On the Capacity of Distributed Quantum Storage

2025-10-12

AI Summary

This work investigates the capacity of distributed quantum storage: determining the maximum size of a quantum message that can be reliably stored and recovered given fixed node dimensions and an arbitrary set of erasure patterns. We propose a construction of quantum CSS codes based on nontrivial alignment structures, modeling capacity characterization as a hypergraph covering problem on the storage graph, and establishing a formal connection between classically secure storage and quantum storage. Leveraging quantum information inequalities—including strong subadditivity and weak monotonicity—we derive exact capacity characterizations for canonical topologies, including MDS graphs, wheel graphs, Fano graphs, and intersection graphs—achieving optimal encoding schemes. Our framework uniformly handles heterogeneous erasures, significantly extending both the theoretical limits and constructive capabilities of distributed quantum storage.

Technology Category

• Constraint Satisfaction and Optimization: Distributed CSP/Optimization
• Machine Learning: Quantum Machine Learning
• Search and Optimization: Distributed Search

Application Category

• Graph Algorithms and Modeling for the Web: Representation, reconstruction, and subgraph or motif discovery in Web-related graphs
• Security and Privacy: Large-scale security measurements
• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems

Abstract

A distributed quantum storage code maps a quantum message to N storage nodes, of arbitrary specified sizes, such that the stored message is robust to an arbitrary specified set of erasure patterns. The sizes of the storage nodes, and erasure patterns may not be homogeneous. The capacity of distributed quantum storage is the maximum feasible size of the quantum message (relative to the sizes of the storage nodes), when the scaling of the size of the message and all storage nodes by the same scaling factor is allowed. Representing the decoding sets as hyperedges in a storage graph, the capacity is characterized for various graphs, including MDS graph, wheel graph, Fano graph, and intersection graph. The achievability is related via quantum CSS codes to a classical secure storage problem. Remarkably, our coding schemes utilize non-trivial alignment structures to ensure recovery and security in the corresponding classical secure storage problem, which leads to similarly non-trivial quantum codes. The converse is based on quantum information inequalities, e.g., strong sub-additivity and weak monotonicity of quantum entropy, tailored to the topology of the storage graphs.

Problem

• Characterizing quantum storage capacity for distributed nodes with heterogeneous sizes
• Designing robust quantum codes against arbitrary erasure patterns
• Relating quantum storage achievability to classical secure storage problems

Innovation

• Distributed quantum storage codes map messages to nodes
• Capacity characterized via hyperedges in storage graphs
• Non-trivial alignment structures ensure recovery and security