Boosting linear-optical Bell measurement success probability with predetection squeezing and imperfect photon-number-resolving detectors
Thomas Kilmer, Saikat Guha · Physical Review A · 2019
Linear-optical realizations of Bell state measurement (BSM) on two single-photon qubits succeed with probability ${p}_{s}$ 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 ${p}_{s}\ensuremath{\approx}0.643$. The ability to achieve ${p}_{s}>0.5$ 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 ${p}_{s}>0.5$ 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 ${p}_{s}>0.5$. Using this, we show that the previously reported ${p}_{s}\ensuremath{\approx}0.643$ 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 ${p}_{s}\ensuremath{\approx}0.59$ with the slightest change in $r$. We, however, show that squeezing-induced boosting of ${p}_{s}$ with USD operation is still possible over a continuous range of $r$, with an experimentally achievable maximum occurring at $r=0.5774$, achieving ${p}_{s}\ensuremath{\approx}0.596$. Finally, deviating from USD operation, we explore a trade space between ${p}_{s}$, the probability with which the BSM circuit declares a ``success,'' versus the probability of error ${p}_{e}$, the probability of an input Bell state being erroneously identified given the circuit declares a success. Since quantum error correction could correct for some ${p}_{e}>0$, this tradeoff may enable better quantum repeater designs by potentially increasing the entanglement generation rates with ${p}_{s}$ exceeding what is possible with traditionally studied USD operation of BSMs.