
Entanglement Made Simple - beefman
https://www.quantamagazine.org/20160428-entanglement-made-simple/
======
biswaroop
I always understand entanglement as 'cannot be factored'. It's really just
that mathematical and simple.

Say there are particles a and b that can be in states 1 or 2

entangled: a1 * b2 - a2 * b1, vs not entangled: (a1+a2)*(b1+b2)

So, when you apply a measurement operator on the state of particle a, you know
something about particle b in the entangled case.

Schrodinger said: "the best possible knowledge of the whole doesn't
necessarily include the best possible knowledge of the parts." An entangled
state should be treated as a whole, and not a sum of parts, kind of like how a
book is treated as a continuous story, not a sum of letters.

~~~
EliRivers
"So, when you apply a measurement operator on the state of particle a, you
know something about particle b in the entangled case."

You do now know something about particle b, but your explanation suggests that
information existed all along.

~~~
biswaroop
The quantum information did exist all along; it just 'leaked' into the
environment through a process known as decoherence:
[https://en.wikipedia.org/wiki/Quantum_decoherence](https://en.wikipedia.org/wiki/Quantum_decoherence)

This is why I object to classical analogies using envelopes and cards and
pennies that end with "Yeah QM is strange". It's really a fundamental
physical/mathematical effect, and it's much less intuitive if you make a
mapping to objects in a classical world. I often feel conceptual maps to
information worlds (like books and the internet) are more intuitive.

------
deciplex
I'm not sure trying to instill an "intuitive" sense of quantum mechanics by
appealing to classical principles in this way is such a great idea. The
example of entanglement given here implies that each system was a circle or a
square "all along" i.e. from the moment of being entangled. That's not
actually how it works, and thinking about it that way will lead to
misunderstandings later on, should you try to study QM more deeply. You will
have to unlearn the lesson taught here.

It also leaves you unequipped to reason about quantum computing, by the way.

Also:

> _1\. A property that is not measured need not exist._

> _2\. Measurement is an active process that alters the system being
> measured._

These are both misleading enough that they can probably just be called 'wrong'
as well. We shouldn't assign mysterious properties to "measurement" as though
it's some magical thing that just makes quantum mechanics happen. Just call it
what it is: entangling the state of your brain with the results of an
experiment. That conveniently also provides for a good jumping off point into
Many Worlds / Relative-State Formulation of QM.

~~~
millstone
Describing measurement as "entangling your brain" is a particular viewpoint
that is not widely accepted. Most physicists would agree that the LHC's
particle collision data constitute measurements, even though most of those
results have never been looked at by a human.

Measurement is at its most mysterious in the MW interpretation, because
measurements are probabilistic and probabilities are hard to get out of a
purely deterministic theory like MW.

~~~
deciplex
It's not clear what point you're trying to argue. Yes, the particle collision
data constitutes a measurement in the sense that it is entangled with whatever
medium the data is being stored on (and, in practice, a while lot else), even
if a human hasn't looked at it yet. Measurement as we usually mean it when
talking about this stuff in the context of QM means a human looking at a
thing, but sure that need not always be the case. I mean if you want to split
hairs we can go back and forth all day, but that doesn't strike me as an
interesting or enlightening avenue of discussion.

------
skc
Every time I read anything on how wierd quantum mechanics is I wonder how
theoretical physicists can stay sane.

It's all so bizarre that I don't see how anyone can look that deeply into it
and not come away thinking our entire existence is one big pointless hoax.

~~~
stared
It is not bizarre; it is being presented as such, though. The actual
mathematics of quantum mechanics is simple (vectors, matrices). What is
confusing is:

\- trying to describe quantum mechanics without mathematics (since we have no
direct intuition/experience, many analogies do not hold),

\- inventing some profound philosophy to describe facts.

For example, my entry on that:
[https://johncarlosbaez.wordpress.com/2015/03/13/quantum-
supe...](https://johncarlosbaez.wordpress.com/2015/03/13/quantum-
superposition/) (not entanglement, but - an electron being in two places at
once).

[Full disclaimer: I am an ex theoretical physicist. I don't claim I am sane,
though.]

~~~
tim333
It's not bizarre if you skip the tricky bits like how does it work, why don't
the equations work for gravity, are there many worlds and so on.

------
Ruud-v-A
Here’s an analogy: I put a red card in one envelope, and a blue card in a
different envelope. I send one envelope to Alice (but I don’t say which one)
and one to Bob. Alice and Bob could be on opposite sides of the planet. When
Alice opens her envelope, she knows which colour she has, but she also
instantly knows which colour Bob has -- without communication with Bob. Bob
might not even have opened his envelope yet. There is no faster than light
communication or magic going on.

~~~
EliRivers
This analogy is fundamentally misleading. In this analogy, the blue card was
always blue in the envelope, and the red card was always red. In this analogy,
this information was set right from the start. It's really misleading.

~~~
adekok
It's an analogy.

The weirdness of QM comes from the following, slightly more complicated,
situation.

You have two cards, a red one and a blue one. You also have two envelopes.
Without looking at anything, you put one card in each envelope. You label
them, and send one each to Alice and Bob.

