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# Tag Info

## Hot answers tagged state-discrimination

7 votes

• 58.8k
4 votes
Accepted

• 58.8k
3 votes
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 ...
• 5,853
3 votes
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 ...
• 2,551
2 votes

### 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 ...
• 25.4k
2 votes
Accepted

• 25.4k
2 votes

### How to discriminate between $N$ states drawn from one of two ensembles?

Unless I'm mistaken, your special case is also the solution to the generalization, up to the fact that you have to redefine $\rho$ and $\sigma$. Forget about $Q$ for now. If Alice gives Bob one copy ...
• 6,462
2 votes
Accepted

### Unambiguous State Discrimination

In general, I think not. You need to be more restrictive on the properties of your sets. To see this, let's define 3 measurement operators: $M_A$, $M_B$ and $M_U$, corresponding to the answers A (...
• 58.8k
2 votes
Accepted

• 25.4k
1 vote

### What's the idea behind "pretty good measurements"?

I'll reproduce here a standard argument used to prove the fundamental bound for pretty good measurements (PGMs), the the most part taken from Watrous' book, with some minor changes in notation, ...
• 25.4k

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