  Bell's theorem implies that the outcomes of local measurements on two
maximally entangled systems cannot be simulated without classical communication
between the parties. The communication cost is finite for n Bell states, but it
grows exponentially in n. Three simple protocols are presented that provide
approximate simulations for low-dimensional entangled systems and require a
linearly growing amount of communication. We have tested them by performing
some simulations for a family of measurements. The maximal error is less than
1% in three dimensions and grows sublinearly with the number of entangled bits
in the range numerically tested. One protocol is the multidimensional
generalization of the exact Toner-Bacon [Phys. Rev. Lett. 91, 187904 (2003)]
model for a single Bell state. The other two protocols are generalizations of
an alternative exact model, which we derive from the Kochen-Specker [J. Math.
Mech. 17, 59 (1967)] scheme for simulating single-qubit measurements. These
protocols can give some indication for finding optimal one-way communication
protocols that classically simulate entanglement and quantum channels.
Furthermore they can be useful for deciding if a quantum communication protocol
provides an advantage on classical protocols.
