  We propose a new algebraic formalism for constructing complex non-Hermitian
$\mathcal{PT}$-symmetric superpartners by extending a conventional
shape-invariant superpotential into the complex domain. The resulting potential
is an unbroken super- and parity-time ($\mathcal{PT}$)-symmetric
shape-invariant potential with real energy eigenvalues, maintaining this
property for all parameter values. In order to restore the probabilistic
interpretation within a true quantum theory, a new inner product called the
$\mathcal{CPT}$-inner product is defined in $\mathcal{PT}$-symmetric quantum
mechanics, replacing the Dirac Hermitian inner product. In this work, we
propose a new version of the inner product called the anti-$\mathcal{PT}$
($\mathcal{APT}$)-inner product, $\langle A|B\rangle\equiv
|A\rangle^{\mathcal{APT}}.|B\rangle$, which replaces the previous versions
without any additional considerations. This $\mathcal{PT}$-supersymmetric
quantum mechanics framework also allows for the unification of various areas of
physics, including classical optics and quantum mechanics. To validate the
theory, we present exact solutions for optical waveguides and the quantum
tunneling probability, demonstrating excellent agreement with experimental data
for the probability of crossing the potential barrier in the $\rm
^{3}H(d,n)^{4}He$ reaction.
