Quantum theory and information

[KipIngram]

I'm trying to get a good feel for quantum information theory, and I'm wondering if this is on the right track:

 

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Consider the simplest possible quantum system (say spin measurements, so there are just two possible outcomes). We can choose to measure spin in any direction, and we'll get "up" or "down." But that quantum system is capable of housing just one quantum bit of information, and by making the measurement against a chosen axis we "use up" that information holding ability. It now "remembers" that it's spin up or down for that axis, and that's the one bit so it can't have any information about a different orthogonal axis.

 

So said another way, by making a measurement we force the limited information retention ability of the system to reflect the result of that measurement. Now if we make another measurement we force the information resources to reflect the new measurement, so it can no longer reflect the old one.

 

In macroscopic systems there's a huge amount of information in the system, so we can extract some without really making much of a difference. The resources can be used to reflect many different things, without conflict.

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That at least feels like it's on the right track, but I'm a noob on this so I thought I'd invite critique.

[studiot]

 

In macroscopic systems there's a huge amount of information in the system,

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Indeed so as the understatement of the year.

 

 

A field with k independent variables has of the order of

 

[math]{\infty ^{k\infty }}[/math]

 

points each of which could hold at least one qbit.

 

Apologies for this notation, but I am following Penrose (road to reality) where the idea is developed (pages 378 - 380) and applied to quantum computers (page 583)

[Mordred]

Lol I love that book

[imatfaal]

...

 

Apologies for this notation, but I am following Penrose (road to reality) where the idea is developed (pages 378 - 380) and applied to quantum computers (page 583)

 

Lol I love that book

I was distinctly underwhelmed - but it was a long time ago. So, StudioT/Mordred, is it worth a retry guys?

 

Sorry for the offtopicness.

[Mordred]

I found it an excellent collection of theories with a basic coverage of each including a helpful mathematical coverage of each. In many ways its akin to "Elements in astrophysics" which I find incredibly useful for similar reasons.

 

Penrose often finds ways to explain mathematical complexity involved in many of the theories he discusses in a manner that makes sense. So yes I find it is a handy reference. It however isn't as good as a textbook dedicated to a particular subject as those textbooks are dedicated to that particular subject.

 

Probably the most useful tool in my repertoire is "Mathematics methods for Physicists"

 

https://www.amazon.com/Mathematical-Methods-Physicists-Seventh-Comprehensive/dp/0123846544

 

It details all the higher mathematics in a well organized model independant manner. That works with all types of physic theories including QM/relativity/group theory etc.

[studiot]

 

I was distinctly underwhelmed - but it was a long time ago. So, StudioT/Mordred, is it worth a retry guys?

 

For books of that size (but several times the cost) I would use that description for the Microsoft Press manuals available with every version of Windows. I'm really glad I don't have to buy them any more.

 

Edited April 25, 2017 by studiot

[KipIngram]

As a follow on to my original question, let's look at another case, say energy levels in an atom. I can't get the information perspective to pan out as nicely here. Yes, the energy levels are discrete, so we're talking about quanta. But in theory there can be any number of them, right? Just plug in N, and get an answer? So that doesn't "restrict" to any particular number of bits of information. So spin looks like a "one bit thing" more strongly than other cases. Spin seems "different" in some way. Anyone have light to shed here?

[studiot]

As a follow on to my original question, let's look at another case, say energy levels in an atom. I can't get the information perspective to pan out as nicely here. Yes, the energy levels are discrete, so we're talking about quanta. But in theory there can be any number of them, right? Just plug in N, and get an answer? So that doesn't "restrict" to any particular number of bits of information. So spin looks like a "one bit thing" more strongly than other cases. Spin seems "different" in some way. Anyone have light to shed here?

 

No there can't be an infinite number of them whilst the particle is in the atom.

 

There is a defined, finite, set of energy levels before any particular electron leaves the electron and the atom becomes an ion.

 

At this point the energy spectrum of the electron becomes continuous, and therefore comprised of an infinitude of levels, although there is some debate as to whether it is actually continuous or made of incredibly finely divided levels.

[KipIngram]

Yes, I was generally familiar with that difference (in atom / out of atom), and had it in mind that that had to do with continuity of the solution (similar to the particle in a box problem, where it's the zero probability boundary conditions at the edges of the box that fix the solutions). I'm just having difficulty seeing that from the "information perspective" as readily as I can see the spin example I cited originally.

 

But your correction for me, specifically, is that you come to an N eventually where you're no longer "in the atom." Thanks - that makes sense.

Edited April 26, 2017 by KipIngram