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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Are almost perfectly distinguishable ensembles almost orthogonal?

Let $\varepsilon>0$ and consider an ensemble of states $\{p_x\rho_x\}_{x\in X}$ and suppose there exists a measurement with POVM representation $\{M_x\}_{x\in X}$ such that $$ \sum_{x\in X} p_x\...
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Are mixtures of pairs of Bell states perfectly distinguishable by local operations?

Consider the four Bell states $$ |\psi^{00}\rangle = \frac{1}{\sqrt{2}}(|00\rangle + |11\rangle), \hspace{2mm} |\psi^{01}\rangle = \frac{1}{\sqrt{2}}(|00\rangle - |11\rangle),\hspace{2mm} |\psi^{10}\...
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Optimality of the SWAP test versus weak Schur sampling for testing unitarily invariant properties

Consider the following setting. I am either given the density matrix $|\psi\rangle \langle \psi|^{\otimes k}$ or the density matrix $\frac{\mathbb{I}^{\otimes k}}{2^{nk}}$, where $\mathbb{I}$ is the $...