Entangling capacity of global phases and implications for the Deutsch-Jozsa algorithm
Hiroo Azuma, Sougato Bose, Vlatko Vedral · Physical Review A · 2001
We investigate the creation of entanglement by the application of phases whose value depends on the state of a collection of qubits. First we give the necessary and sufficient conditions for a given set of phases to result in the creation of entanglement in a state comprising of an arbitrary number of qubits. Then we consider the maximum entanglement generation by global phases. We analyze the creation of entanglement between any two qubits in three-qubit pure and mixed states. We use our result to prove that entanglement is necessary for the Deutsch-Jozsa algorithm to have an exponential advantage over its classical counterpart.