8 problems

Let the noise modes c_i_{i=1}^n be in a product state … of $n$ vacuum states, and assume that $H(A^n)_\rho=n g(N_A)$. Minimum output-entropy conjecture. Then … This conjecture is…

Consider a lossy multimode passive bosonic channel and let the probe be a quantum state prepared in a single spatial mode belonging to the linear span of the modes on which the cha…

Let $\mathcal{E}^{\bar{n}_{\rm B},\eta_s}$ be the channel with background noise $\bar{n}_{\rm B}$ and transmittance $\eta_s$. For two-mode Gaussian input states with a fixed photon…

Let a LTI Gaussian bosonic channel have $n$ input modes and $n$ output modes. Dilation conjecture. Such a channel can be dilated to a unitary map by adding $4n$ additional modes. T…

Let $c_{\rm rel,\chi}=\eta\log\left(1+((1-\eta)\bar{n}_{\rm B})^{-1}\right)$ denote the upper-bound constant for the number of reliably transmissible covert bits over a bosonic cha…

Let a linear bosonic channel be a discrete convex combination of conjugations by different displacement operators. Non-Gaussian dilatability conjecture. All such linear bosonic cha…

Consider a beam splitter receiving two independent input states, each with a prescribed entropy. Thermal Gaussian input states are states whose entropy is determined by their therm…

A bosonic Gaussian channel is a completely positive, trace-preserving map acting on the states of bosonic modes, and an input ensemble is a collection $\mathcal{E}=\{p_j;\rho_j\}$…