How Do Superposition Preparations Differ for Single vs. Entangled States?

[bhobba]

So if the EPR pair and apparatus is still in superposition in some vectors.. and yet they are in mixed state as the particles entanglement broken. Then it means in a system where particle A, B, C are entangled,

It doesn't follow.

You need to learn what superposition and entanglement is.

Before proceeding can you define entanglement concisely?

Thanks
Bill

 

[Edward Wij]

It doesn't follow.

You need to learn what superposition and entanglement is.

Before proceeding can you define entanglement concisely?

Thanks
Bill

This is precisely why I wrote this thread.. trying to inquire how to differentiate (or mathematically specify) between superposition with and without entanglement. In message #1 I stated:

"What is the difference in the preparation of superposition for the 2 cases where:

1. The system is in either one state.. for example.. one electron in spin up or spin down. Do these interfere?
2. The system is in superposition of two states (for example 2 entangled electrons that is spin up and spin down).

Are they both called Superposition? What specific term distinguish them?"

In your first reply to it and succeeding. You didn't specify what distinguish superposition without and with entanglement. That's what I was asking. Again thanks in advanced.

 

[bhobba]

Are they both called Superposition? What specific term distinguish them?"

This is basic stuff.

I thought about a longish post defining this stuff, but really you need to go through it in a systematic way:
http://quantum.phys.cmu.edu/CQT/index.html

Thanks
Bill

 

[Edward Wij]

This is basic stuff.

I thought about a longish post defining this stuff, but really you need to go through it in a systematic way:
http://quantum.phys.cmu.edu/CQT/index.html

Thanks
Bill

Verbally The dead and alive cat is in superposition but not in entanglement.
But when you have two cats. You can entangle them.
So when you have 2 or more copies in the system, you can entangle them.
I think this is the big difference.
Ey. I just want to visualize the concept.

In decoherence, system and environment can be in superposition. But then system and environment are also entangled. Here I concluded the EPR pair can be entangled with the apparatus because system and environment can be entangled. I wonder what erroneous thinking have I made.

 

[bhobba]

Verbally The dead and alive cat is in superposition but not in entanglement.

The dead and alive cat are never in superposition. The superposition is before the particle detector in the nucleus that emits the particle.

Please read the link I gave.

I will be taking my leave of this thread - you need to become acquainted with basic stuff.

Thanks
Bill

 

[Edward Wij]

The dead and alive cat are never in superposition. The superposition is before the particle detector in the nucleus that emits the particle.

Please read the link I gave.

I will be taking my leave of this thread - you need to become acquainted with basic stuff.

Thanks
Bill

The link includes words like Linear Algebra in Dirac Notation. How do you expect us who know only how to add, subtract, multiply divide to comprehend them.
Hope others would give other easier reference with mostly verbal summaries..
Anyway. I think I understood the difference between superposition with and without entanglement.
Here's the summary:

1. Entanglement only works for subatomic particles in pure state, you can't entangle system already in mixed states.
2. Superposition is when the entanglement for instance takes all positions (say in position observable) .
3. The EPR pair can't be in entanglement with the apparatus because the apparatus is in mixed state.. which destroyed the EPR pair in pure state.

If the above are all correct. Then I understood it and end of thread. Hope someone can verify what I learned so far from the exchanges with Mr. Hobba. Thanks to him I grasped more.

 

[bhobba]

The link includes words like Linear Algebra in Dirac Notation. How do you expect us who know only how to add, subtract, multiply divide to comprehend them.

Some things can be explained in English, but physics is written in the language of math, and you soon run into where it must be used. You have ventured into an area that only can be explained in math. Or at least I can't explain it without math.

1. is basically correct. 2. is wrong and 3. is partially correct.

Thanks
Bill

 

[Nugatory]

The link includes words like Linear Algebra in Dirac Notation. How do you expect us who know only how to add, subtract, multiply divide to comprehend them.
Hope others would give other easier reference with mostly verbal summaries..

I understand why you want a mostly verbal summary, but you're posing questions that cannot be answered without more powerful tools than that.

You're understand adding, subtracting, multiplying, and dividing... But how would you explain these concepts to someone who wanted "a verbal summary" that didn't require knowing about numbers and counting?

 

[vanhees71]

There is no other way to understand quantum theory than to learn the appropriate language in which it can be formulated, and this is the language of (rigged) Hilbert spaces. It is impossible to understand quantum theory otherwise. The reason is simple: We are used to experience with macroscopic bodies, and these behave according to classical physics, which in fact is understood nowadays as an effective description following from the quantum behavior of interacting many-body systems.