In the southern suburbs of Paris, at CEA Saclay, the mecca of theoretical physics, two theoretical physicists, Barizien and Bancal, have done something of great importance: they have for the first time fully described all the statistical results that quantum entanglement can produce. Note that not partial, not approximation, not experimental guesswork, is "completely certain". For physics, this is to completely draw the boundary line of the originally chaotic and vague jungle of probability.

It's not that no one has done it before, but no one has done it before. Because entanglement is not something that human intuition can handle.

Two photons, no matter how far apart they are, even if one is on Earth and the other is on the Moon, as long as they are entangled, their measurements will show a surprising correlation. This "non-locality" was the part that Einstein was most reluctant to accept, which he called "ghostly telepathy". But it's so real that it has even become a Nobel Prize-level standard action in physics.

The point is: how strong can this correlation be? And how complex can it be?

Entanglement itself is not unusual, and entanglement doesn't have to be maximized to be useful. The real difficulty is that there are many parameters involved in measuring this "post-entanglement" statistical law: the intensity of entanglement, the direction of measurement, the projection method, and even the source mechanism behind it. These factors are intertwined, resulting in a variety of singular statistical correlations in the experimental results. A two-bit system alone can produce an exponential explosion of possibilities.

Previous studies have focused on:最大糾纏態, because it is mathematically symmetrical and relatively "clean" to analyze. But nature doesn't say it has to be that clean. The vast majority of the entangled states used in reality arePartial entanglement, or "imperfect entanglement". That's where the real challenge lies.

Barizien and Bancal simply broke the math knot.

Their key breakthrough point is a kind of mathematical transformation from maximum entanglement to partial entanglement. This transformation is not only beautiful, but also has a clear physical meaning: the statistical structure of the largest known entanglement is used to map all the partial entanglement statistical results.

The difficulty of this process is comparable to the jump from Newtonian mechanics to quantum field theory. It is not an addition or fitting, but a complete reconstruction. This kind of statistical derivation directly involves one of the most magical concepts in quantum information theory:自測（self-testing）。

What do you mean? That is, we do not rely on any trust in the experimental equipment, nor do we need to know what the light source is in advance, and we can deduce the real state of the system only through the statistics of the measurement results.In other words, the entire quantum system is treated as a black box, and its structure and behavior are inferred from the output alone.

This is a complete reversal of the paradigm of traditional physics. In the past, when we talked about measurement, we had to model, set up experiments, and calibrate equipment. Now it's the other way around: test first, then push the model, and the model is likely to be unique. This ability to "model jump out of data" is called "explainability" in the context of AI, and revolution in quantum.

Until this Nature Physics article, only the self-measured results of the maximum entangled state were complete. No one can handle some of the entanglements.

It's ok now.

All two-bit partially entangled states, all self-testable. All the statistical correlations that can be generated can be clearly judged whether they are quantum states or simply impossible to appear under quantum theory. That is, the statistical boundaries of quantum mechanics are clearly drawn.

Some of the statistical results, which seem random, can actually be deduced from themTrue randomness authentication。 For example, some of the Bell experimental data, if it satisfies a certain non-locality, means that the device, regardless of the hardware, is actually generating quantum random numbers. The method of "proving true randomness" from the measurement results is only reliable under such a complete statistical theory.

Secure quantum cryptography systems finally have a hard-core verification method。 Traditional cryptosystems rely on hardware trust. You have to believe that the chip has not been tampered with, and that there is no backdoor to the letter program. Now with the black box statistical certification, even if the vendor is black-hearted, the supply chain is suspicious, and the programmer secretly leaves a debug opening, as long as the measured data meets the standard, then you know that this thing is indeed "working in a quantum way".

And this framework is not just for photons. Electronics, superconducting circuits, ion traps...... As long as it is entangled, it can be thrown in for testing. It is equivalent to establishing a set of general "entangled state quality detector", which can also be adapted to different platforms.

This is the inverse of the typical physical "superstructure oppresses the bottom experiment".

別忘了，這些理論的物理基礎，仍然是 Bell 不等式——那條1950年代提出，卻在2022年才以諾貝爾獎形式被官方蓋章的最強不等式。經典世界下絕不可能成立的統計結果，量子世界里偏偏常見。人類只能承認：現實不是局域性的。

Of course, the Bell test is a necessary condition, not a sufficient condition. It proves "non-classical", but it does not fully describe "which non-classical". This requires more detailed statistical classification, corresponding physical models, and finally inversion reasoning. And that's where Barizien and Bancal got it.

They give a complete decoded dictionary: from "result statistics" to "system state".

That's why this research isn't just about "learning about nature". It is directly related to quantum communication, quantum encryption, quantum computing, and even deeply linked to the "device-independent authentication protocol" of the quantum Internet.

If the quantum network is really rolled out in the future, nodes and devices will not be able to trust all, and the only way is to measure the output. And this complete set of statistical charts will be the only judgment that can give "believe or not".