Curator's Take
AI Commentary
This article shows that for any pair of qubits the total correlations can be reliably bounded using just two complementary measurement bases, avoiding full state tomography and sidestepping the over‑counting problem that plagues higher‑dimensional systems. By linking the bound to quantum mutual information, the authors turn a simple correlation table into a quantitative certificate of one‑way entanglement‑distillation rates and even a lower bound on a channel’s quantum capacity—tools that could streamline benchmarking of near‑term hardware and sensing platforms. The result is limited to strictly two‑level systems, but within that trusted regime it offers a practical, experimentally friendly shortcut for assessing both resources and performance.
— Mark Eatherly
Summary
Extracting total correlations from a quantum system usually requires reconstructing its state, whereas many experiments access only a few measurement settings. A possible shortcut is to add the mutual informations obtained from complementary measurements; in dimensions above two, however, this procedure can count the same classical correlation twice. We establish that qubits are protected from such overcounting. For every two-qubit state, the correlations observed in two complementary local bases are bounded by the premeasurement quantum mutual information. The proof traces this protection to binary-entropy curvature on the Bloch ball and combines a qubit information-exclusion tradeoff with data processing under local dephasing. Consequently, two correlation tables give a tomography-free lower bound on total correlation. A score above one bit also certifies a quantitative one-way entanglement-distillation rate; when applied to the Choi state of a qubit channel, the same data lower bound its quantum capacity. The theorem therefore identifies both an operational use of complementarity and the trusted two-dimensional setting in which its correlation accounting is valid.