresponding density matrix/projector as $\PP_a$. Any such density matrix can ...
• 19.5k

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