  A linear optics-based scheme to implement various quantum information
processing tasks is of paramount importance due to ease of implementation and
low noise. Many information-theoretic tasks depend on the successful
discrimination of Bell states. A no-go theorem has been proved in literature
which tells that it is not possible to perfectly discriminate among the four
Bell states by restricting measurement apparatus to linear optical elements.
The success probability is only $50\%$. Through using extra resources such as
hyper entanglement, ancillary entanglement, and even a minimum amount of
non-linearity complete Bell-state discrimination can be achieved. The success
probability for Bell-like state discrimination is only $25\%$. We find that
this can be boosted up to $50\%$ using hyperentanglement in polarization,
momentum, or OAM degrees of freedom of the photons which is in contrast to the
Bell-state discrimination scenario where $100\%$ can be achieved. Furthermore,
we find that by using correlation in time of the photons all four Bell states
can be distinguished with $100\%$ success probability while for the Bell-like
state discrimination, it strictly lies between $25\%$ and $50\%$ depending on
the state parameter with only three Bell-like states being distinguishable. We
also observe a similar contrast when we use ancillary entangled photons. While
the success probability for all four Bell-state discrimination increases as
$1-\frac{1}{2^N}$ where N is the number of ancillary photons for Bell-like
states it depends again on the state parameters and can be less than $25\%$ in
some cases. Also adding further ancillary photons decreases the success
probability. We then show that using non-linear gadgets namely SFG $100\%$
success probability can be achieved even for Bell-like state discrimination.
