13 problems

Let $\mathcal{H}=\mathcal{H}_A\otimes\mathcal{H}_B$ be a finite-dimensional Hilbert space of dimension $D=d_A d_B$, and let $W$ be a normalized entanglement witness, so that…

Let $p_x$ be the probability distribution over measurement settings, and let $\Delta s$ denote the score-range quantity entering the concentration-based bounds on the $p$-value and…

Deviation–entanglement conjecture. The larger $\delta$ is, the larger the average entanglement of the analyzed state $|\phi\rangle$.

Let $d$ be the number of fermionic modes, and let $B=[b_k^n]$ be the matrix whose entries are the coefficients appearing in the characterization of $\mathrm{Spin}(2d)$-invariant bi…

Let $\rho$ be a state and let $\rho$ be separable when it can be written as a convex combination of product states. For a positive map…

Extremality conjecture. Both $W[1,1,1,0]$ and $W[1,0,1,1]$ are extremal entanglement witnesses without the spanning property. This parallels the original Choi maps in $M_3$, which…

Korbicz et al.'s conjecture. The structural physical approximation of every optimal entanglement witness defines a separable quantum state.

The witness form of the SPA conjecture. Let $W$ be an optimal entanglement witness with $\operatorname{Tr}(W)=1$. Then $\tilde{W}(p_*)$ defines a separable state.

The SPA conjecture. Let $\Phi$ be an optimal trace-preserving positive map. Then its SPA $\tilde{\Phi}[p_*]$ is an entanglement-breaking channel.

Let $a,b,c$ be nonnegative real numbers, and let $W[a,b,c]$ denote the entanglement witness arising from the generalized Choi map $cPhi[a,b,c]$. In particular, for $calpha$ with…

Optimality conjecture for $\Phi[\alpha]$. For $\frac{\pi}{3}\leq\alpha\leq\frac{5}{3\pi}$, the positive maps $\Phi[\alpha]$ are optimal.

Boundary optimality conjecture. Maps and entanglement witnesses belonging to this boundary are optimal, meaning that they provide the strongest tool for detecting quantum entanglem…

Let $\Lambda:\mathcal{B}(\mathcal{H}_A)\to\mathcal{B}(\mathcal{H}_B)$ be a positive map, and form its structural physical approximation (SPA) by minimally admixing white noise, … w…