28 problems

Triangle inequality conjecture. The quantity $D_{\Delta}$ satisfies the triangle inequality.

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

Gaussian optimizer conjecture. The optimizers belong to the class of pure Gaussian states.

For a bipartite bosonic Gaussian state of modes $A$ and $B$, let $D(A|B)$ denote quantum discord, and let $D_G(A|B)$ denote the quantity obtained by restricting the minimization de…

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

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…

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

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.

Sample-optimal learning conjecture. The correct scaling for learning mixed Gaussian states is

Let $\psi$ be a pure even-parity state for Tests 1 or 2, or a pure state for Tests 4 or 5. In the two-copy cases set $p_{\operatorname{acc}}=\operatorname{Tr}[\psi^{\otimes 2}P]$,…

Let $n$ be the number of modes, and consider the symmetry-based tests for Gaussianity described in the paper. Constant-copy conjecture. An improved analysis can show that these tes…

Let $n$ be the number of modes, $E$ the mean-energy parameter, and let $\varepsilon_B$ denote the far-case testing parameter. The mixed-state lower bound is proved under the restri…

Let $\psi$ be a pure state that is at distance at least $\varepsilon$ from the relevant Gaussian-state set, with $\varepsilon$ sufficiently small. The rotation test has acceptance…

Let the quantum Ornstein–Uhlenbeck semigroup be considered on quantum states, and let the 1-log-Sobolev inequality mean the modified log-Sobolev inequality for this semigroup. Gaus…

Seshadreesan–Lami–Wilde's conjecture. The implication

Consider the left case of the threshold violation, with … Suppose $\rho_\alpha$ is the average state in the optimal encoding, with covariance parameters $\alpha_q$ and $\alpha_p$.…

Let $V_{AB}$ be a covariance matrix (QCM) of a bipartite Gaussian state. Let $E^{\mathrm{\scriptscriptstyle \, G}}_\downarrow(V_{AB})$ denote Gaussian intrinsic entanglement and le…

Let $V_{AB}$ be the covariance matrix (QCM) of an arbitrary bipartite Gaussian state. Let $K^{\mathrm{\scriptscriptstyle \, G}}_\leftrightarrow(V_{AB})$ denote the Gaussian secret…

Let $[... ]$ be the dense domain of finite-particle states generated by Schwartz test functions, contained in the Hilbert space $[... ]$. For a distribution $F[... ]$ such that…

Gaussian extension conjecture. The squashed entanglement of every quantum Gaussian state is achieved by a Gaussian extension.

Exact squashed entanglement conjecture. The squashed entanglement of $\rho_{AB}^{\kappa,E}$ equals the upper bound

Let $V$ be the covariance matrix of an $N$-mode pure Gaussian state, expressed in the factored form above. A linear quantum system generating this state must satisfy the necessary…

Let $\rho_{AB}$ be a two-mode Gaussian state with covariance matrix in standard form, and let $Q_{\mathcal{N}}(\rho_{AB})$ denote its negativity of quantumness, optimized over loca…