Maroulakos D., Chotorlishvili L., Schulz D., and Berakdar J.

Since the foundational development of quantum mechanics, the measurement process and the wave function collapse have been under discussion [1?15]. One aspect is how to quantify and possibly modify the destructive effect of a certain measurement on a quantum state, an issue that is clearly of importance for quantum information transfer and processing. Here, we consider the ?quantum witness? as the measure invasiveness in a combined quantum system. Our system described by the density operator ?rAB consists of two parties A and B that interact with each other either directly A->B or indirectly through the third quantum system f, i.e., A->f->b. Let us consider two types of measurements: (i) We perform a measurement on f, and then on A, in contrast to measuring A directly. (ii) We conduct a measurement on A and then on B. For Case (i), A interacts with f directly. Measurements done on f have a direct influence on the outcome of measurements done on A; this case is referred to as the local quantum witness. In Case (ii), A and B are interrelated via f; a measurement performed on A affects B through the quantum channel f, a case called the non-local quantum witness. One may wonder about

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