What is a non-orthogonal measurement?

[JK423]

As the title sais... Can someone explain to me what is a non-orthogonal measurement?
I searched the web by i can't find any definition

 

[tiny-tim]

Hi JK423!

What is the context?

 

[cesiumfrog]

what is a non-orthogonal measurement?

Do you have a specific experiment in mind?

Orthogonal means perpendicular and uncoupled, like x and y axes in Cartesian space. But you can also use other axes, for example you could obtain x' and y' by rotating everything a few degrees clockwise.

Say you measure the length of the projection along the x-axis of some typical vector v, and record the result. Now, if you were to measure next the y-axis projection of that vector then you would get another result completely independent from your first one, but if instead you had next measured the x' axis projection then you would expect to get a result very closely (though not quite 100%) interrelated with your first one.

Measurements in QM are often mathematically analogous to projecting a vector onto an axis, the angle between axes corresponding with degrees of correlation.

 

[statespace101]

A good experiment right off hand would be the Aharonov-Bohm effect.

 

[JK423]

Thanks for the answers so far..
I'll explain to you my problem a little bit more analytically.
For example, i know that an orthogonal measurement projects a state |Ψ> onto an eigenstate of the observable we are measuring.
Now I am not sure what a non-orthogonal measurement does...
Of what I've understood (from the notes of Preskill I am studying) when we perform a non orthogonal measurement, |Ψ> is projected onto a state |Ψa> from a set of non-orthogonal state {|Ψa>}. [Like in an orthogonal measurement, |Ψ> is projected onto an (eigen)state from a set of orthogonal states (the rest of eigenstates)]
And there i got a problem. How can the set {|Ψa>} be of non-orthogonal states?
Since we are measuring an observable, then |Ψ> should be projected onto an eigenstate of that observable! So i conclude that |Ψa> is an eigenstate! But how can {|Ψa>} be of non-orthogonal eigenstates??

im confused..

 

[tiny-tim]

Hi JK423!

Does this help … http://en.wikipedia.org/wiki/POVM" ? ​

 

[JK423]

Thanks tiny-tim, but i had looked at it but didnt have the info i needed!
My professor helped me and figured it out..! :)

 

[Neo_Anderson]

Guys: Would it be proper to say that 'non-orthogonal' is synonymous with 'isotropic', and in any context?