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The inference of entangled quantum states by recourse to the maximum entropyprinciple is considered in connection with the recently pointed out problem offake inferred entanglement [R. Horodecki, {\it et al.}, Phys. Rev. A {\it 59}(1999) 1799]. We show that there are operators $\hat A$, both diagonal and nondiagonal in the Bell basis, such that when the expectation value $<\hat A>$ istaken as prior information the problem of fake entanglement is not solved byadding a new constraint associated with the mean value of $\hat A^2$ (unlikewhat happens when the partial information is given by the expectation value ofa Bell operator). The fake entanglement generated by the maximum entropyprinciple is also studied quantitatively by comparing the entanglement offormation of the inferred state with that of the original one.Comment: 25 Revtex pages, 5 Postscript figures, submitted to J. Phys. A (Math.  Gen.

On the `fake' inferred entanglement associated with the maximum entropy inference of quantum states