Quantum entanglement inferred by the principle of maximum nonadditive entropy

The problem of quantum-state inference and the concept of quantum entanglement are studied using a nonadditive measure in the form of the Tsallis entropy indexed by the positive parameter q. The maximum entropy principle associated with this entropy along with its thermodynamic interpretation are discussed in detail for the Einstein-Podolsky-Rosen pair of two spin-$\frac{1}{2}$ particles. Given the data on the Bell-Clauser-Horne-Shimony-Holt observable, the analytic expression is presented for the inferred quantum entangled state. It is shown that for $q>\mathrm{}1,$ indicating the subadditive feature of the Tsallis entropy, the entangled region is small and enlarges as one goes into the superadditive regime where $q<\mathrm{}1.\mathrm{}$ It is also shown that quantum entanglement can be quantified by the generalized (Kullback-Leibler) relative entropy.