Entangled or Not 2

Classical Mechanics Level 1

$|\Psi\rangle = \frac{1}{\sqrt{5}}|\uparrow\uparrow\rangle +\frac{\sqrt{2}}{\sqrt{5}} |\downarrow\uparrow\rangle - \frac{\sqrt{2}}{\sqrt{5}} |\downarrow\downarrow\rangle$

Is the state $|\Psi\rangle$ above entangled?

Note : The notation $|\uparrow\downarrow\rangle = |\uparrow\rangle \otimes |\downarrow\rangle$ is a common shorthand for tensor products of spin states.

Yes Maybe No

1 solution

Matt DeCross
Apr 26, 2016

Relevant wiki: Quantum Entanglement

The state can be written as matrix form as:

$|\Psi\rangle = \frac{1}{\sqrt{5}} \begin{pmatrix} 1 & 0 \\ \sqrt{2} & -\sqrt{2} \end{pmatrix}.$

This does not have determinant zero, therefore, the state is not a product state, i.e. it is entangled.

Entangled or Not 2

1 solution

0 pending reports