Coding Theoretic Study of Secure Network Coding and Quantum Secret Sharing

Ryutaroh Matsumoto

The common goal of (classical) secure net- work coding and quantum secret sharing is to encode secret so that an adversary has as little information of the secret as possible. Both can be described by a nested pair of classical linear codes, while the strategies available to the adversary are di erent. The security properties of both schemes are closely related to combinatorial properties of the underlying linear codes. We survey connections among them.

Tao Shang, Jianwei Liu

Tao Shang, Ran Liu, Chengran Fang +1 more

W. K. Yam, C. Wilkinson, S. Gandorfer +6 more

Superconducting microwave quantum networks is a rapidly developing field, enabling distributed quantum computing and holding a promise for hybrid architectures in quantum internet. Quantum secret sharing (QSS) is one of the key protocols for multipartite quantum networks and can provide an unconditionally secure way to share quantum states among $n$ players. Using microwave two-mode squeezed states as an entanglement resource, we experimentally implement a QSS protocol with $n = 3$, where a subset of at least $k = 2$ players must collaborate to faithfully reconstruct the original secret state. We demonstrate reconstructed-state fidelities that surpass the asymptotic no-cloning threshold of $F_\textrm{nc} = 2/3$ and identify a parameter regime that allows for unconditionally secure communication in the presence of an omnipotent dishonest player. Furthermore, we experimentally explore inherent connections between QSS and other important quantum information processing tasks, such as quantum dense coding and elementary quantum error correction of channel erasures. Finally, we discuss extensions of QSS and its relation to the concept of blind quantum computing.

G.H. Wang, Yucheng Chen

Abstract Quantum secret sharing has wide application prospects in quantum communication, quantum network and other fields. It can provide a secure and reliable information sharing method for multi-party communication. In this paper, we mainly study the connection mechanism between the quantum secret-sharing scheme and quantum error-correcting codes. Firstly, we give the necessary and sufficient conditions for the existence of quantum error-correcting codes based on group algebra theory. Secondly, we give the corresponding quantum secret sharing scheme model with local quantum operation and classical communication capability can be constructed by any given quantum error-correcting codes. The advantage of this model is that the corresponding quantum secret-sharing scheme can be found for any quantum error-correcting code.

Tao Shang, Jianwei Liu