# POVM measurement

1. Aug 14, 2012

### Demystifier

I need a simple, intuitive, and easy-to-comprehend example of a POVM measurement, which is not a projective measurement. Any suggestions?

2. Aug 14, 2012

### Jazzdude

Take a system which is a tensor factor of a larger system and perform a projective measurement on that larger system with a basis that does not separate in that tensor factor. The subsystem is then undergoing a POVM measurement.

3. Aug 15, 2012

### Demystifier

Jazzdude, it is clear mathematically but not physically. How a measurement in such a mixed basis can be performed in practice? Any simple example?

4. Aug 15, 2012

### Staff: Mentor

Indeed - mathematically I love that explanation - but physically its meaning is unclear. Physically I think the following is better - see page 14-16:
http://arxiv.org/pdf/quant-ph/0205039v1.pdf

Its basically what results when you let a measuring system interact with the system being measured then observe the measuring system.

Also note the cool almost trivial proof of Gleasons Theorem with POVM's.

Thanks
Bill

Last edited: Aug 15, 2012
5. Aug 15, 2012

### Jazzdude

Take a system of two particle with nonzero spin and measure the total spin. Then you can describe the measurement as a POVM measurement for each individual particle.

In quantum information theory one often considers measuring an entangled system in the Bell basis, which also results in a POVM for each subsystem.

Does that make it clearer? If you're asking how you actually perform an experiment to measure those I must admit that I have almost no knowledge about that.

Cheers,
Jazz

6. Aug 15, 2012

### A. Neumaier

The family of coherent states is a POVM of the kind you want, describing a simultaneous but unsharp measurements of position and momentum.

7. Aug 16, 2012

### Demystifier

Thank you all. The example by Neumaier satisfies my criteria the best.