Quantum Communication Under Memory and Entanglement Constraints

Entanglement is usually treated as a free boost for quantum communication. The question is whether that still holds when memoryistight. Themodelhaseachsidewith S qubitsofworkspaceand E shared ebits. The multi-round Kadison–Schwarz packing lemma is extended to this assisted setting to test if entanglement expands the effective Hilbert–Schmidt budget or not. The outcome lands in two cases. Either \( T\sqrt{S+\alpha E} \geq \Omega(k\sqrt{n}) \) meaning entanglement helps dimensionally but not asymptotically, or \( T\sqrt{S} \geq \Omega(k\sqrt{n}) \) with no E dependence, meaning it does nothing at all. If the second holds, workspace limits are the real bottleneck. Even perfect EPR pairs cannot replace local coherence.