Digital quantum simulation of bosonic systems and quantum complementarity

In this manuscript, the authors address the digital simulation of quantum systems based on bosonic degrees of freedom by means of state-of-the-art quantum computers. In particular, they discuss the quantum complementary principle in the context of two experiments proposed by Pessoa Júnior. These experiments aim to both simulate the main features of Afshar’s experiment and provide an interpretation in the framework of the complementary principle. Therefore, the authors provide a comparison between theoretical probabilities, classical simulations and demonstrative results obtained by means of IBMQ quantum computers. The manuscript presents broad reviews of the mathematical background, yet it lacks in the exposition of valid new results. To motivate this statement, I list three main reasons below:

1. The authors have extensively illustrated the technique introduced by Mohan et al., extending the method to a set-up embracing more than two bosons. In Mohan et al., the bosonic nature of the particles they simulated covers a fundamental role, since they were interested in the simulation of the HOM effect. On the contrary, all experimental schemes discussed in this manuscript require only one quantum excitation in total. The high (infinite) dimensionality of the Hilbert space of bosonic degrees of freedom hence does not seem to play any relevant role in the discussion, since the presence (or absence) of the quanton in a specific mode can all in all be described in terms of single qubit modes without invoking any bosonic framework. The authors should better motivate the choice of extending and employing such mathematical apparatus.

2. In both Fig.8 and Fig.11 demonstrations and theoretical/simulation data show important fluctuations. Authors claim that this is due to the presence of noise and losses. Nevertheless, these discrepancy sources have an impactful effect on the outcomes. In some histogram the discrepancy between the expected and the observed data even amounts to over 40%, such as in Fig.11A in 0001, where the expected value is 0.02, whereas the demonstration displays the value 0.011. In Fig.8 the demonstrations display fluctuations as wide as or even wider than the expectation values in other plots. These results seem to lead to the conclusion that the instruments used for the demonstrations are not enough accurate for this kind of measurements.

3. A last relevant remark concerns their analysis in the light of the quantum complementarity principle. In their discussions, authors recall and report the results achieved in [37], where the quantum complementarity principle has been applied to both the BMZI and the Unruh experiment. Moreover, they claim that “The explanation of the experiment in Fig. 2 using the QCP also extends to the modified Unruh’s experiment (Fig. 4) and Pessoa Júnior’s experiment (Fig. 9). This follows from the fact that BBS1 in these setups is a generalization of BS1, which corresponds to the specific case where T1 = R1 = 1/√2. Since all these experimental configurations are designed to analyze the quanton’s dual behavior after the first beam splitter, their description follows naturally from the QCP framework”. This seems to be the core of their theoretical results. Yet, they do not provide any further concrete mathematical analysis to support it. Moreover, the BMZI, which includes biased BS, has already been discussed in [37]. If both the description of both the modified Unruh’s experiment and Pessoa Júnior’s experiment follows from the QCP framework so naturally that it does not even require a more detailed analysis, it is not clear what are the elements of novelty of the manuscript.

Therefore, I would not recommend the publication unless the authors properly address the issues presented above.

Finally, some relatively minor issues related to the readability of the manuscript: 1) In Fig.3 detector D(A) and D(B) should be switched. Or the sentence on page 5 and the caption of Fig.3 must be changed. According to both Afshar’s experiment and the current notation on the figure, closing the slit A we should observe a click on the detector B. 2) What phase phi_H and phi_E have been used for the histograms in fig.8? Are they phi_E=1/2 and phi_H=0? 3) In the end of page 12, state B_1 has six digit. 4) In Fig.10, the action of BS_2, U_M and BS_3 seems to involve all four modes, whereas it actually involves only two of them. For this reason, as an attachment I prepared an alternative scheme I believe more suitable for fig.10. The authors may consider this scheme instead of that in Fig.10. If not, they should better explain the switch between P and M after U_M.

Download attachment

Ask for major revision

scipost_202503_00053v1

The Afshar experiment, a variation of the double-slit experiment in quantum mechanics, was devised and conducted by Shahriar Afshar in 2004. Afshar asserted that the experiment provides information about the path a photon takes through the apparatus while simultaneously allowing for the observation of interference between the paths. He claimed that this finding contradicts the complementarity principle of quantum mechanics. In response, several experiments have critiqued Afshar's work, including one by Unruh. Unruh, like Kastner, set up a configuration he believes is both equivalent and simpler. His approach magnifies the effect, making it easier to identify flaws in the logic. This article presents a detailed overview of Afshar's original experiment, along with Unruh's experiment and a modified version (Pessoa Junior's), to examine the issues raised by Afshar concerning a potential violation of the complementarity principle.

The authors have digitally simulated interferometric variants of Afshar's experiment using IBM's quantum computers. They have explored the analogous experiments conducted by Unruh and Pessoa Júnior, delving into discussions regarding the apparent violation of Bohr's complementarity principle in the context of the entire experimental setup. Additionally, they have analyzed these experiments within the framework of an updated quantum complementarity principle, which applies to specific quantum state preparations while remaining consistent with the foundational principles of quantum mechanics.

I believe that much of the calculations, except for minor errors (e.g. A1 to A5) and analysis is fine. However, I think using a digital simulator on an IBM machine may be a little heavy handed. The analysis could proceed with simple optical experiments on an optical bench, although it may somehow lose some oomphs and also some of the experiments may have already been demonstrated. So, aside from the usual arguments from the proponents and critiques of the original exeriment, what really is new aside from a somewhat trivial application of a quantum simulator.

Overall, I think the paper is more suitable for a pedagogical journal. I do not recomment it for SciPost.

I think the article is better suited for a pedagogical journal.

Accept in alternative Journal (see Report)