Comment on J.Qin et al., Unconditional and Robust Quantum Metrological Advantage beyond N00N States, PRL 130, 070801 (2023) and J.A. H. Nielsen et.al., Deterministic Quantum Phase Estimation beyond N00N States. PRL 130, 123603 (2023)

In the quiet corner of physics dedicated to measuring the world with extreme precision, scientists have long sought a way to see beyond the limits of classical instruments. This field, known as quantum metrology, asks a simple but profound question: can the strange rules of the quantum world allow us to measure things like time, distance, or magnetic fields with a sharpness that ordinary tools simply cannot match? For years, researchers have believed that special quantum states of light, particularly those involving squeezed vacuum, could offer a decisive edge. The promise is that by manipulating the inherent fuzziness of light, one could extract more information from every single photon than is possible with standard laser beams. If true, this would revolutionize technologies ranging from gravitational wave detection to medical imaging, allowing us to peer deeper into the universe with fewer resources.

However, a recent critique by Zdeněk Hradil and Jaroslav Řeháček challenges the way this potential advantage has been claimed in two high-profile studies published in 2023. These studies reported that their methods using squeezed light provided an "unconditional" quantum advantage, meaning they were superior to classical methods regardless of the situation. The authors of the new critique argue that this conclusion rests on a statistical misunderstanding. They contend that the researchers focused too heavily on the information gained from a single measurement event while ignoring the total cost of the experiment. In the real world, a measurement is not a one-off event; it is a process of gathering many data points to build a reliable picture. The critique asserts that when you account for the total number of photons and the number of times an experiment must be repeated to get a clear answer, the supposed quantum advantage disappears, leaving the performance scaling no better than what classical physics predicts.

The core of the disagreement lies in how scientists count their resources. The 2023 studies calculated their success based on how much information a single detection event could provide, a value known as the Fisher information. They found that for their squeezed light setups, this value was very high, suggesting a massive advantage. Hradil and Řeháček point out that this approach is like judging a runner's speed by looking at a single stride without considering how many strides they need to take to finish the race. In any real measurement, you cannot determine a value with certainty from just one observation. You must repeat the experiment many times to build a statistical estimate. The total resource cost is the product of the number of photons used in each trial and the number of trials required. When the critics apply this full accounting, they find that the squeezed light protocols require so many repetitions to overcome statistical noise that the total number of photons needed to reach a specific precision scales in the same way as classical methods.

The critique highlights a specific flaw in the experimental designs of the papers being reviewed. In one of the studies, the researchers used a very small number of photons per trial, roughly 1.8, but relied on a dataset of 1,000 independent measurements to calculate their final result. In the other, the data was so smooth that it implied an even larger number of repetitions. The critics argue that the "quantum advantage" was inferred solely from the high information content of a single trial, while the massive number of repetitions needed to make that trial useful was ignored. This omission changes the fundamental nature of the claim. While the quantum setup might offer a better numerical factor, it does not change the underlying scaling law. The performance still degrades as the inverse of the total resources, just like a classical system, rather than offering the dramatic improvement that was suggested.

Another significant issue raised is the dependence of these methods on knowing the answer in advance. The sensitivity of the squeezed light protocols is not uniform; it is extremely high only within a very narrow range of the parameter being measured. If the unknown value falls outside this narrow window, the sensitivity drops off rapidly. To make these protocols work in practice, an experimenter would first need to perform a separate, resource-intensive process to locate the correct operating point before the high-precision measurement could begin. The critics compare this to a stopped clock that happens to show the exact time twice a day. While the clock is perfectly accurate at those specific moments, it is useless for telling time unless you already know exactly when those moments occur. Without accounting for the resources needed to find that operating point, the claim of an "unconditional" advantage is misleading.

The authors of the critique are careful to state that their objection is not with the experimental hardware or the physical implementation of the squeezed light, which they acknowledge is well done. Their concern is strictly with the statistical interpretation of the results and the definition of what constitutes a quantum advantage. They argue that the field has become too focused on maximizing a theoretical quantity called the Quantum Fisher Information, treating it as a direct substitute for real-world performance. They warn that this quantity can sometimes suggest infinite precision even when the actual signal is vanishingly small. True metrology, they insist, is about inferring unknown parameters from finite data, a task governed by the laws of statistics as much as by the laws of quantum physics.

Ultimately, the paper calls for a more rigorous and consistent way to define and demonstrate quantum advantages. It suggests that the community needs to move away from shortcuts that equate high theoretical information with practical superiority. Instead, future claims should be backed by consistent resource accounting, explicit construction of the estimators used to find the answer, and statistical validation that reflects the total cost of the experiment. The goal is to ensure that when scientists say they have achieved a quantum advantage, they are describing a genuine, operational improvement that holds up under the full weight of real-world constraints, rather than a theoretical artifact that vanishes when the full picture is considered.