arXiv2026
A linear optics-based scheme to implement various quantum information processing tasks is of paramount importance due to its ease of implementation and low noise. Many information-theoretic tasks depend on the successful discrimination of Bell states. A no-go theorem states that it is not possible to perfectly discriminate among the four Bell states when the measurement apparatus is restricted to linear optical elements. The success probability is only $50\%$. Using extra resources such as hyperentanglement, 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 $25\%$. Bell-like states are non-maximally entangled two-qubit states that resemble Bell states in structure but have unequal Schmidt coefficients. We find that this can be boosted to $50\%$ using hyperentanglement, where extra ancillary degrees of freedom (DOF) of photons, such as polarization, momentum, or OAM, are also entangled along with the system DOF. This contrasts with Bell-state discrimination, where $100\%$ can be achieved. Furthermore, we find that using correlations in the photons' arrival times, all four Bell states can be distinguished with $100\%$ success probability, while for Bell-like state discrimination, it increases only to $37.5\%$ from $25\%$. We observe a similar contrast when using ancillary entangled photons. While the success probability for discriminating all four Bell states increases as $1-\frac{1}{2^N}$, where $N$ is the number of ancillary photon pairs, for Bell-like states, it depends 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.