Verification of the quantum-domain process using two nonorthogonal states

If a quantum channel or process cannot be described by any measure-and-prepare scheme, we may say the channel is in the quantum domain (QD) since it can transmit quantum correlations. The concept of the QD clarifies the role of the quantum channel in quantum-information theory based on the local operation and classical communication (LOCC) paradigm: The quantum channel is useful only if it cannot be simulated by LOCC. We construct a simple scheme to verify that a given physical process or channel is in the QD by using two nonorthogonal states. We also consider its application for experiments such as the transmission or storage of quantum optical coherent states, single-photon polarization states, and squeezed vacuum states.

Figure 1

(a) Relation between the average fidelity $\overline{F}$ and the classical boundary $F_c$ as a function of the prior probability $p_{+}$. (b) Classical-quantum boundary for the fidelities $a$ and $b$ specified by criterion (30) for $B=0.1$, 0.5, 0.9, and 0.99.