  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.
