15 problems

Let $\rho=\sigma_{\mathrm{A}}\otimes\sigma_{\mathrm{B}}$ be a product state, where $\sigma_{\mathrm{A}}$ and $\sigma_{\mathrm{B}}$ are states of independently prepared subsystems.…

Let $n\geqslant3$, let $d\geqslant2$, and let $(\psi_1,\ldots,\psi_n)$ be an $n$-tuple of pure states in $\mathbb{C}^d$. Write $4\psi_k=|\psi_k\rangle\langle\psi_k|4$ and choose pu…

Large-dimension extendibility conjecture. For sufficiently large $d$, every $(1,n)$-extendible Brauer state is also $(n,n)$-extendible.

Let $|0\rangle$ and $|1\rangle$ denote the spin-up and spin-down states of a spin-$\frac{1}{2}$ particle, and let … where $0\leq s\leq \frac{1}{2}$. For each subset…

Higher quantum states conjecture. There are corresponding higher quantum states that may not yet be detectable by present-day technology.

Let $\frac{1}{\lambda}\hat{S}_\lambda$ be the sine operator appearing in the loop quantum cosmology kinematics, where $\lambda$ is the holonomy length. Consider its eigenstates as…

Andai's separability probability conjecture. The geometric separability probability of two-qubit quantum systems is

Let $\rho_1,\sigma_1\in\mathrm{S}(\mathbb{C}^{d_1})$ and $\rho_2,\sigma_2\in\mathrm{S}(\mathbb{C}^{d_2})$, and define … Assume that $\nu$ is finite, equivalently…

Let $A_k$ denote the $k$-sector length of an $n$-qubit quantum state. Asymptotic sector-length conjecture. For all $k$ there exists an $n_0$ such that, for all $n\geq n_0$, every…

Let Alice and Charlie share a bound entangled state, and let Bob and Charlie share a bound entangled state. Consider an entanglement-swapping protocol in which Charlie performs a m…

Let $\mathcal{D}(d)$ denote the set of $d$-dimensional quantum states. Let $f:\mathcal{D}(d)\to\mathbb{R}$ be concave and symmetric, let $\rho_1,\rho_2,\rho_3\in\mathcal{D}(d)$ be…

Absolutely separable–PPT conjecture. For all $n$ and $k$,

Let $\rho_{AB}$ and $\sigma_{AB}$ be quantum states on $\mathcal{H}_A\otimes\mathcal{H}_B$, with reduced states $\rho_A$, $\rho_B$, $\sigma_A$, and $\sigma_B$ on the corresponding…

The mean-energy ensemble is expected to exhibit concentration weaker than the standard Gaussian rate, with coordinate functions providing the least concentrated examples. Worst-cas…

NPT bound-entanglement conjecture. There exist bipartite NPT states which are not distillable.