Abstract
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. However, for such a complete tomographic reconstruction to work, full knowledge of both input probes and output measurements is required. Such an assumption is not only experimentally demanding, but also logically questionable, as it produces a circular argument in which the characterization of unknown devices appears to require other devices to have been already characterized beforehand. Here, we introduce a method to overcome such limitations present in usual tomographic techniques. We show that, even without any knowledge about the tomographic apparatus, it is still possible to infer the unknown device to a high degree of precision, solely relying on the observed data. This is achieved by employing a criterion that singles out the minimal explanation compatible with the observed data. Our method, that can be seen as a data-driven analog of tomography, is solved analytically and implemented as an algorithm for the learning of qubit channels.
Highlights
We introduce a method to overcome such limitations present in usual tomographic techniques
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
Even without any knowledge about the tomographic apparatus, it is still possible to infer the unknown device to a high degree of precision, solely relying on the observed data
Summary
We derive the theoretical results on which this work is based. We introduce a parametrization for binary conditional probability distributions and discuss its symmetries. We introduce qubit dihedrally-covariant channels and discuss their covariances under unitary and anti-unitary transformations. We derive the set of binary conditional probability distributions which are compatible with any given qubit dihedrally covariant channel. We derive the equivalence classes of qubit dihedrally covariant channels which are data-drivenly indistinguishable
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