Neumark dilation and entanglement

  • Context: Graduate 
  • Thread starter Thread starter naima
  • Start date Start date
  • Tags Tags
    Dilation Entanglement
Click For Summary

Discussion Overview

The discussion revolves around the Neumark dilation theorem, its implications for quantum measurements, and potential experimental setups to illustrate these concepts. Participants explore theoretical aspects, propose modified experiments, and question the relationship between measurement models and state distinguishability.

Discussion Character

  • Exploratory
  • Technical explanation
  • Debate/contested
  • Mathematical reasoning

Main Points Raised

  • One participant inquires about experiments demonstrating the Neumark dilation theorem in the context of interacting particles.
  • Another participant suggests a modified EPR experiment involving pairs of particles with two degrees of freedom and questions the feasibility of illustrating the Neumark theorem through this setup.
  • A query is raised regarding the pre-measurement phase and its relation to the Schmidt decomposition, specifically whether there is an axiom that guarantees this outcome based on the meter's orthonormal basis.
  • One participant argues that the outcome of the pre-measurement phase depends on the Hamiltonian governing the meter-system interaction, referencing literature that discusses the implementation of POVMs and the limitations imposed by conservation laws.
  • Another participant references a thread discussing the distinction of non-orthogonal states and questions whether Nielsen's work implies that certain experimental setups are not possible.
  • There is a discussion about the equivalence between distinguishing non-orthogonal states and the cloning problem in quantum mechanics.

Areas of Agreement / Disagreement

Participants express differing views on the implications of the Neumark theorem, the nature of pre-measurement interactions, and the feasibility of distinguishing non-orthogonal states. The discussion remains unresolved with multiple competing perspectives presented.

Contextual Notes

Participants reference specific literature and concepts, indicating a reliance on definitions and theoretical frameworks that may not be universally accepted or agreed upon. The discussion includes assumptions about Hamiltonians and conservation laws that are not fully explored.

naima
Gold Member
Messages
936
Reaction score
54
Do you know if there are experiments on particles having interacted which illustrate the Neumark dilation theorem?
 
Physics news on Phys.org
I'm sorry you are not finding help at the moment. Is there any additional information you can share with us?
 
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
 
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?
 
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:
@atyy
please read RobikShresta thread.
The question is about distinguishing non orthogonal states.
The exercise is in
http://www.johnboccio.com/research/quantum/notes/QC10th.pdf
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:

Similar threads

  • · Replies 8 ·
Replies
8
Views
1K
  • · Replies 1 ·
Replies
1
Views
395
  • · Replies 2 ·
Replies
2
Views
1K
Replies
10
Views
2K
  • · Replies 3 ·
Replies
3
Views
2K
  • · Replies 23 ·
Replies
23
Views
2K
  • · Replies 5 ·
Replies
5
Views
2K
  • · Replies 7 ·
Replies
7
Views
7K
  • · Replies 4 ·
Replies
4
Views
785