On the Capacity of Erasure-prone Quantum Storage with Erasure-prone Entanglement Assistance

2025-10-20

AI Summary

This work investigates the fundamental capacity limits of entanglement-assisted quantum storage over erasure channels: a quantum message is encoded across $N$ storage nodes, aided by $N_B$ pre-shared $lambda_B$-dimensional maximally entangled states (accessible via $K_B$ auxiliary nodes); perfect recovery must be possible from any $K$ storage nodes and any $K_B$ auxiliary nodes. We fully characterize the exact quantum storage capacity as a function of $N$, $K$, $N_B$, $K_B$, and $lambda_B$. Leveraging a rigorous analogy with classical linear erasure codes, we translate classical constraints into quantum achievability conditions. Combining entanglement-assisted coding, shared randomness modeling, and information-theoretic analysis, we prove that—except in an intermediate parameter regime—the quantum capacity equals the Shannon capacity of the corresponding classical problem, revealing a profound duality between classical and quantum erasure resilience. The capacity characterization remains open only for that intermediate regime.

Technology Category

• Machine Learning: Quantum Machine Learning
• Reasoning under Uncertainty: Graphical Models
• Knowledge Representation and Reasoning: Qualitative Reasoning

Application Category

• Search and Retrieval-Augmented AI: Web evaluation methodologies and metrics
• Security and Privacy: Large-scale security measurements
• Graph Algorithms and Modeling for the Web: Querying, indexing, and retrieval in Web-related graphs

Abstract

A quantum message is encoded into $N$ storage nodes (quantum systems $Q_1dots Q_N$) with assistance from $N_B$ maximally entangled bi-partite quantum systems $A_1B_1, dots, A_{N_B}B_{N_B}$, that are prepared in advance such that $B_1dots B_{N_B}$ are stored separately as entanglement assistance (EA) nodes, while $A_1dots A_{N_B}$ are made available to the encoder. Both the storage nodes and EA nodes are erasure-prone. The quantum message must be recoverable given any $K$ of the $N$ storage nodes along with any $K_B$ of the $N_B$ EA nodes. The capacity for this setting is the maximum size of the quantum message, given that the size of each EA node is $λ_B$. All node sizes are relative to the size of a storage node, which is normalized to unity. The exact capacity is characterized as a function of $N,K,N_B,K_B, λ_B$ in all cases, with one exception. The capacity remains open for an intermediate range of $λ_B$ values when a strict majority of the $N$ storage nodes, and a strict non-zero minority of the $N_B$ EA nodes, are erased. As a key stepping stone, an analogous classical storage (with shared-randomness assistance) problem is introduced. A set of constraints is identified for the classical problem, such that classical linear code constructions translate to quantum storage codes, and the converse bounds for the two settings utilize similar insights. In particular, the capacity characterizations for the classical and quantum settings are shown to be identical in all cases where the capacity is settled.

Problem

• Determining quantum storage capacity with erasure-prone entanglement assistance
• Characterizing exact capacity for quantum message recovery conditions
• Establishing classical-quantum equivalence for storage capacity bounds

Innovation

• Uses erasure-prone quantum storage with entanglement assistance
• Encodes messages across multiple storage and EA nodes
• Characterizes capacity for quantum erasure channels exactly