Questions tagged [state-discrimination]

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

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Conditional Statements on a Quantum Computer

I've been struggling with this for a while now, and whilst I suspect the answer is unknown or very complicated, I thought I'd ask regardless. Suppose I have some states $|\psi_i\rangle = \sum_{j=1}^n ...
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How to find the POVM the optimally distinguishes two given states?

A quantum state preparation machine emits a state $\rho_0$ with probability $2/3$ and emits the state $\rho_1$ with probability $1/3$. We aim to make the best guess which one is it using a set of two ...
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Is the quantum state discrimination success probability always $\lambda_0\langle\mu(0),\rho_0\rangle+\lambda_1\langle\mu(1),\rho_1\rangle$?

Consider the standard quantum state discrimination setup: Alice sends Bob either $\rho_0$ or $\rho_1$. She picks $\rho_0$ and $\rho_1$ with probabilities $\lambda_0$ and $\lambda_1$, respectively. Bob ...
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In classical state discrimination, why does the trace distance quantify the probability of success?

Consider the following task: we are given a probability distribution $p_y:x\mapsto p_y(x)$ with $y\in\{0,1\}$ (e.g. we are given some black box that we can use to draw samples from either $p_0$ or $...
4
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Finding the optimal projective measurement to distinguish between two pure states

I would like some help on what should be a simple computation that I'm failing to see through to the end. Suppose I have a qubit which can be in the state $|v\rangle$ with probability $p$, or $|w\...