Abstract
The double slit experiment provides a clear demarcation between classical and quantum theory, while multi-slit experiments demarcate quantum and higher-order interference theories. In this work we show that these experiments pertain to a broader class of processes, which can be formulated as information-processing tasks, providing a clear cut between classical, quantum and higher-order theories. The tasks involve two parties and communication between them with the goal of winning certain parity games. We show that the order of interference is in one-to-one correspondence with the parity order of these games. Furthermore, we prove the order of interference to be additive under composition of systems both in classical and quantum theory. The latter result can be used as a (semi)device-independent witness of the number of particles in the quantum setting. Finally, we extend our game formulation within the generalized probabilistic framework and prove that tomographic locality implies the additivity of the order of interference under composition. These results shed light on the operational meaning of the order of interference and can be important for the identification of the information-theoretic principles behind second-order interference in quantum theory.
Highlights
As Richard Feynman famously put it, “the double slit experiment is absolutely impossible to explain in any classical way and has in it the heart of quantum mechanics
Sorkin [2] analyzed multi-slit experiments and noticed that quantum mechanics exhibits second-order interference only, meaning that any measurement pattern produced by a quantum system is reducible to the combination of double-slit interferences
In this work we introduced a class of information-theoretic games, which generalize standard multi-slit interference experiments
Summary
As Richard Feynman famously put it, “the double slit experiment is absolutely impossible to explain in any classical way and has in it the heart of quantum mechanics. Sorkin [2] analyzed multi-slit experiments (i.e. generalizations of the double slit experiment to three or more slits) and noticed that quantum mechanics exhibits second-order interference only, meaning that any measurement pattern produced by a quantum system is reducible to the combination of double-slit interferences. Together with an information-theoretic perspective, our findings can be seen in light of paving an alternative way towards understanding the physical principles behind the order of interference of quantum theory: we suspect that an important clue might be provided by the composition of systems and by the tensor-product structure. Our work deepens the connection between interference and information processing which has already been alluded to in various contexts involving two-way communication [14,15,16], information speed [17], quantum acausal processes [18], superposition of orders [19] and directions [20], quantum combs [21], quantum switch [22] and quantum causal models [23]
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