Figure 1
Evaluating dynamical processes with process capability measures. The five different capabilities in the dynamics \({\chi }_{{\rm{expt}}}(t)\) of two coupled qubits under a single-qubit depolarizing channel are examined using the capability measures (a) α, (b) β, and (c) capability criterion. Note that the coherence and superposition of the states are defined in the bases \(\{|00\rangle ,|01\rangle ,|10\rangle ,|11\rangle \}\) and \(\{|00\rangle \), \((|00\rangle +|01\rangle )/\sqrt{2}\), \((|00\rangle +|10\rangle )/\sqrt{2}\), \((|00\rangle +|11\rangle )/\sqrt{2}\}\), respectively. For comparison with the capability change over time under qubit depolarization, the insets show the corresponding cases without noise. The depolarizing rate \(\gamma \) affects the curves of \(\alpha \), \(\beta \), and \({F}_{{\rm{expt}}}\). Here we set \(\gamma =0.02\) in the present example. It is worth noting that \({\chi }_{{\rm{expt}}}(t)\) can serve as a controlled-Z (CZ) gate at a proper interaction time36. When setting this gate operation as the target process, the process fidelity \({F}_{{\rm{expt}}}\) varies with time. As indicated in (c), the capability thresholds \({F}_{ {\mathcal I} }\) for superposition, entanglement generation, non-classical dynamics, and coherence preservation are: 0.750, 0.500, 0.467 and 0.250, respectively. Since the CZ gate can be described by incapable processes \({\chi }_{ {\mathcal I} ,{\rm{cre}}}\), and is not a proper target process for coherence creation, such process capability is not considered in (c). Note that, in (a), for coherence preservation, the process is always a capable process, since the depolarization only acts on one of the qubits and another qubit can still preserve coherence of single qubit. According to the definition of the incapable process of coherence preservation (i.e., all the output states must be incoherent states), this process is always capable process of coherence preservation.
