Quantum Process Nonclassicality

We propose a definition of nonclassicality for a single-mode quantum-optical process based on its action on coherent states. If a quantum process transforms a coherent state to a nonclassical state, it is verified to be nonclassical. To identify nonclassical processes, we introduce a representation for quantum processes, called the process-nonclassicality quasiprobability distribution, whose negativities indicate nonclassicality of the process. Using this distribution, we derive a relation for predicting nonclassicality of the output states for a given input state. We experimentally demonstrate our method by considering the single-photon addition as a nonclassical process and predicting nonclassicality of the output state for an input thermal state.

Figure 1

The NQD for the output of the single-photon subtraction process, acting on a squeezed vacuum state with variances $V_x=0.5$ and $V_p=3.0$. We used the filter function (2) with the filter width $w=1.5$. The negativities indicate the nonclassicality of the state.

Figure 2

The PNQD of the cat-generation process, for an input coherent state with $\alpha =2.0$. The filter function is the same as in Fig. 1.

Figure 3

PNQD of the single-photon-addition process with $w=1.2$ at different amplitudes $\alpha =0.00$, $\alpha =0.46$, and $\alpha =1.12$ of input coherent state (from left to right).

Figure 4

PNQD with $w=1.2$ for different input amplitudes $\alpha$ for the single-photon-addition process, evaluated at $\beta =0$. The error bars correspond to one standard deviation. The green solid line represents the theoretical expectation.

Figure 5

Estimated NQD of the output state of the single-photon-addition process for a thermal input state with mean thermal photon number $\overline{n}=0.5$. The standard deviation, shown by the blue (dark) shaded area, is mostly hidden by the linewidth, the systematic error is displayed by the red (gray) shaded area; see Ref. 16.