Boosting linear-optical Bell measurement success probability with predetection squeezing and imperfect photon-number-resolving detectors

Linear-optical realizations of Bell state measurement (BSM) on two single-photon qubits succeed with probability ps no higher than 0.5. However, predetection quadrature squeezing, i.e., quantum noise limited phase sensitive amplification, in the usual linear-optical BSM circuit, can yield ps≈0.643. The ability to achieve ps>0.5 has been found to be critical in resource-efficient realizations of linear-optical quantum computing and all-photonic quantum repeaters. Yet, the aforesaid value of ps>0.5 is not known to be the maximum achievable using squeezing, thereby leaving it open whether close-to-100% efficient BSM might be achievable using squeezing as a resource. In this paper, we report insights on why squeezing-enhanced BSM achieves ps>0.5. Using this, we show that the previously reported ps≈0.643 at single-mode squeezing strength r=0.6585 - for unambiguous state discrimination (USD) of all four Bell states - is an experimentally unachievable point result, which drops to ps≈0.59 with the slightest change in r. We, however, show that squeezing-induced boosting of ps with USD operation is still possible over a continuous range of r, with an experimentally achievable maximum occurring at r=0.5774, achieving ps≈0.596. Finally, deviating from USD operation, we explore a trade space between ps, the probability with which the BSM circuit declares a "success," versus the probability of error pe, the probability of an input Bell state being erroneously identified given the circuit declares a success. Since quantum error correction could correct for some pe>0, this tradeoff may enable better quantum repeater designs by potentially increasing the entanglement generation rates with ps exceeding what is possible with traditionally studied USD operation of BSMs.