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Path predictability and quantum coherence in multi-slit interference

In an asymmetric multislit interference experiment, a quanton is more likely to pass through certain slits than some others. In such a situation one may be able to predict which… Click to show full abstract

In an asymmetric multislit interference experiment, a quanton is more likely to pass through certain slits than some others. In such a situation one may be able to predict which slit a quanton is more likely to go through, even without using any path-detecting device. This allows one to talk of {\em path predictability}. It has been shown earlier that for a two-slit interference, the predictability and fringe visibility are constrained by the inequality $\mathcal{P}^2+\mathcal{V}^2\le 1$. Generalizing this relation to the case of more than two slits is still an unsolved problem. A new definition for predictability for multi-slit interference is introduced. It is shown that this predictability and {\em quantum coherence} follow a duality relation $\mathcal{P}^2+\mathcal{C}^2\le 1$, which saturates for all pure states. For the case of two slits, this relation reduces to the previously known one.

Keywords: predictability; quantum coherence; multi slit; slit interference; predictability quantum; path predictability

Journal Title: Physica Scripta
Year Published: 2019

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