Abstract
It is natural in a quantum network system that multiple users intend to send their quantum message to their respective receivers, which is called a multiple unicast quantum network. We propose a canonical method to derive a secure quantum network code over a multiple unicast quantum network from a secure classical network code. Our code correctly transmits quantum states when there is no attack. It also guarantees the secrecy of the transmitted quantum state even with the existence of an attack when the attack satisfies a certain natural condition. In our security proof, the eavesdropper is allowed to modify wiretapped information dependently on the previously wiretapped messages. Our protocol guarantees the secrecy by utilizing one-way classical information transmission (public communication) in the same direction as the quantum network although the verification of quantum information transmission requires two-way classical communication. In the protocol, some nodes may share secret randomness as resources in advance. Our secure network code can be applied to several networks including the butterfly network.
Highlights
In order to realize quantum information processing protocols to overwhelm the conventional information technologies among multiple users, it is needed to build up a quantum network system among multiple users
PREPARATION FROM SECURE CLASSICAL NETWORK CODING we introduce classical network coding and its secrecy and recoverability analysis which is necessary for analyzing the security of the derived quantum network codes
We derive a quantum network code from a linear classical network code, and analyze the security of the quantum network coding based on the properties of the original classical network coding which are discussed in the previous section
Summary
In order to realize quantum information processing protocols to overwhelm the conventional information technologies among multiple users, it is needed to build up a quantum network system among multiple users. Leung et al [9] investigated several types of networks when classical communication is allowed Based on these studies, Kobayashi et al [10] made a code to transmit quantum states based on a linear classical network code. After the conference version [29] of this paper, several studies [30], [31], [32] investigated the security for the quantum network code when an adversary attacks the quantum network They did not discuss a method for converting an existing classical network code to a quantum network code. We generally construct a quantum linear network code in the multiple-unicast setting whose security is guaranteed. Our code is canonically constructed from a classical linear network code in the multiple-unicast setting, and it certainly transmits quantum states when there is no attack. Appendix B gives the precise constructions of the matrices appearing in the main body
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
