Complementary Quantum Correlations Are Universal for Qubits

Abstract: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.

arXiv:2608.04916 [quant-ph]

(or arXiv:2608.04916v1 [quant-ph] for this version)

https://doi.org/10.48550/arXiv.2608.04916 Focus to learn more arXiv-issued DOI via DataCite (pending registration)

qubit_half_information_exclusion.py

requirements.txt

test_qubit_half_information_exclusion.py

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