Phase of |0> when it appears in a product

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Discussion Overview

The discussion revolves around the phase of the vacuum state |0> when it appears in a product, particularly in the context of a beam splitter. Participants explore the implications of the vacuum state and its associated phase in quantum mechanics, focusing on theoretical aspects and interpretations.

Discussion Character

  • Exploratory
  • Technical explanation
  • Debate/contested

Main Points Raised

  • One participant questions whether the phase factor "i" from the vacuum term |0_B> needs to be tracked in calculations involving beam splitters and seeks its physical interpretation.
  • Another participant expresses confusion regarding the notation and the meaning of products of ket vectors, suggesting a lack of clarity in the original post.
  • A later reply clarifies that the reference material does keep track of the vacuum term, implying that there is a precedent for considering the phase in such contexts.

Areas of Agreement / Disagreement

Participants exhibit disagreement regarding the clarity and correctness of the initial state representation, with some confusion about the notation used. However, there is a recognition that the reference cited addresses the concern about the vacuum term.

Contextual Notes

The discussion highlights potential limitations in notation and understanding of quantum state products, as well as the need for clarity in referencing sources. There is an unresolved aspect regarding the physical interpretation of the phase factor associated with the vacuum state.

Swamp Thing
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In a beam splitter with one vacuum input, the output looks like ##\frac{1}{\sqrt 2}(|1_A\rangle +i|0_B \rangle)\frac{1}{\sqrt 2}(-i|1_A\rangle +|0_B \rangle)##.
If there is some further processing, the vacuum ##i|0_B\rangle##, along with the i , could end up multiplied with some non-vacuum term.

Do we need to keep track of that "i" that originates from such a vacuum term? If so, what is the physical interpretation?
 
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Please make it a habit to cite your sources and explain your notation.

The state you have given doesn't make sense to me. Are you really familiar with what a products of ket vectors signifies?
 
Actually, they do keep track of the vac term in that reference so I guess that answers my question.
 

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