Drawbacks of the use of fidelity to assess quantum resources

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.