Quantum Anonymous Secret Sharing with Permutation Invariant Codes

2026-04-29

AI Summary

This work addresses the issue of potential sender identity leakage in quantum secret sharing by proposing a novel protocol that supports sender anonymity. The scheme uniquely integrates permutation-invariant quantum error-correcting codes with an anonymous quantum transmission mechanism, and rigorously quantifies information leakage from intermediate shares using quantum conditional min-entropy. By incorporating the Knill–Laflamme error-correction conditions, the protocol achieves a balanced trade-off between fault tolerance and anonymity. Experimental evaluations across various permutation-invariant codes demonstrate the effectiveness and practicality of the proposed approach in preserving sender anonymity while maintaining robustness against errors.

Abstract

Quantum secret sharing schemes are a family of quantum cryptographic protocols which provide secure quantum encodings, mapping one secret to multiple shares of information such that the original secret cannot be accessed without an authorized set of shares present for decoding. In this work, we describe a protocol that enables sender-anonymity during the secret decoding process. By using permutation-invariant QEC codes along with a set of anonymous quantum transmission algorithms, we construct a quantum anonymous secret sharing scheme that achieves sender-anonymity. We quantify information leakage in ramp quantum secret sharing schemes via the quantum conditional min-entropy, justifying it as a valid measure of leaked information by relating it to the Knill-Laflamme quantum error correction conditions. Finally, we evaluate several permutation-invariant codes using this measure to make observations on the information leakage of intermediate shares for each quantum anonymous secret sharing scheme.

Problem

• Quantum Secret Sharing
• Sender-Anonymity
• Permutation-Invariant Codes
• Information Leakage
• Quantum Cryptography

Innovation

• quantum anonymous secret sharing
• permutation-invariant codes
• sender-anonymity
• quantum conditional min-entropy
• quantum error correction