# Neumark dilation and entanglement

1. Aug 24, 2014

### naima

Do you know if there are experiments on particles having interacted which illustrate the Neumark dilation theorem?

2. Aug 28, 2014

### Greg Bernhardt

I'm sorry you are not finding help at the moment. Is there any additional information you can share with us?

3. Aug 29, 2014

### naima

would it be possoble to make a modified EPR experiment
There is a device that create pairs of particles with 2 degrees of freedom
one "1" goes to the left and the other "2" goes to the left.
When "1" is projected on (1 0) "2" is projected on |v1> and
when "1" is projected on (0 1) "2" is projected on |v2> (v1 and v2 are not orthogonal)

PDC produce such pairs with v1 and v2 orthogomal. Could it be possible to adjust the interaction creating pairs so that it would illustrate the Neumark theorem POVM <----- -------> PVM

4. Aug 31, 2014

### naima

Could you explain what is happening during the pre measurement phase?
Suppose we start with a particle in a given state (2 dof) and a meter (apparatus) in a given pointer state (2 possible pointer states)
they interact. It is the pre measurement.
The meter has a natural orthonormal basis.
Is there an axiom which says that pre measurement leads to the Schmidt decomposition based on this basis?

5. Aug 31, 2014

### atyy

I don't think so. I think it depends on the Hamiltonian describing the meter-system interaction.

I have seen it said that [STRIKE]every POVM can be implemented by an appropriate Hamiltonian[/STRIKE], if there are no conservation laws. http://arxiv.org/abs/0810.3536 (section 6.2.1)

Edit: I think what it says is that every measurement model defines an instrument, but it doesn't say that every instrument has a measurement model.

I think with conservation laws there are limitations. http://arxiv.org/abs/1012.4362

Last edited: Aug 31, 2014
6. Oct 8, 2014

### naima

@atyy
The question is about distinguishing non orthogonal states.
The exercise is in
http://www.johnboccio.com/research/quantum/notes/QC10th.pdf [Broken]
Nielsen writes that
non-orthogonal states can’t be reliably distinguished (Box 2.3)
I wrote:
would it be possible to make a modified EPR experiment
There is a device that create pairs of particles with 2 degrees of freedom
one "1" goes to the left and the other "2" goes to the left.
When "1" is projected on (1 0) "2" is projected on |v1> and
when "1" is projected on (0 1) "2" is projected on |v2> (v1 and v2 are not orthogonal)
Does Nielsen says that this is not possible?

Do you see the equivalence between distinguishing non orthogonal
states and cloning possibility?

Last edited by a moderator: May 7, 2017