  Every measurement determines a single value as its outcome, and yet quantum
mechanics predicts it only probabilistically. The Kochen-Specker theorem and
Bell's inequality are often considered to reject a realist view but favor a
skeptical view that measuring an observable does not mean ascertaining the
value that it has, but producing the outcome, having only a personal meaning.
However, precise analysis supporting this view is unknown. Here, we show that a
quantum mechanical analysis turns down this view. Supposing that two observers
simultaneously measure the same observable, we can well pose the question as to
whether they always obtain the same outcome, or whether the probability
distributions are the same, but the outcomes are uncorrelated. Contrary to the
widespread view in favor of the second, we shall show that quantum mechanics
predicts that only the first case occurs. We further show that any measurement
establishes a time-like entanglement between the observable to be measured and
the meter after the measurement, which causes the space-like entanglement
between the meters of different observers. We also show that our conclusion
cannot be extended to measurements of so-called `generalized' observables,
suggesting a demand for reconsidering the notion of observables in foundations
of quantum mechanics.
