Schmidt decomposition vs singular value decomposition

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Nusc
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What's the difference between Schmidt and Single valued decomposition?

https://www.physicsforums.com/showthread.php?t=323859

How could I find it for

[tex] <br /> |\psi>_{AB} = const( |0>_A|0>_B+ |1>_A|1>_B) + const( |0>_A|1>_B+|1>_A|0>_B)<br /> [/tex]

?
 
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I haven't thought about how to do the Schmidt decomposition of that state vector, but you might find this thread more useful than the one you linked to.