13 problems

Let $E_I^D$ denote the distillable entanglement of a cubic region $I=[1,\ldots,m]^{\times D}$, and write the area law as … Here criticality is characterized by two-point correlatio…

Let $I=[1,\ldots,m]^{\times D}$ be a cubic region in a $D$-dimensional lattice, and let $E_I^S$ denote its geometric entropy. For the interaction matrix with off-diagonal entries…

Mutual-entropy ground-state area-law conjecture. The area law for ground states can be formulated in terms of mutual entropy instead of von Neumann entropy.

The standard-path insufficiency conjecture. The standard adiabatic path condition alone is insufficient to ensure the generalized area law.

Logarithmically enhanced area-law conjecture. As $L\to\infty$ and $B\to0$,

Logarithmic enhancement conjecture. Any enhancement of the area law for $S_{E}(H,\Lambda_{L})$ should not be stronger than logarithmic.

Commuting frustration-free representative conjecture. For a very large class of physical systems, there is a commuting, frustration-free Hamiltonian in the same phase; this Hamilto…

Kitaev–Bravyi conjecture. The same bound should hold in the presence of ancillas: $\Gamma(H,\psi)\leq c\lVert H\rVert\log(d)$, with a constant $c$ independent of the ancillas and t…

Area law conjecture. For general gapped quantum spin systems with finite-range interactions, the entropy scales as the area of $X$:

Area-law conjecture. If the system has a constant spectral gap $\epsilon>0$, its ground state necessarily obeys an area law. The conjecture is a central claim about entanglement in…

Area-law conjecture. Under rather general assumptions, the entanglement entropy associated with $A$ satisfies an area law, meaning that it is bounded in terms of the boundary area…

Area bound conjecture. There exists such a function $f$ for every gapped one-dimensional model, so the entanglement entropy is bounded in terms of the ratio of the Lieb–Robinson ve…

Forward-backward correlation conjecture. There exists a function $f(D_{eff})$ such that