Can Before and After Be Superposed?
Over the past century, we have mostly gotten used to the concept of quantum superposition: A particle can exist as a combination of multiple states at once, as famously dramatized by Schrödinger’s cat. But quantum mechanics may allow for an even more mind-boggling type of superposition, called “indefinite causal order,” where the superposition is not between states but between a sequence of events. A few experiments have delivered hints of indefinite causal order, but they all had several “loopholes”—assumptions that leave room for classical explanations.
Now Carla Richter of the University of Vienna and colleagues have devised and performed a new experiment intended to reduce the number of assumptions involved [1]. While some loopholes remain open, the experiment is a useful step toward showing that “we actually have this superposition of orders that cannot be explained classically,” Richter says.
The ideas behind indefinite causal order emerged in the mid-2000s and early 2010s in pioneering work by Lucien Hardy, Giulio Chiribella, Ognyan Oreshkov, and others, says Lee Rozema of the University of Vienna. In this framework, two events can occur in a coherent superposition of one happening before the other and vice versa, so that no single causal order is well-defined—defying the roots of our classical intuition.
The concept evokes baffling thought experiments that echo Schrödinger’s cat. Imagine making a cake. In the classical world, “I mix the ingredients, I bake them, I let the cake cool down, and then I eat it,” says Krister Shalm of the National Institute of Standards and Technology in Colorado, who was not involved in the work. “In quantum mechanics, in some cases, you can still be mixing the ingredients and already be eating [the fully baked cake].”
Experiments testing indefinite causal order typically involve optical setups. Imagine a photon passing through two optical elements, A and B, that modify its state, such as by rotating its polarization. Ordinarily, the photon would encounter A before B or B before A. But if the photon’s path is placed in a quantum superposition—so that along one path it goes through A then B and along another through B then A—then the sequence itself becomes superposed. In that case, it is impossible to say which device acted first: The order of events exists in a quantum superposition.
In the past decade, experimentalists have created optical setups to realize such thought experiments. The approach is similar to that used in Bell tests, foundational experiments designed to rule out local realist explanations of the world. As in those tests, experiments on causal order look for violations of specific mathematical inequalities: If one is violated, the order of the events must be indefinite.
In the new experiment, Richter’s team uses a device called a quantum switch to route a single photon in a superposition of two paths. The paths both contain two polarizers that each act as a quantum gate, performing a different operation (a polarization measurement) on a photon that encounters it. On the two paths, the photon experiences the gates in reverse order.
To reveal causal-order violations, the team entangled the polarization state of each photon that goes through the setup with that of a second photon that does not. One can show that the second photon’s polarization is correlated to the order in which the first photon encounters the quantum gates. Only if a causal-order superposition is present will the polarization states of the two photons be entangled, Rozema says.
Measurements of the second photon’s polarization were indeed consistent with indefinite causal order. However, the researchers concede that the setup isn’t loophole free. For one, it is subject to a “closed lab” loophole: The assumption that only one photon goes through the quantum switch, and that each quantum gate only acts on the photon once. Researchers in the field don’t yet agree on how to close this loophole, Rozema says. What’s more, because the experiment incorporates a Bell test, it inherits the test’s usual locality requirement: The relevant parts of the setup must be separated enough that no signal traveling at light speed could connect them during the measurement. In this case, Shalm says, they are not far enough apart, leaving a “locality” loophole.
Muddying the waters further, physicists still disagree over the fundamental theory describing indefinite causal order. Tein van der Lugt of the Perimeter Institute in Canada, whose theoretical work [2] underpins this experiment, thinks that the field has not satisfactorily defined what constitutes an “event.” He expresses his concerns through an analogy—one he heard from a researcher—with the British tradition of cream tea. If sipping tea and eating a scone overlap in time, it’s unclear what “came first.” He argues that suggested violations of causal order may hinge on a similar ambiguity. If the quantum operations in the setup aren’t sharply localized, the effect may be no more “quantum” than a cream tea, Van der Lugt says. Citing this lack of theoretical clarity, he has recently moved on from the field.
According to Augustin Vanrietvelde of Télécom Paris, some of this conceptual fog can be lifted by viewing indefinite causal order through the lens of a quantum reference frame (QRF), which describes events relative to a quantum system (the photon) rather than to the lab. If one adopts the team’s event definition in a QRF perspective, the measured correlations violate the inequality certifying indefinite causal order, he says. And while the work cannot yet close all loopholes—nor prove that the quantum reference frame exists as a literal physical entity—it stands out because it both sharpens the theoretical description of the scenario and pushes its experimental test to new standards, Vanrietvelde says.
Confirming indefinite causal order without loopholes will likely require many generations of experiments, Shalm says, suggesting that the field’s trajectory may parallel that of Bell tests, which took decades of work to become loophole free. The researchers “are going the right direction,” he says.
–Sophia Chen
Sophia Chen is a freelance science writer based in Columbus, Ohio.
References
- C. M. D. Richter et al., “Toward an experimental device-independent verification of indefinite causal order,” PRX Quantum 7, 010354 (2026).
- T. van der Lugt et al., “Device-independent certification of indefinite causal order in the quantum switch,” Nat. Commun. 14, 5811 (2023).