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.

中文翻译：

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通过具有均匀和不均匀时间间隔的连续中间测量，对阻尼和驱动量子比特的量子见证

测量可以揭示量子物理学与经典物理学之间的差异。近来，提出了一种量子见证\（W_q \）来表征量子性（Li等人，在Sci Rep 2：885，2012； Kofler and Brukner在Phys Rev A 87：052115，2013）。它建立在无信令及时条件的基础上，并且只有一次中间测量。作为扩展，我们在这里考虑在不同时间进行多次中间测量。我们讨论了阻尼和驱动量子比特的量子。分别考虑了统一的，准周期的和随机的时间间隔序列（TIS）。数值结果表明，当测量次数为N时，\（W_q \）取决于TIS的种类。小于10，而当N较大时，它几乎与TIS的种类无关。此外，对于所有情况，\（W_q \ le W_q ^ {max}（N）=（1- \ frac {1} {2N}）e ^ {-\ gamma \ tau} \），其中\（\ tau \）是进化时间，\（\ gamma \）是移相强度，\（W_q ^ {max}（N）\）是对量子见证相等性的最大违反。