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Reassessing the Boundary between Classical and Nonclassical for Individual Quantum Processes

Yujie Zhang1,2,3,*, David Schmid2,†, Yìlè Yīng2,3,‡, and Robert W. Spekkens2

  • *Contact author: yujie4physics@gmail.com
  • †Contact author: dschmid1@pitp.ca
  • ‡Contact author: yying@pitp.ca
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Phys. Rev. X 16, 021050 – Published 4 June, 2026

DOI: https://doi.org/10.1103/vqfz-wzjg

Abstract

There is a received wisdom about where to draw the boundary between classical and nonclassical for various types of quantum processes. For multipartite states, it is the divide between separable and entangled; for channels, the divide between entanglement breaking and not; for sets of measurements, the divide between compatible and incompatible; for assemblages, the divide between unsteerable and steerable. However, these choices have not been motivated by any unified notion of what it means to be classically explainable. One well-motivated notion of classical explainability is the one based on generalized noncontextuality: A set of circuits is classically explainable if a generalized-noncontextual ontological model can realize the statistics they generate. In this work, we show that this notion can be leveraged to define a classical-nonclassical divide for individual quantum processes of arbitrary type. A set of measurements, for example, is judged to be classical if and only if a particular set of circuits—the one obtained by contracting these measurements with every possible quantum state—is classically explainable in the sense just articulated. We begin the task of characterizing where the classical-nonclassical divide lies according to this proposal for a variety of different types of processes. In particular, we show that all of the following are judged to be nonclassical: every entangled state, every set of incompatible measurements, every non-entanglement-breaking channel, and every steerable assemblage. Our proposal differs from the received wisdom, however, insofar as it also judges certain subsets of the complementary classes to be nonclassical, including certain separable states, compatible sets of measurements, entanglement-breaking channels, and unsteerable assemblages. Finally, we prove structure theorems characterizing the classical-nonclassical divide based on whether a process admits of a specific type of frame representation.

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Popular Summary

Determining the precise boundary between classical and nonclassical quantum processes has traditionally relied on disparate criteria such as entanglement for states or incompatibility for measurements. We propose a unified principle for this divide based on generalized noncontextuality, where a process is classical if and only if any circuit leveraging it produces statistics explainable by a noncontextual ontological model. We demonstrate that while this definition recovers standard markers of quantumness, it also reclassifies certain separable states, compatible measurements, and entanglement-breaking channels as intrinsically nonclassical. Furthermore, we prove structure theorems showing that a process is classical only if it admits a specific product dual-frame representation. This framework provides a rigorous, universal method for identifying and certifying genuine quantum resources, offering a more consistent foundation for discovering quantum-over-classical advantages across various information-processing tasks.

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Phys. Rev. X 16, 021050– Published 4 June, 2026
  • Received 18 April 2025
  • Revised 28 January 2026
  • Accepted 14 April 2026
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