96 problems

Logarithmic entanglement-scaling conjecture. The entanglement entropy of any such block, to leading order, scales as

Frobenius light-cone conjecture. Entanglement is governed by the Frobenius light cone for power-law interactions.

Nielsen's incomparability conjecture. The relative volume of pairs of LOCC-convertible bipartite pure states vanishes in the limit of large dimensions; equivalently, for two indepe…

Consider an $N$-mode Gaussian state distributed among parties $\mathcal{S}_1,\ldots,\mathcal{S}_N$, with each party owning one mode. Let $E$ be a proper measure of bipartite entang…

Bell-pair superadditivity conjecture. There is an experiment on pairs of Bell singlets, of the $2\times4\times4$ type, more than twice as strong as CHSH, and involving joint measur…

Two-copy superadditivity conjecture. The best experiment based on two copies of the Bell singlet state is more than twice as good as the best experiment based on single states.

CHSH optimality conjecture. The best experiment with the Bell singlet state is the CHSH experiment.

Let $\omega$ be a translationally invariant state on an infinite quantum spin chain, let $\mathcal{A}_L$ and $\mathcal{A}_R$ denote the left and right half-chain algebras, and let…

Consider a general SU(2)-invariant model with integer spin $S$, and let the AKLT point denote the parameter value corresponding to the Affleck–Kennedy–Lieb–Tasaki valence-bond-soli…

Let the entanglement entropy (EE) be the von Neumann entropy of the reduced density matrix of a subsystem in a quantum spin chain. Consider a large block of spins in either a gappe…

Monogamy conjecture. High values of $|{\cal J}_A|$ must be linked to low values of $S_A$:

Multipartite mutual-information conjecture. The EHLs can be associated with multipartite mutual informations.

Consider a pair of non-overlapping modes, with the formal proof restricted to modes having super-Hubble support. Non-overlapping-mode extension conjecture. The result applies to an…

Let $RH$ denote the dimensionless product of the mode's support scale $R$ and the Hubble parameter $H$. Proposition vNgeneral concerns single modes supported in super-Hubble region…

The MPS construction gives an upper bound on the number of non-zero entanglement eigenvalues of the ground state. Jones's optimality conjecture. For $N=2$, this construction should…

The influence matrix (IM) is a quantum state encoding the complete non-equilibrium dynamics of a boundary degree of freedom, and the temporal transfer matrix has the IM as its uniq…

Let $S$ be the average single-qubit linear entropy and let $S_{Max}$ denote its maximal value. Consider the normalized entropy ratio $\langle S\rangle/S_{Max}$ as the system size…

LOCC monotonicity conjecture. LOCC transformations cannot decrease the maximal extendibility numbers of a state.

A beam splitter transforms an input state in one mode together with the vacuum in the other mode into a two-mode output state. The reflection and transmission probabilities are equ…

Entanglement-bootstrap representative conjecture. Every two-dimensional gapped phase with gappable boundary has a representative state satisfying the entanglement bootstrap axioms…

Existence conjecture. For all integers $k\geq 1$ and all $\delta>-1$, $\mathcal{Z}_k(\delta)$ is well-defined and the limit $\mathcal{Z}_k(\infty)$ exists.

Lovas' conjecture. The ratio

Let $h_x=\lambda \xi_x$, where $(\xi_x)_{x\in\mathbb Z}$ is a sequence of independent identically distributed random variables whose density is positive at $0$. Consider the one-di…

Rank conjecture. For every $\alpha\geq-\frac{1}{r}$,

Horodecki's conjecture. The Werner state $\rho_{\alpha}$ is $n$-undistillable for every $n\in\mathbb{N}$ if and only if $\alpha\geq-\frac{1}{2}$.