  The problem of finding a vector $x$ which obeys a set of quadratic equations
$|a_k^\top x|^2=y_k$, $k=1,\cdots,m$, plays an important role in many
applications. In this paper we consider the case when both $x$ and $a_k$ are
real-valued vectors of length $n$. A new loss function is constructed for this
problem, which combines the smooth quadratic loss function with an activation
function. Under the Gaussian measurement model, we establish that with high
probability the target solution $x$ is the unique local minimizer (up to a
global phase factor) of the new loss function provided $m\gtrsim n$. Moreover,
the loss function always has a negative directional curvature around its saddle
points.
