Self-testing of physical theories, or, is quantum theory optimal with respect to some information-processing task?

Abstract

Self-testing usually refers to the task of taking a given set of observed correlations that are assumed to arise via a process that is accurately described by quantum theory, and trying to infer the quantum state and measurements. In other words it is concerned with the question of whether we can tell what quantum black-box devices are doing by looking only at their input-output behaviour and is known to be possible in several cases. Here we introduce a more general question: is it possible to self-test a theory, and, in particular, quantum theory? More precisely, we ask whether within a particular causal structure there are tasks that can only be performed in theories that have the same correlations as quantum mechanics in any scenario. We present a candidate task for such a correlation self-test and analyse it in a range of generalised probabilistic theories (GPTs), showing that none of these perform better than quantum theory. A generalisation of our results showing that all non-quantum GPTs are strictly inferior to quantum mechanics for this task would point to a new way to axiomatise quantum theory, and enable an experimental test that simultaneously rules out such GPTs.

6 pages; v2: close to published version; v3: typos corrected; v4: typo corrected in winning condition of game; v5: small error corrected in Figure 3

References in corpus (7)

• Private Randomness Expansion With Untrusted Devices
• Beyond Bell's Theorem: Correlation Scenarios
• Almost quantum correlations
• Simulating quantum systems using real Hilbert spaces
• Emergence of Quantum Correlations from Non-Locality Swapping
• Couplers for Non-Locality Swapping
• Towards correlation self-testing of quantum theory in the adaptive Clauser-Horne-Shimony-Holt game

Cited by in corpus (18)

• Quantum theory based on real numbers can be experimentally falsified
• Bell nonlocality in networks
• General probabilistic theories: An introduction
• Entanglement swapping and quantum correlations via Elegant Joint Measurements
• Any Physical Theory of Nature Must Be Boundlessly Multipartite Nonlocal
• Hierarchical certification of nonclassical network correlations
• Operational Theories in Phase Space: Toy Model for the Harmonic Oscillator
• Covariance Decomposition as a Universal Limit on Correlations in Networks
• Advantages of multi-copy nonlocality distillation and its application to minimizing communication complexity
• Towards correlation self-testing of quantum theory in the adaptive Clauser-Horne-Shimony-Holt game
• Post-quantum nonlocality in the minimal triangle scenario
• Multi-system measurements in generalized probabilistic theories and their role in information processing
• Two convergent NPA-like hierarchies for the quantum bilocal scenario
• Tsirelson's Inequality for the Precession Protocol is Maximally Violated by Quantum Theory
• Entanglement-swapping in generalised probabilistic theories, and iterated CHSH games
• Experimental genuine quantum nonlocality in the triangle network
• Quantum non-classicality in the simplest causal network
• Intermediate determinism in general probabilistic theories