Secure $N$-dimensional Simultaneous Dense Coding and Applications

TL;DR

This paper introduces new protocols for $N$-dimensional simultaneous dense coding using various entangled states and locking operators, enhancing fairness and security, and demonstrating applications in contract signing and teleportation.

Contribution

It proposes three novel simultaneous dense coding protocols with different entanglement resources and introduces two new locking operators, improving fairness and security.

Findings

Three protocols using Bell, W, and GHZ states.

Two new locking operators: double CNOT and SWAP.

Enhanced fairness and security in the protocols.

Abstract

Simultaneous dense coding guarantees that Bob and Charlie simultaneously receive their respective information from Alice in their respective processes of dense coding. The idea is to use the so-called locking operation to "lock" the entanglement channels, thus requiring a joint unlocking operation by Bob and Charlie in order to simultaneously obtain the information sent by Alice. We present some new results on simultaneous dense coding: (1) We propose three simultaneous dense coding protocols, which use different $N$-dimensional entanglement (Bell state, W state and GHZ state). (2) Besides the quantum Fourier transform, two new locking operators are introduced (the double controlled-NOT operator and the SWAP operator). (3) In the case that spatially distant Bob and Charlie have to finalise the protocol by implementing the unlocking operation through communication, we improve our protocol's fairness, with respect to Bob and Charlie, by implementing the unlocking operation in series of steps. (4) We improve the security of simultaneous dense coding against the intercept-resend attack. (5) We show that simultaneous dense coding can be used to implement a fair contract signing protocol. (6) We also show that the $N$-dimensional quantum Fourier transform can act as the locking operator in simultaneous teleportation of $N$-level quantum systems.