Entanglement of Josephson junctions revisited

The recent experimental evidence for entangled states of two Josephson junction (JJ) qubits seems to support the picture of JJ as a "macroscopic quantum system". On the other hand the interpretation of experimental data strongly depends on the assumed theoretical model. Namely, the qubit states are supposed to be spanned by the orthogonal quantum states of a certain well-separated subsystem. We analyse the possible states of JJ for three models : two-mode Bose-Hubbard model, its large $N$ aproximation called quantum-phase model, and the many-body description within the mean-field approximation (Gross-Pitaevski equation). While the first two models support the picture of JJ being a quantum subsystem of a single degree of freedom, the last approach yields the structure of accessible quantum states which cannot correspond to a qubit. The phenomenology of the mean-field model is briefly discussed and, in particular, the absence of observable entanglement for two coupled JJ's is shown. As the many-body mean-field theory seems to be more fundamental and better suited for the description of critical phenomena than the others, the standard interpretation of the JJ experiments becomes questionable