95 problems

Coffman–Kundu–Wootters conjecture. For an $N$-qubit system, the entanglement between one qubit and the remaining $N-1$ qubits should be at least the sum of its pairwise entanglemen…

Gaussian contangle monogamy conjecture. The monogamy inequality should hold for all multimode Gaussian states:

Gaussian valence-bond representability conjecture. Every pure $N$-mode Gaussian state should admit a description as a GVBS.

GMPS representation conjecture. All pure $N$-mode Gaussian states can be described as GMPS.

Tetrahedral degeneracy conjecture. The vanishing of the other three invariants somehow characterizes more intricate degeneracies involving the lines and planes of the tetrahedron.

Dual-role conjecture. The invariants $I_4-I_2$ and $I_1^2-I_2$ should play a dual role.

Let $E^{i|(j_1,\ldots,j_n)}$ denote the bipartite entanglement between mode $i$ and the remaining modes, and let $E^{i|j_l}$ denote the entanglement between modes $i$ and $j_l$, wi…

Gaussian decomposition conjecture. For all two-mode Gaussian states, the decomposition over all pure Gaussian states is optimal in the definition of the EoF.

Gaussian EoF conjecture. The Gaussian EoF is the true EoF for a broader class of Gaussian states beyond the symmetric ones.

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…

Let $\mathcal{G}_{n}^{c}$ be the set of all connected graphs on $n$ vertices, and let $G\in\mathcal{G}_{n}^{c}$ with $|V|=pq$. Star graph maximizer conjecture. … This asserts that…

Let $G$ be a graph with $|V|=pq$ and $m$ edges. For each edge, let $\sigma(k)$ denote the pure density matrix associated with the $k$-th edge. If $\sigma(G)$ is entangled in…

Let $G$ be a graph with $|V|=pq$, and let $entangled edges$ mean edges whose associated pure states are entangled. One-entangled-edge and common-vertex conjecture. If $G$ has only…

A finitely correlated state is a pure state on a quantum spin chain with an associated finite-dimensional memory system. Consider a spin and a subset of other spins, and suppose th…

Munro–Milburn conjecture. The best way to see the quantum nature of correlations in entangled states is through measurement of the observable canonically conjugate to photon number…

Cyclotomic phase-locking conjecture. Cyclotomic aspects in phase-locking could play an important role in many fundamental tests of quantum mechanics related to quantum entanglement…

Entanglement–geometry conjecture. Quantum entanglement is necessary for connected spacetime geometry.

Sector-resolved oscillation conjecture. To leading order in $1/\log\ell$, the flux-dependent oscillatory corrections can be absorbed into the sector projection so that

No-PPT-entanglement conjecture. For local dimensions $d=3,4$, there is no PPT entanglement in the class of mixtures of Dicke states for any number of systems.

Let $n\geq 3$ and let $\vec{d}$ be a dimension vector. Write $P^{\mathrm{W}}_n(y)=P\left(\lvert\mathrm{W}_{n,\vec{d}}\rangle;y\right)$. Mainiero's generalized W Poincaré polynomial…

Let $n\geq 3$ and let $\vec{d}$ be a dimension vector. Write $P^{\mathrm{GHZ}}_n(y)=P\left(\lvert\mathrm{GHZ}_{n,\vec{d}}\rangle;y\right)$. Mainiero's generalized GHZ Poincaré poly…

Quantum geometric Langlands Eisenstein-induction conjecture. The $\mathrm{GL}_r$-eigenobject attached to $(E,\nabla)$ on $\operatorname{Bun}_{\mathrm{GL}_r}$ is Eisenstein-induced…

Let the sets of absolutely separable and absolutely PPT states be viewed in their respective matrix spaces, with the Hilbert-Schmidt Euclidean metric and centered at the maximally…

Let $M_3\otimes M_n$ be equipped with the Hilbert-Schmidt norm, and let $I/(3n)$ denote the maximally mixed state. Consider the smallest Euclidean ball centered at $I/(3n)$ that co…

Let $\rho\in M_3\otimes M_n$ be an absolutely PPT state with $n\geq 2$, and let $\lambda_1,\ldots,\lambda_{3n}$ be its eigenvalues. Maximum-purity conjecture. The maximum purity of…