Rabsan Galib Ahmed

Rabsan Galib Ahmed, Graeme Smith

Photon loss in optical channels fundamentally limits long-range reliable quantum communication. A standard approach to overcoming this limitation is the use of quantum repeater nodes, which typically perform experimentally demanding non-Gaussian operations. However, whether Gaussian repeater protocols can enhance quantum communication rates over bosonic attenuation channels has remained open. In this work, we prove a no-go theorem for Gaussian quantum repeaters in a quantum network. Specifically, we show that any repeater chain composed of Gaussian operations, homodyne measurements, and arbitrary classical communication cannot enhance the quantum capacity of a pure-loss attenuation channel beyond that achievable by direct transmission. Our proof introduces a generalisation of $k$-extendibility to a notion of fractional extendibility for Gaussian states and establishes some of its useful properties, thereby providing a powerful framework for analysing Gaussian quantum networks.

Rabsan Galib Ahmed, Graeme Smith, Peixue Wu

The one-way distillable entanglement is a central operational measure of bipartite entanglement, quantifying the optimal rate at which maximally entangled pairs can be extracted by one-way LOCC. Despite its importance, it is notoriously hard to compute, since it is defined by a regularized optimization over many copies and adaptive one-way protocols. At present, single-letter formulas are only known for (conjugate) degradable and PPT states. More generally, it has remained unclear when one-way distillable entanglement can still be additive beyond degradability and PPT settings, and how such additivity relates to additivity questions of quantum capacity of channels. In this paper, we address this gap by identifying three explicit families of non-degradable and non-PPT states whose one-way distillable entanglement is nevertheless single-letter. First, we introduce two weakened degradability-type conditions--regularized less-noisy and informationally degradable--and prove that each guarantees additivity and hence a single-letter formula. Second, we show a stability result for orthogonally flagged mixtures: when one component has orthogonal support on Alice's system and zero one-way distillable entanglement, the mixture remains single-letter, even though degradability is typically lost under such mixing. Finally, we propose a generalized spin-alignment principle for entropy minimization in tensor-product settings, which we establish in several key cases, including a complete Rényi-2 result. As an application, we obtain additivity results for generalized direct-sum channels and their corresponding Choi states.