Complementary Quantum Correlations Are Universal for Qubits

• URL: http://arxiv.org/abs/2608.04916v1
• Date: Wed, 05 Aug 2026 14:39:55 GMT
• Title: Complementary Quantum Correlations Are Universal for Qubits
• Abstract summary: We prove that qubits are protected from overcounting in quantum systems.<n>For every two-qubit state, the correlations observed in two complementary local bases are bounded by premeasurement quantum mutual information.<n>A score above one bit also certifies a quantitative one-way entanglement-distillation rate.
• Score: 3.3788644177253624
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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.

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