A Summary of Which Way Experiments
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If we consider interference and entanglement as the most distinctive mysteries of quantum world, then Which Way (WW) experiments will be at the heart of quantum experiments which dramatically illustrate the differences between classical and quantum conceptions of nature.
The idea of WW experiments could be traced back to the famous double-slit experiment with movable slit proposed by Einstein to show the inconsistency of orthodox interpretation of quantum theory. After that, in his response to the so-called EPR paradox, Bohr gave an account of this experiment based on his interpretation of quantum mechanics. Later, Wootter and Zureck investigated this problem by quantum mathematical formalism. Since then, all the conceptual and experimental problems concerning WW experiments have been analyzed theoretically or experimentally in light of different viewpoints. Generally, two types of patterns should be carefully distinguished in WW experiments: a referent (or integrated) interference pattern which is obtained by the observed positions of the interfering particles on the interference region (e.g., the detector plate in double-slit setup), and mutual interference patterns which are obtained by a hypothetical extraction of the particular observed positions of interfering particles on the interference region when a specific result has been observed on the system in which the WW information is deposited (stored). The mutual interference patterns encompass the referent interference patterns, i.e. the latter can be obtained by the sum over the former patterns. In fact, the visibility of the referent and the mutual interference patterns (the visibility of patterns is equivalent to the manifestation of a wave-like behavior) and the existence of WW information (this is equivalent to the manifestation of a particle-like behavior. The terms "corpuscular-like behavior", "existence of WW information", and "particle-like behavior" are interchangeable and have the same meaning, here) both behave in a complementary manner. This distinct quantum behavior is usually termed as wave-particle duality: Under different experimental conditions, matter behaves more like a wave or more like a particle, but always, in certain ways, like both together. We should, however, remind that the visibility of the integrated interference pattern is contingent upon on how much WW information exists in principle, not on what has been observed on the system in which WW information is deposited. M. Bahrami and A. Shafiee (2009), Postponing the Past: An Operational Analysis of Delayed-Choice Experiments (accepted for publication in Foundations of Physics).
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