Times of Execution of the Quantum NOT Gate Operating on One of Two Interacting Qubits

Abstract

It is generally believed that entanglement speeds up Quantum Information Processing (QIP). However, we prove that for a system of two interacting qubits through a XXZ Hamiltonian that are maximally entangled, it is not possible to execute a quantum NOT gate operating on one of these two qubits. The interaction between the two qubits means presence of noise in one of them. If the two interacting qubits are not entangled the times of execution of the quantum NOT gate operating on one of the two qubits are not small enough. We conclude that the execution of the quantum NOT gate operating on one of two interacting qubits is not possible.