Schmidt Decomposition: Is It Enough to Find States?

  • Context: Graduate 
  • Thread starter Thread starter ber70
  • Start date Start date
  • Tags Tags
    Decomposition
Click For Summary
SUMMARY

Schmidt decomposition is a critical tool for analyzing bipartite quantum systems. It establishes that a bipartite state is entangled if it has more than one Schmidt coefficient in its decomposition. Every bipartite state possesses a Schmidt decomposition, but only entangled states exhibit multiple coefficients. This discussion highlights the importance of understanding Schmidt decomposition in the context of quantum entanglement.

PREREQUISITES
  • Understanding of quantum mechanics principles
  • Familiarity with bipartite quantum systems
  • Knowledge of entanglement and its implications
  • Basic grasp of linear algebra and eigenvalues
NEXT STEPS
  • Research the mathematical foundations of Schmidt decomposition
  • Explore applications of Schmidt decomposition in quantum information theory
  • Study the relationship between entanglement and quantum state measurements
  • Learn about other decomposition methods in quantum mechanics, such as the Singular Value Decomposition (SVD)
USEFUL FOR

Quantum physicists, researchers in quantum information science, and students studying quantum mechanics will benefit from this discussion on Schmidt decomposition and its role in understanding entangled states.

ber70
Messages
47
Reaction score
0
Is entangle enough to find that given states have Schmidt decomposition?
 
Physics news on Phys.org
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...:-)
 

Similar threads

Graduate Schmidt decomposition - How do I find the matrix related to the state?
  • · Replies 1 ·
Replies
1
Views
1K
Undergrad The Schmidt decomposition in QC
  • · Replies 5 ·
Replies
5
Views
2K
Undergrad Schmidt decomposition and entropy of the W state
  • · Replies 1 ·
Replies
1
Views
2K
Undergrad Spectral Decomposition of the State Space
  • · Replies 18 ·
Replies
18
Views
2K
Graduate I have some naive questions about the Reeh-Schlieder theorem
  • · Replies 1 ·
Replies
1
Views
993
High School Direct sum decomposition into orthogonal subspaces
  • · Replies 2 ·
Replies
2
Views
1K
Graduate Are There Only 4 Bell States According to Wikipedia's Definition?
  • · Replies 2 ·
Replies
2
Views
2K
Graduate Is the cluster decomposition equivalent to no phase transitions?
  • · Replies 16 ·
Replies
16
Views
2K
Undergrad Arguments against instantaneous collapse
  • · Replies 1 ·
Replies
1
Views
1K
Graduate What is the Schmidt Rank and Its Role in Measuring Entanglement?
  • · Replies 3 ·
Replies
3
Views
3K