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The range of a quantum measurement is the set of outcome probability distributions that can be produced by varying the input state. We introduce data-driven inference as a protocol that, given a set of experimental data as a collection of outcome distributions, infers the quantum measurement which is, i) consistent with the data, in the sense that its range contains all the distributions observed, and, ii) maximally noncommittal, in the sense that its range is of minimum volume in the space of outcome distributions. We show that data-driven inference is able to return a unique measurement for any data set if and only if the inference adopts a (hyper)-spherical state space (for example, the classical or the quantum bit). In analogy to informational completeness for quantum tomography, we define observational completeness as the property of any set of states that, when fed into any given measurement, produces a set of outcome distributions allowing for the correct reconstruction of the measurement via data-driven inference. We show that observational completeness is strictly stronger than informational completeness, in the sense that not all informationally complete sets are also observationally complete. Moreover, we show that for systems with a (hyper)-spherical state space, the only observationally complete simplex is the regular one, namely, the symmetric informationally complete set.
Data-driven inference was recently introduced as a protocol that, upon the input of a set of data, outputs a mathematical description for a physical device able to explain the data. The device so inferred is automatically self-consistent, that is, ca
Given a physical device as a black box, one can in principle fully reconstruct its input-output transfer function by repeatedly feeding different input probes through the device and performing different measurements on the corresponding outputs. Howe
Knowledge about data completeness is essentially in data-supported decision making. In this thesis we present a framework for metadata-based assessment of database completeness. We discuss how to express information about data completeness and how to
We train convolutional neural networks to predict whether or not a set of measurements is informationally complete to uniquely reconstruct any given quantum state with no prior information. In addition, we perform fidelity benchmarking based on this
Maximum-likelihood estimation is applied to identification of an unknown quantum mechanical process represented by a ``black box. In contrast to linear reconstruction schemes the proposed approach always yields physically sensible results. Its feasib