  Operations on a pair of entangled qubits are conventionally presented as the
application of the tensor product of operations. The tensor product is linearly
extended to act synchronously across the entire entangled system. When
simulating an entangled system, the conventional approach is possible and
practical if both parts of the entangled system exist within the same physical
simulator. However, if we wish to simulate an entangled system across a
distributed network, sending half of the entangled pair to another simulator on
another computer system, the synchronous approach becomes difficult. In the
first part of this paper, we demonstrate a method of simulating operations on
entangled states in a distributed environment which is equivalent to the
conventional approach. The advantage to our approach is that we can simulate
distributed quantum systems on physically distributed hardware. Such a system
advances the possibilities of demonstrating distributed quantum algorithms for
research, teaching, and learning.
  Further, the security of quantum key exchange depends on successfully
detecting the presence of an eavesdropper. In most cases this is done by
comparing the errors introduced by an eavesdropper with the channel error rate.
In other words, the communicating parties must tolerate some errors without
losing a significant amount of key information. In the second part of this
paper, we characterize the effects of amplitude damping errors on quantum key
distribution protocols and explore allowable tolerances. Through simulations we
observe that the effect of these errors, in some cases, is highly dependent on
where the eavesdropper is located on the channel.
  In this paper, we also briefly describe the development of a new quantum
simulation library called QooSim.
