Can entanglement be detected in a single Bell pair?

In summary, it is not possible to detect entanglement in a single Bell pair through traditional measurements. However, a recent experiment using weak measurements has allowed for the measurement of the Bell parameter for each individual pair. This approach eliminates the need to choose between different measurement bases and shows that the pair still has a significant amount of entanglement after the measurement. While this method has a large uncertainty, it is a breakthrough in being able to evaluate the entire Bell parameter individually for each entangled pair.
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DrChinese
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Can entanglement be detected in a single Bell pair?

The canonical answer is NO, you can only see the entanglement in an ensemble of Bell pairs. For example, you could look at a stream of photon pairs coming from a PDC source. If you apply the CHSH formula (usually presented as an "S" value) on the observed dataset (perhaps consisting of hundreds or thousands of data points), then you might observe S=2.50 for the full ensemble. S>2.00 confirms that entanglement is present. The upper limit (Tsirilson bound) is 2.82.

However, a recent experiment using so-called "weak measurements" does in fact allow S to be measured and presented for each and every Bell pair. A weak measurement is one in which there is only partial collapse* of the wave function. By way of analogy: when a person walks through a door that is 3 meters high by 1 meter wide, a weak measurement of that person's height and width is being performed. You know that person is no more than 3 meters tall by 1 meter wide, but you don't know more precisely than that.

In the quantum laboratory world, most observations are intended to yield high precision. But when a weak measurement is done, you can perform additional tests on a particle and gain additional information. In our example of a person going through a door: suppose after walking through the door, there was scale to measure the person's weight. The weight, coupled with outcome of the previous weak size measurement, might give you a lot more information than can be deduced from the individual measurements alone.

In the experiment, an S value is calculated on each individual pair of over 1,000,000 pairs. See the (partial) plot of those values in Fig. 2. Although there were values of S that did not indicate entanglement, most did. The average S value was -2.79+/-0.18, very close to the theoretical expectation value.

https://arxiv.org/abs/2303.04787
Single-pair measurement of the Bell parameter
Salvatore Virzì, Enrico Rebufello, Francesco Atzori, Alessio Avella, Fabrizio Piacentini, Rudi Lussana, Iris Cusini, Francesca Madonini, Federica Villa, Marco Gramegna, Eliahu Cohen, Ivo Pietro Degiovanni, Marco Genovese (2023)

Abstract: "Bell inequalities are one of the cornerstones of quantum foundations, and fundamental tools for quantum technologies. Recently, the scientific community worldwide has put a lot of effort towards them, which culminated with loophole-free experiments. Nonetheless, none of the experimental tests so far was able to extract information on the full inequality from each entangled pair, since the wave function collapse forbids performing, on the same quantum state, all the measurements needed for evaluating the entire Bell parameter. We present here the first single-pair Bell inequality test, able to obtain a Bell parameter value for every entangled pair detected. This is made possible by exploiting sequential weak measurements, allowing to measure non-commuting observables in sequence on the same state, on each entangled particle. Such an approach not only grants unprecedented measurement capability, but also removes the need to choose between different measurement bases, intrinsically eliminating the freedom-of-choice loophole and stretching the concept of counterfactual-definiteness (since it allows measuring in the otherwise not-chosen bases). We also demonstrate how, after the Bell parameter measurement, the pair under test still presents a noteworthy amount of entanglement, providing evidence of the absence of (complete) wave function collapse and allowing to exploit this quantum resource for further protocols."*I am using "collapse" in the same manner in which the paper's authors use the term. I am not using it in a manner that might favor one QM interpretation over another.
 
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The catch is large uncertainty. As they say in Introduction: "Our result represents a breakthrough application of them, since, for the first time, they allow evaluating the entire Bell parameter individually from each entangled pair detected (although with a large uncertainty, typical of weak measurements)." Fig. 2 illustrates well how large this uncertainty is.
 
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