Efficiency of an enhanced linear optical Bell-state measurement scheme with realistic imperfections

Abstract

We compare the standard 50%-efficient single beam splitter method for Bell-state measurement to a proposed 75%-efficient auxiliary-photon-enhanced scheme [W. P. Grice, Phys. Rev. A 84, 042331 (2011)] in light of realistic conditions. The two schemes are compared with consideration for high input state photon loss, auxiliary state photon loss, detector inefficiency and coupling loss, detector dark counts, and non-number-resolving detectors. We also analyze the two schemes when multiplexed arrays of non-number-resolving detectors are used. Furthermore, we explore the possibility of utilizing spontaneous parametric down-conversion as the auxiliary photon pair source required by the enhanced scheme. In these different cases, we determine the bounds on the detector parameters at which the enhanced scheme becomes superior to the standard scheme and describe the impact of the different imperfections on measurement success rate and discrimination fidelity. This is done using a combination of numeric and analytic techniques. For many of the cases discussed, the size of the Hilbert space and the number of measurement outcomes can be very large, which makes direct numerical solutions computationally costly. To alleviate this problem, all of our numerical computations are performed using pure states. This requires tracking the loss modes until measurement and treating dark counts as variations on measurement outcomes rather than modifications to the state itself. In addition, we provide approximate analytic expressions that illustrate the effect of different imperfections on the Bell-state analyzer quality.

Resource requirements for efficient quantum communication using all-photonic graph states generated from a few matter qubits

“…If the photon travels to a quantum repeater, it is possible to deterministically entangle the QM and the photon, so the entanglement probability is only bounded by the photonic losses. If the photon travels to an intermediate node, the entanglement generation procedure uses linear optics and has a success probability that cannot reach more than 1/2 (unless ancillary photonic qubits are used, but this requires another quantum emitter to produce them [52][53][54]).…”

“…Two photons generated at adjacent repeater nodes arrive at the same measurement node situated halfway between the two repeaters, where they are measured in a Bell state basis. Because a photon Bell state measurement using only linear optics succeeds with probability at best 1/2 (without ancillary qubits or QND measurements [49][50][51][52][53][54]), the overall success probability of the distant heralded entanglement generation is P ent ≤ 1/2. It is worth mentioning that a method for achieving heralded entanglement generation with higher success probability has been proposed [55], but its efficacy is restricted to qubits separated by a short distance, so we exclude this from our analysis (see Supplementary Materials for more details).…”

Filtration Mapping as Complete Bell State Analyzer for Bosonic Particles

“…The auxiliary-photon-enhanced scheme suggested in 7 to improve the probability of discrimination uses a pair of ancillary entangled photons to increase the probability up to 75%. More generally, according to 8 , introducing 2 N − 2 ancillary photons may enhance the success rate of linear-optic measurements up to 1 − 1/2 N .…”

Filtration mapping as complete Bell state analyzer for bosonic particles

“…The auxiliary-photon-enhanced scheme suggested in 24 to improve the probability of discrimination uses a pair of ancillary entangled photons to increase the probability up to 75%. More generally, according to 25 , introducing ancillary photons may enhance the success rate of linear-optic measurements up to .…”