Theoretical physicists fully determine the statistics of quantum entanglements

For the first time, theoretical physicists at the Institute of Theoretical Physics (IPHT) in Parisaclei have fully determined the statistics that can be generated by the system using quantum entanglement. This achievement paves the way for a thorough testing procedure for quantum devices.

This study has been published in the journal Nature Physics.

After the advent of transistors, lasers and atomic clocks, the intertwining of quantum objects is similar to photons, electrons, superconducting circuits, and so on, and is at the heart of the second quantum revolution, where quantum communication and quantum computing are visible.

What does it have to do with it? Two objects prepared together in the quantum state (e.g., horizontal or vertically polarized photons) return a memory of their common origin, even if they are moving far apart from each other. When the quantum state of two intertwined objects is measured, the proposed example measures the polarization of the polarization, but a clear correlation is observed between the measurement results.

Measurements according to quantum statistics

What does this correlation depend on? First, the degree of entanglement between two objects may vary depending on the nature of the source of the intertwined quantum object. In the example, horizontally polarized photons may be produced more frequently than vertically polarized photons. Next, you need to make measurement choices, such as selecting the direction in which the polarization will be measured that may affect the outcome.

To generate meaningful quantum correlations, it is actually essential to measure each object using at least two different measurements, each providing at least two potential outcomes.

Therefore, in the simplest experiments that reveal the degree of quantum entanglement, five parameters can affect measurement statistics. The degree of entanglement between the two directions in which the object and both devices perform the measurement. However, generally speaking, quantum physics allows complex systems with varying degrees of freedom, resulting in a variety of correlations.

Extract knowledge from a black box

Quantum correlations have a prominent property, particularly the ability to pass the Bell test. When this occurs, the results of quantum experiments are “non-local” in the sense that they cannot be explained in terms of local hidden variable models that capture an intuitive understanding of correlation. An experimental demonstration of this impressive property was celebrated in 2022 by the Physics Nobel Prize awarded to Alaine’s side, John F. Krauser and Anton Saylinger. However, quantum correlations have multiple tricks.

It can be seen that physical attributes can often be estimated directly from statistics obtained when measuring intertwined quantum states. For example, observed correlations can prove that observed measurements are random. Importantly, this conclusion can be achieved from measurement results alone, without assumptions regarding the operation of quantum devices at hand, which are considered “black boxes.” Ultimately, some quantum statistics have the properties that completely identify physical models describing intertwined objects.

The degree of quantum correlation will be announced

This stunning property, known as “self-test,” plays an important role in device-independent quantum information protocols. These protocols do not rely on any assumptions regarding the proper functioning of the source and measuring device, thus providing unparalleled reliability. So far, we have obtained some self-test results. For example, it is known that all qubit states are self-tested, but all possible self-tests are not yet known. In fact, only self-tests that correspond to the maximally intertwined state of two qubits are fully characterized.

IPHT theoretical physicists Victor Barizien and Jean-Daniel Bancal have demonstrated that it is also possible to accurately and fully describe the statistics obtained when measuring partially intertwined objects.

“A cute but difficult idea to explain was to use my understanding of the maximally intertwined states to explain statistics from the partially intertwined states. We found mathematical transformations that allow for fruitful physical interpretations,” the researchers say.

A complete explanation of quantum statistics was then provided by identifying all correlations that could self-test partially intertwined two-kit states.

A considerable range, basic and applicable

Having complete knowledge of quantum statistics that can be achieved when entanglement is involved has great results. On the one hand, it identifies the limitations of quantum theory itself. In doing so, it bounds the extent of experimental results that can be expected to be observed, provided that nature adheres to the rules of quantum physics. On the other hand, it provides a highly effective testing procedure that can be applied to all types of intertwined objects and measurements, and therefore various types of systems.

In particular, the security of devices using quantum entanglement can be enhanced by testing based on observations made on each instant, rather than on the physical properties of the device that are likely to evolve over time. More generally, new protocols are open for quantum testing, communication, encryption, and calculations.