Comment on "Franson Interference Generated by a Two-Level System"

TL;DR

This paper critically examines a recent Franson interferometry experiment with quantum dot photon pairs, clarifying misconceptions about the reported visibility and its implications for Bell inequality violations.

Contribution

It provides a detailed critique of the previous experiment's interpretation and offers corrections to accurately assess quantum correlations.

Findings

The reported 66% visibility does not surpass the classical limit.

The claim of approaching Bell inequality violation is unfounded without proper analysis.

The paper clarifies the conditions needed for genuine Bell inequality violations.

Abstract

In a recent Letter [Phys. Rev. Lett. 118, 030501 (2017)], Peiris, Konthasinghe, and Muller report a Franson interferometry experiment using pairs of photons generated from a two-level semiconductor quantum dot. The authors report a visibility of 66% and claim that this visibility "goes beyond the classical limit of 50% and approaches the limit of violation of Bell's inequalities (70.7%)." We explain why we do not agree with this last statement and how to fix the problem.

Full text

In a recent Letter PKM17 , Peiris, Konthasinghe, and Muller report a Franson interferometry experiment using pairs of photons generated via frequency-filtered scattered light from a two-level semiconductor quantum dot. The authors report a visibility of $66\%$ and claim that this visibility “goes beyond the classical limit of $50\%$ and approaches the limit of violation of Bell’s inequalities ($70.7\%$).” In the following we explain why we do not agree with this last statement.

A violation of the Clauser-Horne-Shimony-Holt (CHSH) Bell inequality CHSH69 without supplementary assumptions (so that it is loophole-free and therefore potentially usable for device-independent applications) using a maximally entangled state is only possible in a very small region of values of the overall detection efficiency $\eta$ and the visibility $V$. Specifically, it must occur that $V\geq(2/\eta-1)/\sqrt{2}$ Larsson99 . Therefore, the 70.7% visibility bound mentioned by Peiris, Konthasinghe, and Muller only holds under the assumption that $\eta=1$.

The problem is that this value is impossible to achieve in the Franson interferometer, even ideally. As the authors correctly point out, in the Franson interferometer there is a crucial postselection step which requires discarding, on average, 50% of the recorded photons. Therefore, even in the ideal case that the detectors and couplings were perfect, the effective $\eta$ falls to $50\%$. This implies that it is possible to produce a classical local hidden variable models while retaining the same output statistics as predicted by quantum theory AKLZ99 ; CRVDM09 ; JL14 .

In fact, the above problem has recently been exploited to experimentally show that the security proof in Franson-based quantum key distribution schemes can be circumvented, exposing its users to eavesdropping JEABL15 . In these attacks, tailored pulses of classical light are used, which indicates that the $50\%$ “classical limit” can be beat even in a purely classical setting.

However, as described in AKLZ99 , there is a possibility of detecting a genuine violation of a Bell inequality in the setting of Peiris, Konthasinghe, and Muller. It requires using a different Bell inequality, namely, a three-setting chained Bell inequality introduced by Pearle Pearle70 . This modification allows for a genuine violation of local realism, but requires a higher visibility: At least, $94.63\%$ AKLZ99 ; JL14 . Although demanding, a recent work TMJVLV17 shows that such an experiment is feasible.

In conclusion, while the setup in PKM17 is promising, the experimental data does not rule out all classical descriptions. A test of the three-setting chained Bell inequality could be a more suitable application for this correlated photon pair source. However, the corresponding experiment would be much more challenging as it requires a visibility of, at least, $94.63\%$.