Solution
= Solution
The sign factor separates as $(-1)^{x+y}=(-1)^x(-1)^y$. Consequently the <quantum state> factors into a <tensor product of quantum systems>:
$$
\frac12\sum_{x,y=0}^1(-1)^{x+y}|x\rangle|y\rangle
=\left(\frac{|0\rangle-|1\rangle}{\sqrt2}\right)\otimes\left(\frac{|0\rangle-|1\rangle}{\sqrt2}\right)
=\boxed{|-\rangle\otimes|-\rangle.}
$$
It is a <product state>, so \b[it is not entangled].