The change of probability

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Two photons income a 50:50 beam splitter from a and b respectly. splitter There are four results. result. If the two photons are identical in their physical properties and indistinguishable, we cannot distinguish between the output states of possibilities 2 and 3, and the probability of possibilities 2 and 3 is 50%.
If they arrive at the splitter simultaneously, as demonstrated in reference 1
|ψf⟩=12√2[(αγ+βδ)(|H⟩1|H⟩2+|V⟩1|V⟩2)⋅i(|c⟩1|c⟩2+|d⟩1|d⟩2)=12√2+(αγ−βδ)(|H⟩1|H⟩2−|V⟩1|V⟩2)⋅i(|c⟩1|c⟩2+|d⟩1|d⟩2)=12√2+(αδ+βγ)(|H⟩1|V⟩2+|V⟩1|H⟩2)⋅i(|c⟩1|c⟩2+|d⟩1|d⟩2)=12√2+(αδ−βγ)(|H⟩1|V⟩2−|H⟩1|V⟩2)⋅(|d⟩1|c⟩2−|c⟩1|d⟩2)]


the probability of 2 and 3 changes from 50% to 18|αδ−βγ|2
In section 3.2.2 of reference 1, which explains the concept of quantum teleportation, the probability of 2 and 3 changes to 25%. Because photon 2 and 3 are entangled and by rewriting the state of photon 1,2 and 3 it is easy to find that the probability of |Ψ−⟩12 is 25%. And we can find in eq(1)) that |Ψ−⟩12means probability of 2 and 3 happens.

Reference

  1. Quantum Teleportation and Multi-photon Entanglement, Jian-Wei Pan
  • Post author: Gong Siqiu
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