34 problems

Zero-entropy-density conjecture. The entropy density vanishes for every translation-invariant pure state on the spin chain; equivalently, $S_N$ is sublinear.

Let $\mathcal{A}$ and $\mathcal{B}$ be the algebras associated with the two intervals, let $\omega$ denote the vacuum state, and let $a$ and $d$ be the parameters appearing in the…

Let $S_{\rm topo}$ denote the topological entanglement entropy associated with a chosen partition or contour, and let TQO denote topological quantum order. Contour-independence con…

Let $\Gamma$ range over allowed contours separating regions in a lattice system, and let $S_{\rm ent}$ be the entanglement entropy used to diagnose topological quantum order. Conto…

Let $\Gamma$ be a boundary surface of size $R$ separating two regions, and let $S_{\rm ent}$ denote their entanglement entropy. In $D=2$, suppose the entropy has the asymptotic are…

Let $f$ denote the subsystem fraction, and let $\braket{S_A}_{J=0,J_z=0}$, $\braket{S_A}_G$, and $S^{j=0}_{\mathrm{CG}}$ denote the symmetry-resolved average entanglement entropy,…

Let … be the three-qubit W-state, and let $c_{\mathrm{W}}$ be a numerical constant greater than $1$. Let $S_1^{(3)}[\mathrm{W}]$ and $\mathrm{GM}_1^{(3)}[\mathrm{W}]$ denote, respe…

Let $A$, $B$, and $C$ be subsystems with associated Hilbert spaces of dimensions $\dim \mathcal{H}_A$, $\dim \mathcal{H}_B$, and $\dim \mathcal{H}_C$, respectively. Let…

Let $F(A)$ denote the universal term in the entanglement entropy associated with an entangling region $A$ in a five-dimensional conformal field theory. Five-dimensional unboundedne…

Let $F(A)$ denote the universal term in the entanglement entropy associated with a region $A$ in a three-dimensional conformal field theory, and let $F_0$ be its value for a round…

Let $\ket{D^N_1}$ denote the $N$-qubit Dicke state with one excitation, and let $(HC)_{1,2}$ denote circuits generated by Hadamard and controlled-not gates acting on qubits $1$ and…

Exponential generating-function conjecture. In the case $n=0$,

Let the Hamiltonian be time-independent and contain a metastable part, and let the initial state be arbitrary, potentially non-Gaussian. Generic logarithmic-growth conjecture. The…

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

Sarkar–Kumar conjectures. The average quantum purity and average von Neumann entropy are

Conformal-block conjecture. The edge contribution to the entanglement entropy is a particular linear combination of these conformal blocks, very much like correlation functions in…

Let $m$ and $n$ be the dimensions of the two subsystems, let $c=m/n$, and let $X$ be the standardized von Neumann entropy. Consider the fixed-trace ensemble of reduced density matr…

Let a quantum many-body system be divided into a subregion and its complement, and let the entanglement entropy quantify the entanglement between them. The area-law conjecture stat…

Let $f^{(\nu)}$ be the symbol defined on $[-\pi,\pi)$ by … with $\nu\geq0$, and let $s_k^{(\nu)}$ denote the Fourier coefficients of $\log f^{(\nu)}$, with $s_0^{(\nu)}$ its zeroth…

Let $S(x)$ be the entanglement entropy of the interval $[x,\infty)$ near the right edge, let $x_{\rm e}$ denote the edge position, and let $\ell_\Delta$ be the edge length scale. L…

The $p$-adic BTZ background is obtained as a genus-$1$ quotient geometry, with boundary qubits whose reduced-state entanglement entropy is compared with the length of bulk geodesic…

Let $L$ be the spatial circle length, $\ell$ the interval length, $\epsilon$ a UV cutoff, and $\tau$ the torus modular parameter. Let $E_4(\tau)$ and $E_6(\tau)$ be the Eisenstein…

Let $A$ and $B$ be complementary regions in a lattice realization of the quantum Lifshitz model, with interface length $L$. Let $\widetilde{S}_A$ denote the ground-state entangleme…

All-n Rényi trace conjecture. For the symmetric case $\alpha=\beta$,

Möbius covariance conjecture. The entropy transformation