  Fidelity is a figure of merit widely employed in quantum technology in order
to quantify similarity between quantum states and, in turn, to assess quantum
resources or reconstruction techniques. Fidelities higher than, say, 0.9 or
0.99, are usually considered as a piece of evidence to say that two states are
very close in the Hilbert space. On the other hand, on the basis of several
examples for qubits and continuous variable systems, we show that such high
fidelities may be achieved by pairs of states with considerably different
physical properties, including separable and entangled states or classical and
nonclassical ones. We conclude that fidelity as a tool to assess quantum
resources should be employed with caution, possibly combined with additional
constraints restricting the pool of achievable states, or only as a mere
summary of a full tomographic reconstruction.
