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Fidelity is a figure of merit widely employed in quantum technology in orderto quantify similarity between quantum states and, in turn, to assess quantumresources or reconstruction techniques. Fidelities higher than, say, 0.9 or0.99, are usually considered as a piece of evidence to say that two states arevery close in the Hilbert space. On the other hand, on the basis of severalexamples for qubits and continuous variable systems, we show that such highfidelities may be achieved by pairs of states with considerably differentphysical properties, including separable and entangled states or classical andnonclassical ones. We conclude that fidelity as a tool to assess quantumresources should be employed with caution, possibly combined with additionalconstraints restricting the pool of achievable states, or only as a meresummary of a full tomographic reconstruction.

Drawbacks of the use of fidelity to assess quantum resources