Quantum physics

Correlations without parts

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Quantum correlations between the parts of composite systems have long fascinated physicists. There is now compelling evidence that such correlations can also occur in systems in which no parts can be identified. See Letter p.490

Quantum mechanics is arguably the most accurate and successful theory in the history of science. But unlike the case for special relativity, for which two physical principles suffice to derive the whole theory, physicists are still seeking the entire set of underlying principles for quantum mechanics. Recently1,2, they have been trying to understand one of the most intriguing predictions of quantum mechanics: that quantum correlations violate mathematical relationships known as Bell inequalities, which are valid for any local realistic (classical) theory, but that they do so only up to a certain value, whereas more general theories allow violations up to greater values. On page 490 of this issue, Lapkiewicz et al.3 describe an experiment suggesting that a wider perspective, beyond Bell inequalities, is needed to understand why quantum correlations can attain only certain values.

In Bell-inequality experiments (Fig. 1a), tests are performed on two widely separated parts of a composite system. The experimenters then extract the correlations between the outcomes of each of several pairs of tests. In any theory in which the outcomes of these tests are pre-established, the sum of these correlations cannot take a value beyond a certain upper limit. However, quantum mechanics predicts greater values.

Figure 1: Comparing separate and sequential tests.

a, In a Bell experiment, a source emits a pair of particles (a and b), and an observer (Alice) performs one of two possible measurements (1 or 2) on particle a. The measurement has two potential outcomes (either the red light or the blue light flashes). Similarly, a second observer (Bob) performs one of the two measurements on particle b. In this example, the red light flashes as a result of measurement 2 on particle a and the blue light flashes as a result of measurement 1 on particle b. b, In an experiment involving sequential compatible measurements, such as that performed by Lapkiewicz and colleagues3, a source emits particle a on which compatible measurements 2 and 1 are performed sequentially. c, Measurements 1 and 2 are compatible when, for each particle prepared by any source, each measurement always gives the same outcome, no matter how many times the measurements are performed or in which order.

In Bell-inequality experiments, the physical separation between the tests has a crucial role: if it is large enough, then the decision of what test is performed in one location cannot influence the outcome of the test performed in the other location, unless there is an instantaneous influence of the two tests on each other. If the outcomes were pre-established, then instantaneous influences would be required to explain quantum correlations. But this is too high a price to pay, because it is impossible to fit instantaneous influences into any theory in which such influences travel at a finite speed.

Quantum correlations have been experimentally observed in tests that are separated widely enough to prevent any influence that travels at the speed of light4 (Fig. 1a). However, they have been found to have the same values whether the distance between the two experiments is one metre5 or a few micrometres6. What's more, quantum correlations display the same values when two compatible tests are performed on a single system7 (Fig. 1b, c). Therefore, although distance makes quantum correlations more fascinating, it apparently plays no part in the values that quantum correlations can attain.

Why should one care about quantum correlations between compatible sequential tests on the same physical system instead of about Bell experiments? There are two reasons. The first is that, to violate a Bell inequality, a particular type of quantum state is needed; these are called entangled states and cannot be prepared by local operations and classical communication. This might suggest that composite systems and entangled states are essential for quantum correlations. However, before Bell inequalities were introduced, Kochen and Specker8 noticed that quantum mechanics is in conflict with classical physics even for non-composite systems. This conflict can be converted into experimentally testable violations of classical correlation inequalities9 and into experiments10,11 showing that quantum correlations occur for any quantum state — not necessarily just for entangled ones.

The second reason is the one that makes Lapkiewicz and colleagues' experiment3 special. Whereas all previous experiments were performed on systems in which two parts can be defined, the work of Kochen and Specker suggests8 that quantum correlations should occur even in simpler systems, in which no parts can be defined. They identified8 a physical system in which three states can be distinguished (a 'qutrit') as the simplest one in which the predictions of quantum mechanics clash with those of theories in which unperformed experiments have pre-established outcomes. The authors' experiment3 provides compelling evidence for quantum correlations in just such a system.

The experiment3 is conceptually simple: a photon that can travel along three different paths is subjected to several pairs of compatible measurements (such as in Fig. 1b). If the results of these measurements were pre-established and were independent of the compatible measurements, then the correlations would not exceed a certain number. However, the experiment shows a clear violation of this limit, in agreement with the predictions of quantum mechanics.

Lapkiewicz and colleagues' results can still be explained using 'contextual' models, in which the outcome of one measurement depends on the previous (compatible) measurement. But there is no difficulty in converting quantum correlations produced in sequential compatible tests on single systems into correlations between separated systems in which contextual models become 'non-local'12.

The authors' findings are therefore of fundamental importance, because they confirm that quantum correlations also occur in systems in which entanglement, which is supposed to be the most emblematic feature of quantum mechanics, cannot be defined. It seems that Bell experiments, composite systems and entangled states are not enough to provide a complete understanding of the physical principles behind quantum mechanics: quantum correlations exist without them.


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Correspondence to Adán Cabello.

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Cabello, A. Correlations without parts. Nature 474, 456–458 (2011) doi:10.1038/474456a

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