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

TL;DR

This paper investigates how pre-detection squeezing can enhance the success probability of linear-optical Bell state measurements beyond 50%, identifying optimal squeezing parameters and exploring trade-offs with error probabilities for improved quantum communication.

Contribution

It provides new insights into squeezing-enhanced Bell measurement success probabilities, correcting previous overestimations, and explores a trade-off between success and error probabilities for quantum repeater applications.

Findings

Maximum success probability with squeezing is approximately 0.596 at optimal squeezing.

The previously reported success probability of 0.643 is experimentally unachievable.

Trade-off analysis suggests potential for higher entanglement rates with acceptable error levels.

Abstract

Linear optical realizations of Bell state measurement (BSM) on two single-photon qubits succeed with probability $p_s$ no higher than $0.5$. However pre-detection quadrature squeezing, i.e., quantum noise limited phase sensitive 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 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 new insights on why squeezing-enhanced BSM achieves $p_s > 0.5$. Using this, we show that the previously-reported ${p_s \approx 0.643}$ at single-mode squeezing strength $r=0.6585$---for unambiguous state discrimination (USD) of all four Bell states---is an experimentally unachievable point result, which drops to $p_s \approx 0.59$ 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 ${p_s \approx 0.596}$. 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.