The 2024 Developer Survey results are live! See the results

# Questions tagged [state-discrimination]

the distinguishability of quantum systems in different states, and the general process of extracting classical information from quantum systems

49 questions
Filter by
Sorted by
Tagged with
1 vote
57 views

• 1,383
107 views

### Niemark's theorem - simulating POVMs with PVMs

I am having trouble understanding Niemark's theorem from books (e.g watrous). The wikipedia page is clearer but most calculations are not justified. I want to contruct the PVM associated with the ...
• 127
1 vote
22 views

### The lower bound on the probability of error in quantum hypothesis testing

Prove the following lower bound on the probability of error $P_e$ in a quantum hypothesis test to distinguish $\rho$ from $\sigma$: \begin{align} P_e \geq \frac{1}{2} \left(1-\sqrt{1-F(\rho, \...
• 579
1 vote
63 views

### geometric intepretation of Helstrom formula

Let's suppose Alice transmit to Bob either one of the two states: $$|\psi_{\pm}\rangle = \cos(\theta)|H\rangle \pm \sin(\theta)|V\rangle, \quad \theta \in [-\frac{\pi}{4}, +\frac{\pi}{4}]$$ The ...
• 518
103 views

• 1,383
423 views

### Do entangled measurements across multiple copies help in state distinguishability?

Consider two density matrices $\rho$ and $\sigma$. The task is to distinguish between these two states, given one of them --- you do not know beforehand which one. There is an optimal measurement to ...
• 1,383
458 views

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

Consider two density matrices $\rho$ and $\sigma$. The task is to distinguish between these two states, given one of them --- you do not know beforehand which one. There is an optimal measurement to ...
• 1,383