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Linear optical realizations of Bell state measurement (BSM) on twosingle-photon qubits succeed with probability $p_s$ no higher than $0.5$.However pre-detection quadrature squeezing, i.e., quantum noise limited phasesensitive amplification, in the usual linear-optical BSM circuit, can yield${p_s \approx 0.643}$. The ability to achieve $p_s > 0.5$ has been found to becritical in resource-efficient realizations of linear optical quantum computingand all-photonic quantum repeaters. Yet, the aforesaid value of $p_s > 0.5$ isnot known to be the maximum achievable using squeezing, thereby leaving it openwhether close-to-$100\%$ efficient BSM might be achievable using squeezing as aresource. In this paper, we report new insights on why squeezing-enhanced BSMachieves $p_s > 0.5$. Using this, we show that the previously-reported ${p_s\approx 0.643}$ at single-mode squeezing strength $r=0.6585$---for unambiguousstate discrimination (USD) of all four Bell states---is an experimentallyunachievable point result, which drops to $p_s \approx 0.59$ with the slightestchange in $r$. We however show that squeezing-induced boosting of $p_s$ withUSD operation is still possible over a continuous range of $r$, with anexperimentally achievable maximum occurring at $r=0.5774$, achieving ${p_s\approx 0.596}$. Finally, deviating from USD operation, we explore atrade-space between $p_s$, the probability with which the BSM circuit declaresa "success", versus the probability of error $p_e$, the probability of an inputBell state being erroneously identified given the circuit declares a success.Since quantum error correction could correct for some $p_e > 0$, this tradeoffmay enable better quantum repeater designs by potentially increasing theentanglement generation rates with $p_s$ exceeding what is possible withtraditionally-studied USD operation of BSMs.

Boosting Linear-Optical Bell Measurement Success Probability with Pre-Detection Squeezing and Imperfect Photon-Number-Resolving Detectors