#### Bulg. J. Phys. vol.45 no.1 (2018), pp. 001-006

#### A Quick and Easy Test for Deciding Entanglement Status of an *N*-Qubit Pure Quantum State

D.P. Mehendale

go back^{}, P.S. Joag^{}*Department of Physics, Savitribai Phule University of Pune, Pune, India-411007*Abstract.We develop a simple criterion in terms of a necessary-sufficient condition (NScondition) for deciding separability of an arbitraryn-qubit pure quantum state. ThisNScondition provides a quick and easy test procedure to determine the entanglement status of a pure quantum state. We normalize the given quantum state and using this normalized state we can easily build a simplest system of equations containing trigonometric functions by making use of the well known Bloch Sphere representation for single qubit states and check whether or not this system of equations is consistent. According to proposedNScondition the given pure quantum state is separable (entangled) if and only if the above mentioned system of equations is consistent (inconsistent). We build this system of equations by equating the coefficients of computational basis states in the superposition representing the given pure quantum state with certain products of trigonometric functions obtained using standard Bloch Sphere representation for single qubit states. To establish separability of given state one requires to find a valid solution of the above mentioned system of equations but entanglement on the other hand follows when any two equations in this system of equations are mutually inconsistent. Thus, entanglement of the state can follow easily if one succeeds in finding any two mutually inconsistent equations in the above mentioned system of equations.