SciPost Submission Page
A physical noise model for quantum measurements
by Faedi Loulidi, Ion Nechita, Clément Pellegrini
Submission summary
| Authors (as registered SciPost users): | Faedi Loulidi · Ion Nechita |
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| Preprint Link: | https://arxiv.org/abs/2305.19766v2 (pdf) |
| Date submitted: | 2023-07-21 15:47 |
| Submitted by: | Loulidi, Faedi |
| Submitted to: | SciPost Physics |
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| Academic field: | Physics |
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| Approach: | Theoretical |
Abstract
In this paper, we introduce a novel noise model for quantum measurements motivated by an indirect measurement scheme with faulty preparation. Averaging over random dynamics governing the interaction between the quantum system and a probe, a natural, physical noise model emerges. We compare it to existing noise models (uniform and depolarizing) in the framework of incompatibility robustness. We observe that our model allows for larger compatibility regions for specific classes of measurements.
Current status:
Reports on this Submission
Report
The authors propose a mathematical model for quantum measurements based on an indirect measurement scheme that involves fluctuations of a probe coupled to the system of interest.
The ms has a strong mathematical flavor. Taken alone, this aspect is certainly not a disadvantage. However, at the same time, the manuscript lacks physical context.
The physical noise models based on indirect measurement processes, introduced in Sect. 3, are nothing other than the well-known definition of POVM in terms of the environment that is traced at the end of the (measurement-like) interaction. This is textbook material. I see no progress in this area by examining the formal aspects of this process.
Over the last 30-40 years, numerous measurement schemes have been proposed in the physical and mathematical literature on quantum information and applications, based on the simple von Neumann scheme or the POVM. The advantage of such models is that they are simple. It is easy to understand what a depolarizing of a dephasing channel is, what the physical implications are, and what the meaning of physical quantities such as T1 and T2 is. The noise model proposed in the manuscript is not simple and, in my opinion, does not increase or refine our understanding of a quantum measurement. The authors argue that they obtain noises that have not been analyzed before in the literature and which are physically motivated. I can agree with the first statement (although let me note that it is not difficult to propose models that have never been studied before), but I find it difficult to agree with the second statement: a model can be physically motivated by the experiment or by an overwhelming theoretical evidence, and this is certainly not the case. It is not possible to motivate a model for quantum measurement by examining the results and consequences of a noise model for a probe, unless there is experimental evidence that the probe characteristics are correctly reproduced by the analysis.
Finally, let me note that applying noise models to incompatible measurements is the essence of quantum measurements; the result shown in Fig. 4 is not sufficient to claim novelty.
In conclusion, this manuscript is technically valid, but not very relevant from a physical point of view. It does not increase our understanding of a measurement process. It is probably suitable for a technical journal (possibly mathematics oriented). I do not recommend publication in SciPost.
Report
The manuscript builds a novel and physically motivated noise model for quantum measurements. The noise model is based on fluctuations that may happen when preparing the auxiliary states on a measurement model. The effect of these fluctuations on the POVMs realized on the system is the type of noise under interest, is clearly derived, and is applied to an example case on measurement incompatibility. This leads to the realization that the type of noise used in the manuscript can be more harmful for measurement resources than the typical depolarizing or uniform noise models.
In my view, the manuscript is well written and provides sufficient details to support the claims. The work opens a pathway in an established direction of research and, hence, meets the necessary criterion of the journal. Hence, my recommendation is acceptance.
Author: Faedi Loulidi on 2024-01-31 [id 4295]
(in reply to Report 1 on 2023-09-27)We thank the referee for the careful reading of our manuscript. We fully agree with hers/his comments on the new noise model introduced in our work.
Author: Faedi Loulidi on 2024-01-31 [id 4294]
(in reply to Report 2 on 2024-01-12)We thank the referee for the careful reading of our manuscript. We would like to address, point by point, the comments in the report.
We would like to start by dissipating some potential confusion about the scope of our paper. The goal of our work is to describe a noise model for POVMs which comes from a faulty probe preparation in an indirect measurement scheme. It is clear that the indirect measurement point of view for POVMs is textbook material, and we do not contribute to this direction, nor to foundational questions such as the measurement problem or the collapse of the wavefunction. The purpose of our work is to compare the new noise model to existing noise models in the mathematical physics literature which did not have any physical foundation. We are only concerned with very general noise models, such as the ones described in the introduction, below eq. (1). Clearly, these are mathematical models that are very general and lack physical grounding (such as a description of a Hamiltonian, interaction with the environment, etc). Physical quantities such as T1 and T2 times are inaccessible at this level of generality, and we do not claim that our model would be able to describe and predict such model-dependent quantities. In a future revision of our manuscript we shall address these items, in order to better explain the scope and goals of our work.
The novelty of our noise model comes from the the fact that the effective noisy POVMs are described from the following simple assumptions:
-The process is an indirect measurement consisting of the preparation of a probe, an interaction probe - system, and finally the measurement of the probe
-The probe preparation is faulty, and we assume that some preparation error occurs with a non-zero probability; this error probability is a tunable parameter that will also appear in the effective noisy POVM
-The probe-system interaction is generic, in the sense that we select at random a joint unitary evolution among those which yield the given POVM in the absence of the preparation error.
-Finally, the probe is measured in a fixed basis. We assume that the measurement of the probe is perfect, in the sense that the basis in which the probe is measured is perfectly known.
These very simple, natural, and realistic hypotheses lead to the new effective noise model on POVMs. For these reasons, we call our model “physically motivated”. The price to pay for this level of generality is the lack of microscopic description of the model (system + probe). On the other hand, the new noise model is applicable to very general situations. Moreover, it can be tuned and made more precise using the exact physics of particular models if needed.
We then analyze the new model and compare it to the existing ones. We chose to use the robustness of measurement incompatibility to noise in order to show some new behavior. Our choice is motivated by the importance of incompatibility in quantum theory. Figure 4 in the manuscript shows that the new model behaves differently than the uniform noise and the depolarizing noise, two of the most widely used models in the literature. The presence of the blue region in Figure 4 shows that measurement incompatibility (for the two fixed POVMs we consider in the manuscript) is less robust to the new noise model than to the other two ad-hoc noise models.
In conclusion, we will prepare a new version of the manuscript emphasizing the points above raised by the referee. We are grateful for the observations in the report which will make our work more relevant from the physical perspective and dissipate some possible confusions regarding the scope and the goals of our contributions.