Schmidt Decomposition: Is It Enough to Find States?

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Discussion Overview

The discussion revolves around the Schmidt decomposition in the context of bipartite quantum systems, specifically addressing whether entanglement is sufficient to determine the existence of Schmidt decomposition for given states.

Discussion Character

  • Exploratory, Conceptual clarification

Main Points Raised

  • One participant questions whether entanglement is sufficient to conclude that given states have Schmidt decomposition.
  • Another participant asserts that Schmidt decomposition is a useful tool for bipartite systems, stating that if a state admits a decomposition with more than one Schmidt coefficient, it indicates that the state is entangled.
  • The same participant clarifies that every bipartite state has a Schmidt decomposition, but only entangled states will have more than one coefficient in the expansion.
  • There are expressions of frustration regarding the lack of responses to initial posts.

Areas of Agreement / Disagreement

Participants express differing levels of engagement, but there is no clear consensus on the initial question regarding the relationship between entanglement and Schmidt decomposition.

Contextual Notes

The discussion does not fully explore the implications of the definitions of entanglement and Schmidt decomposition, nor does it address potential limitations or assumptions underlying the claims made.

ber70
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Is entangle enough to find that given states have Schmidt decomposition?
 
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Why didn't anyone reply me?
 
Hello,
Schmidt decomposition is a usefull tool for bipartite systems: if it admits a decomposition with more than one Schmidt coefficient, then the overall state is an entangled one. So every bipartite state has a Schmidt decomposition, but only if it's entangles there's more than one coefficinet in the expansion.
 
ber70 said:
Why didn't anyone reply me?

are you cute? you waited 6hours only?
 
I'm sorry you waited so long, but I just signed in yesterday and life is so involving that someone sometimes has to wait a little...:-)
 

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