A Barandes's Unistochastic Refomulation Applied to Entanglement Swapping

[Morbert]

So, QM(Barandes)=GR?

Or, by definition, is it just as irreconcilable as nonlocal QM like Copenhagen?

QM(Copenhagen)=QM(Barandes)≠GR?

What is GR? General relativity? The correspondence is between unistochastic systems and quantum theory.

That the swap of (2&3) are considered strictly local processes does not restrict the existence of non-local consequences, (1&4).

Under Baradnes's theory of causality, the stochastic processes in entanglement swapping experiments are local throughout. Charles, performing a measurement of any kind on 2 & 3, has no nonlocal influence on 1 & 4.

 

[javisot]

What is GR? General relativity? The correspondence is between unistochastic systems and quantum theory.

Under Baradnes's theory of causality, the stochastic processes in entanglement swapping experiments are local throughout. Charles, performing a measurement of any kind on 2 & 3, has no nonlocal influence on 1 & 4.

QM(Barandes)=QM(Copenhagen)?

 

[Lord Jestocost]

QM(Barandes)=QM(Copenhagen)?

No!
The minimalist ‘Copenhagen’ interpretation doesn't at least assume anything one cannot strictly talk about.

 

[pines-demon]

QM(Barandes)=QM(Copenhagen)?

Mathematically, yes (or at least that's the claim). Interpretationally, very different.

 

[javisot]

No!
The minimalist ‘Copenhagen’ interpretation doesn't at least assume anything one cannot strictly talk about.

Mathematically, yes (or at least that's the claim). Interpretationally, very different.

Barandes claims yes, but I have not been able to verify the veracity of his statements (and by "verify the veracity" I mean checking if all the mathematics of "stochastic-quantum correspondence" is correct). We are talking about different interpretations that must explain the same experimental results.

 

[pines-demon]

@Morbert I am wondering, can you easily recover the usual entanglement result $P(\theta)=\cos^2(\theta/2)$ using Barandes approach?

 

[Morbert]

QM(Barandes)=QM(Copenhagen)?

If you are asking whether Barandes's interpretation is just the Copenhagen interpretation, then no. Instead, Barandes argues a general class of stochastic systems, characterised by a configuration space and a stochastic map, are describable by quantum theories, and hence quantum theories can be interpreted as theories of a general class of stochastic systems.

 

[Morbert]

@Morbert I am wondering, can you easily recover the usual entanglement result $P(\theta)=\cos^2(\theta/2)$ using Barandes approach?

The Bell-inequality-violating correlations would be read from the (undirected) conditional probabilities like $p(a_\theta, t | b_{\theta'}, t)$ where $a_\theta$ and $b_{\theta'}$ are the relevant magnitudes that depend on the system's configuration (Alice, Bob, and their particles, with $\theta$ being Alice's choice of basis and $\theta'$ being Bob's choice of basis). We would arrive at those conditional probabilities with the right stochastic map. So given some initial state $\ket{\Psi}_0 = |\psi\rangle_{12}|\Omega_0\rangle_\mathrm{Alice}|\Omega_0\rangle_\mathrm{Bob}$, we would construct the relevant stochastic map $\Gamma(t)$ where $\Gamma_{\theta\theta',0}(t) = \mathrm{tr}(U^\dagger(t)P_{\theta\theta'} U(t) P_0)$ will reproduce the relevant correlations.

 

[pines-demon]

The Bell-inequality-violating correlations would be read from the (undirected) conditional probabilities like $p(a_\theta, t | b_{\theta'}, t)$ where $a_\theta$ and $b_{\theta'}$ are the relevant magnitudes that depend on the system's configuration (Alice, Bob, and their particles, with $\theta$ being Alice's choice of basis and $\theta'$ being Bob's choice of basis). We would arrive at those conditional probabilities with the right stochastic map. So given some initial state $\ket{\Psi}_0 = |\psi\rangle_{12}|\Omega_0\rangle_\mathrm{Alice}|\Omega_0\rangle_\mathrm{Bob}$, we would construct the relevant stochastic map $\Gamma(t)$ where $\Gamma_{\theta\theta',0}(t) = \mathrm{tr}(U^\dagger(t)P_{\theta\theta'} U(t) P_0)$ will reproduce the relevant correlations.

I kind of get that. But how pragmatic is to derive actual predictions from Barandes’ interpretation compared to the usual way?

 

[Morbert]

I kind of get that. But how pragmatic is to derive actual predictions from Barandes’ interpretation compared to the usual way?

I don't know if there are any uses over and above standard QM yet. Barandes speculates on some possibilities in the timestamp below, but ultimately it is all speculative for now.

[edit] - Fixed timestamp

 

[pines-demon]

I don't know if there are any use over and above standard QM yet. He has remarked that some of his colleagues. Barandes speculates on some possibilities in the timestamp below, but ultimately it is all speculative for now.

[edit] - Fixed timestamp

I know he also said that he is working in a draft of an example calculation, I'm waiting for that...