On the
quantumness of a Hilbert space (pp467-478)
Chris A. Fuchs
doi:
https://doi.org/10.26421/QIC4.6-7-6
Abstracts:
We derive an exact expression for the quantumness of a
Hilbert space (defined in C.A. Fuchs and M. Sasaki, Quant. Info. Comp.
{\bf 3}, 377 (2003)), and show that in composite Hilbert spaces the
signal states must contain at least some entangled states in order to
achieve such a sensitivity. Furthermore, we establish that the
accessible fidelity for symmetric informationally complete signal
ensembles is equal to the quantumness. Though spelling the most trouble
for an eavesdropper because of this, it turns out that the accessible
fidelity is nevertheless easy for her to achieve in this case: Any
measurement consisting of rank-one POVM elements is an optimal
measurement, and the simple procedure of reproducing the projector
associated with the measurement outcome is an optimal output strategy.
Key words:
quantumness, quantum measurement |