10 problems

General CKW conjecture. The general CKW inequality should hold for all nonsymmetric $N$-mode Gaussian states. Numerical evidence supports this conjecture. It is already known for a…

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…

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…

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.

Majorization conjecture along the family $\widetilde{W}_u$. There is a Wigner majorization order along the family $\widetilde{W}_u$ only when $u>1/2$.

Majorization conjecture for $\hat{\rho}_0$. Any mixed state with a positive Wigner function is majorized by $\hat{\rho}_0$ under the Wigner majorization ordering.

Van Herstraeten–Jabbour–Cerf conjecture. Every Wigner-positive state is majorized by a coherent state under the Wigner majorization ordering.

Effective-squeezing lower-bound conjecture. The effective squeezing satisfies

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…