Entanglement-Assisted Bosonic MAC: Achievable Rates and Covert Communication

We consider the problem of covert communication over the entanglement-assisted (EA) bosonic multiple access channel (MAC). We derive a closed-form achievable rate region for the general EA bosonic MAC using high-order phase-shift keying (PSK) modulation. Specifically, we demonstrate that in the low-photon regime the capacity region collapses into a rectangle, asymptotically matching the point-to-point capacity as multi-user interference vanishes. We also characterize an achievable covert throughput region, showing that entanglement assistance enables an aggregate throughput scaling of (O(\sqrt{n} \log n)) covert bits with the block length $n$ for both senders, surpassing the square-root law as in the point-to-point case. Our analysis reveals that the joint covertness constraint imposes a linear trade-off between the senders throughput.

💡 Research Summary

The paper investigates covert communication over an entanglement‑assisted (EA) bosonic multiple‑access channel (MAC). The authors consider two transmitters, each sharing a two‑mode squeezed vacuum (TMSV) state with the receiver (Bob) but not with each other. The transmitters modulate their modes using high‑order phase‑shift keying (PSK) and send the signals through a linear optics network characterized by a beam‑splitter with transmissivity τ, followed by a lossy bosonic channel with transmissivity κ and thermal noise N_B. The receiver jointly measures the channel output together with the stored idler modes, while an eavesdropper (Willie) observes the complementary output.

Main Contributions

1. Achievable Rate Region for EA Bosonic MAC
   Using a single‑layer high‑order PSK codebook and a finite‑dimensional truncation of the receiver’s Hilbert space, the authors apply a one‑shot coding lemma for multiple‑access channels (Lemma 2.1). By employing heterodyne detection on the idlers and the chain rule for mutual information, they decouple the joint mutual information into single‑user terms. In the asymptotic limit (large block length n) the achievable region is described by three inequalities:
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