Science-II: Structures for Data Representations for Quantum Computing

Science-II: Structures for Data Representations for Quantum Computing and Classical Systems

Introduction

Entanglement is a terribly explained subject and much of it has to do with the plethora of analogies that try to explain it - I will not claim to do any better but I make an attempt to provide an alternative view.

Shrodinger coined the term in 1935.

You can find a really great introduction to the concept of entanglement at the Stanford link:  Quantum Entanglement explained by the Stanford Encyclopedia of Philosophy

That is the best explanation available on the web and draws heavily from Shrodinger's original - you cannot do better.  Mine is not better.  But if that's too long, then, here's mine, a different take.

Let me start with an observation:  all the explanations that you typically find when searching for an explanation of entanglement lead to some sort of statement about the existence of things that you can "see" (or observe or measure) and the concept of the "state" of quantum system, usually particles of some kind.

These explanations fail to address the fact that most folks think in terms of "sets" of objects and "observations" as some form of properties in the set.  Nothing could be further away and more misleading when it comes to quantum systems since quantum systems are not related to sets of objects but are rather related to the possibilities for describing objects relative to you, their observer.  These possibilities are infinite and are described in ways that take those infinities of possibilities into account - they are described by a choice of functions (and that universe of choices by which to choose functions that can describe the objects is itself infinite).  Think of a description like this:  there are an infinite number of ways to write a description for the number "7" - here are a few:
1.  0 + 7 = 7
2.  3 + 4 = 7
3.  1 + 2 + 4 = 7
4.  0 + 0 + 1 + 6 = 7
5.  etc ...

But now I am diving into an area that I will defer so back to entanglement.  Some popular descriptions, as I noted, lead you immediately into trouble because the counter-intuitive nature is difficult while thinking of a quantum system like a classical system (which is thought of like a set of things that you can describe with certitude).  Quantum systems are spaces of inter-relating entities whose futures are created in part by their past interactions and your choice of how and what you wish to observe.  Those choices lead to connected behaviours that Shrodinger called "entangled".

Here are some of the the other popular explanations, for example:

Science Daily Definition of Entanglement

Wikipedia's Definition of Quantum Entanglement

So I offer the following instead:   a quantum system is not a set, but, a weird kind of "flow" or "flows".  Think of air flow - you cannot see it but a flag waves in the wind.  The quantum flows are invisible - in fact, they are so very invisible that even those qualified in the art cannot picture them so whatever I share with you is going to be a hack.  Reading my description in the last few sentences, I am already in despair!  Let me try again:

Another way to think of it is this: imagine two flags, waving in the wind.  Certainly, they will not wave in opposite directions!  Their waviness will in some ways appear to be similar, but, not identical. However, if one flag is waving this way, the other flag might be waving that way, and, there may appear to be a kind of regularity.  In other words, because we have a the wind, blowing in the same direction, and generally with the same forces, both flags wave in a similar, correlated way.  But this is not Quantum. This is Classical. Complicated classical but not quantum.

Quantum entanglement is not like that kind of correlation with the "flows" being a kind of wind of motions and the particles being like the flags.  Quantum entanglement is more like the idea that I wanted to see a flag, so I took a bike ride and saw two flags blowing in the wind *because* I wanted to see a flag and took a bike ride --- yes, I know, this sounds weird.

This example or analogy, which it is not of entanglement, is difficult to picture because it is as if I am a participant in creating the outcome - well, actually, I am.  That is a quantum feature (my being a participant in creating the outcome).

Here's another one:  toss a coin.  It can land heads or tails.  If I toss the coin and it lands "heads" you know that the other side is "tails" that it has landed on. Imagine now two sheets of paper: one has the words "heads" on one and the other has the word "tails".   If I put the papers into two separate envelopes and I ask you to go home with the sealed envelope, you don't know if it has heads or tails written on it.  But, if I call you and tell you that my envelope has "heads" then you never need to open your envelope because you have the information and you can infer that the contents of the envelope is "tails".   Put another way, imagine you have a coin, say a nickel, and I have a coin, say a quarter and we toss them: every single time, without fail, when your nickel lands on "heads", my quarter just so happens to land on "tails" and vice versa: so it is as if they are invisibly connected but not in any way we can see.  If you go home and I go to my home and we repeat the coin tosses, the results are still the same - we can call each other to check on it, after we have tossed the coins and they have landed. Mine lands "heads" and yours is, of course, "tails".  

Quantum entanglement is not like this either, but I am trying. 

Let me try again:  things that you can say get related because of an association or reason might be as disparate as the concept of carrying an umbrella out into sunny skies because the news reported it might rain - this correlation or association between two different things, one of which is observed, you carrying and umbrella, and the other which is hidden, the rain, because the skies are sunny, is like getting closer to the idea of entanglement.

But even this metaphor is not entanglement.

I guess you see where I am going with this.   There is a kind of connection that is like a correlation or association but does not really involve anything other than that some information exists.  How that information is related to the coin toss, or the umbrella and the rain, is not known - only that it is repeatable and regular in how we can, as outsiders, see the outcomes.

The principle that is strange in entanglement is that of "nonlocality".  Imagine our two coins sent with us in opposite directions and the state of one of them is altered (like I turn my quarter to "heads"), the second instantly alters its state (your nickel becomes "tails") in response no matter how far apart the two may be. This physical example is just not realistic but that is what happens at the microscopic level (e.g. photons that are entangled but going in opposite directions).

Albert Einstein he called it "spooky action at a distance" because there was no apparent physical connection underlying the phenomena and no apparent way to explain it.

Some entanglement phenomena are only just emerging such as as association between time and energy:    "Now, physicists are unmasking a more fundamental source for the arrow of time: Energy disperses and objects equilibrate, they say, because of the way elementary particles become intertwined when they interact — a strange effect called “quantum entanglement.” ... “Finally, we can understand why a cup of coffee equilibrates in a room,” said Tony Short, a quantum physicist at Bristol. “Entanglement builds up between the state of the coffee cup and the state of the room.”  - quoted from Time’s Arrow Traced to Quantum Source

So now we come to the really, really tough part of this blog:  how can we represent entanglement?

1.  Conceptual Entanglement - we can look at concepts of entanglement for computer systems by looking at the semantics of concept combinations and their representations.  A good place to start is Quantum Entanglement in Concept Combinations

2. Representating Entanglement as an artifact in a graph structure:  a paper to ideate with is:  Entangled graphs: Bipartite entanglement in multi-qubit systems

3. Entanglement polytopes:  there are geometries that may prove useful as representational structures and the following two papers should prove sufficient to get you started:   Convex polytopes and quantum separability and, the paper here:  Entanglement Polytopes

4.  Hidden Symmetries, Hidden Variable, Knot Topological and representations of entanglements that are not really "quantum" but are quantum inspired or quasi-quantum (since the work of several physicists has shown that there are no hidden variables):   Quantum logic as superbraids of entangled qubit world lines ; Experimental Demonstration of the Topological Phase for Entangled Qubits ; and other references that are simply just way out on the edge (and perhaps a new mathematical model, or physics will be needed to produce a better representation concept for entanglement); and finally (at least on this short list):

5. Using Alternative Probabilistic models such as Quantum Bayesianism to specify models in which entanglement can be represented.

Well, that's all for now, until next time, when we look at Science of Quanta.  What is a quantum of information? Is there a quantum of knowledge? Of wisdom? And how could we represent such things, if it is even possible?