Complementary Resource Relation of Concurrence and Roughness for atwo Qubits State

Abstract

Quantum resources lie at the core of quantum computation as they are responsible for the computational advantage in many tasks. The complementary relations are a pathway to understanding how the physical quantities are related. Here it was shown that there is a complementary relationship that evolves quantumness of a two qubits state and the degree of entanglement, respectively measured by Roughness and Concurrence. It was shown that there is a R 2 surface that characterizes these quantities and can be understood as a projection of the Bloch Sphere. The distribution of states on the surface shows a concentration in the region of lower roughness and Concurrence, i.e., in the subset of states of greater entropy.

Simulation of Afshar's Double Slit Experiment

“…For a closed bipartite entangled system, the EGY duality relation becomes a triality relation and distinguishability becomes D 2 = C 2 + P 2 , where C is concurrence and P is predictability [14] . These relations are relevant to quantum computing as they identify the relationship between quantum resources [15,16]. For open systems, as in real experiments, the validity of the complementarity relations is limited [17,18,19].…”