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

Abstract

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.