Narrow Results

We review series of multiqubit Bell's inequalities which apply to correlation functions and present conditions that quantum states must satisfy to violate such inequalities.

We investigate the GHZ paradox as embodied in Mermin’s machine. We begin by showing that this machine is impossible to implement within the context of classical physics. Then we go on to show how it can be implemented within quantum mechanics.

We push this investigation to its limits using some of the most recent advances in quantum computation and quantum information science. The detailed wiring diagram constructed herein provides an explicit and revealing definition of the machine. In particular, it makes explicit how paradoxical indeterminism and nonlocality can be quantified and mathematically captured by the second elementary Boolean function. It also gives an illustration of the many subtleties involved in the quantum control of distributed quantum systems.

Within this paper, we introduce two new mathematical constructs, i.e., Boolean unitaries and Boolean observables, that provide a useful mathematical formalism for analyzing problems within quantum information science.