Quantum witness of a damped and driven qubit by sequential intermediate measurements with uniform and nonuniform time intervals

Measurement can reveal the difference between quantum physics and classical one. Recently, a quantum witness \(W_q\) was proposed to characterize quantumness (Li et al. in Sci Rep 2:885, 2012; Kofler and Brukner in Phys Rev A 87:052115, 2013). It is built upon the no-signaling-in-time condition, and there is only one-time intermediate measurement. As an extension, we consider here multiple intermediate measurements at different moments of time. And we discuss the quantumness of a damped and driven qubit. Uniform, quasiperiodic and random time-interval sequences (TISs) of measurements are considered, respectively. Numerical results show that \(W_q\) depends on the kind of TISs when the number of measurements N is less than 10, while it is almost independent of the kind of TISs when N is larger. Further, \(W_q\le W_q^{max}(N)=(1-\frac{1}{2N}) e^{-\gamma \tau }\) for all cases, where \(\tau \) is the evolution time, \(\gamma \) is the dephasing intensity, and \(W_q^{max}(N)\) is the maximum violation of the quantum witness equality.