If we do optimal state estimation on an unknown qubit, we can recreate a state with fidelity $F_c=2/3$ with respect to the original. Let us define the "quantum information content" $I_q=1-2/3=1/3$ as the "amount of fidelity lost" in this measurement procedure.

If we, instead of measuring, decide to clone the qubit using an optimal cloning machine, we can obtain two imperfect copies with fidelity $F_q=5/6$ each. The "quantum information content" of the two qubits is now $I_q=2 \times (5/6-2/3)=1/3$. Note that the value is the same as in the measurement procedure above.

This conservation of "quantum information content" holds more generally: it is true for symmetric, $N \to M$ system cloning, for systems of any dimensionality (see reference [1]). The question then is: is there a deeper principle or operational justification that can be invoked to justify this curious fidelity balance result? I originally raised this question in my PhD thesis (ref. [2] below, section 4.3.4).

References:

[1] M. Keyl and R. F. Werner. Optimal cloning of pure states, testing single clones. J. Math. Phys., 40(7):3283–3299 (1999).

[2] E. F. Galvão, PhD thesis, http://arxiv.org/abs/quant-ph/0212124

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