Now, we know for sure that when Alice opens her envelope and looks at the
card, we immediately know which card Bob has. There is no information being
exchanged, so Alice knows what card Bob has immediately when she opens her
envelope.

The weirdness of QM comes from looking at the _intermediate_ states. i.e. the
states _before_ Alice opens her envelope. There are (waving wands) ways to
tell what the intermediate states _could_ be, by varying certain (QM) magical
properties of the experiment.

The weirdness of QM is this. _Every single idea you have about the
intermediate state is wrong_.

What do I mean by that?

You could say there are "hidden variables". i.e. one envelope "really has" a
red card in it, and the other envelope "really has" a blue card in it. This
interpretation is _wrong_.

Every experiment shows that the envelopes are in a "superposition" of states.
That is, the envelopes don't contain either a red card or a blue card. They
carry... something... that is maybe red and maybe blue.

That seems strange, but OK. What happens when Alice opens her envelope?

When Alice opens her envelope, the card which is "maybe blue, maybe red"
suddenly becomes either 100% blue, or 100% red.

The weird part is the next step.

When Alice opens her envelope, Bob's card _immediately_ becomes the opposite
color. This happens _no matter how far away Bob is from Alice_.

So is information traveling faster than the speed of light? No. We knew
Alice's card was red or blue, so Bob's card must have been blue or red. Lo and
behold, Bob's card turns out to be one of those colors.

And yes, Bob's card _really is_ in an indeterminate state prior to Alice
opening her envelope. And once Alice opens her envelope, Bob's card _really
is_ 100% either red or blue.

The confusion comes from what is _really_ happening behind the scenes. i.e.
What is the _real_ explanation?

The current QM research shows that the answer is "Uh... right... we're not
actually sure."

Somehow the two cards are connected (QM people say "entangled"), because when
you look at one, the other immediately "decides" (?) what color it is. But
there's no information being passed between the cards. There's nothing
exchanged between the cards. Yet somehow Bob's card "knows" that Alice has
looked at her card.

This is profoundly strange and confusing. No one has any idea what's going on.
Physicists have many theories, but it's difficult to either prove or disprove
most of them. That takes time, money, expertise, etc.

So we're left with "QM is strange". As Richard Feynman said, "QM is not only
stranger than you can imagine, it's stranger than you can possibly imagine."

~~~
danbruc
_But there 's no information being passed between the cards._

I am not sure that this is the correct or best way to describe it. That
looking at the cards does not allow exchanging any information between Alice
and Bob does not necessarily imply that the process of determining the colors
of the cards does not involve any information exchange. It seems almost
necessary that an information exchange happens between the two cards, after
all they have to acquire different colors and they have no definite color
before looking at them. That this process can not be exploited by Alice and
Bob to exchange any information is a wholly different issue.

~~~
adekok
> I am not sure that this is the correct or best way to describe it.

That's how physicists describe it. So it is the best way.

The thing to remember is that information (in physics) means "particles". The
screen gives your eyes information in the form of photons.

In the case of QM entanglement, _nothing_ is exchanged. So no information is
exchanged.

> It seems almost necessary that an information exchange happens between the
> two cards, after all they have to acquire different colors and they have no
> definite color before looking at them.

That's the issue with QM. You would _like_ to think that something happens.
But as I said, whatever _really_ happens is different than what you think.

~~~
danbruc
_That 's how physicists describe it. So it is the best way._

I am not sure that this is correct. I think the usual statement is that it
does not allow Alice and Bob to exchange information, not that no information
exchange is involved. When Alice looks at her card and sees that it is red
something happens, i.e. red as a possible colors for Bob's card is eliminated.
The wave function collapses if you want to use that picture. The state of
Bob's cards changes instantly from maybe red or maybe blue to definitely blue.
One can now argue whether that change should be called information or whether
the term information should be reserved for things that can be exploited by
Alice and Bob but that does not change the fact that a non-local instantaneous
effect changed the state of Bob's card.

 _The thing to remember is that information (in physics) means "particles"._

That is pretty vague and might or might not be true. Do you mean every
information exchanges between two spatially separated parties necessarily
requires the exchange of (real) particles?

 _That 's the issue with QM. You would like to think that something happens._

Something happens, the wave function changes.

~~~
adekok
> I am not sure that this is correct.

<sigh> So you're smarter than every physicist alive.

Well... no.

> One can now argue whether that change should be called information ...

No, you can't. You're using colloquial English to reason about physics. This
is wrong. Physicists have a very specific definition for "information" (as I
already said, and you ignored). And in this case, no information is exchanged.

> That is pretty vague and might or might not be true.

As the published nuclear physicist in the argument... yes, yes, it's true.

> Do you mean every information exchanges between two spatially separated
> parties necessarily requires the exchange of (real) particles?

Yes.

~~~
danbruc
_< sigh> So you're smarter than every physicist alive.

Well... no._

The usual statement is that entanglement can not be used to exchange
information between spatially separated observers, right? I totally agree with
that. But what about the wave function? If the wave function is spatially
extended, then the change of the wave function has to propagate through space
if one assumes that the change is caused by a local measurement. And the wave
function contains the information that fully describes the state of the system
but one can not learn the wave function in general because some operators are
not commutative. Nonetheless a change of the wave function means a change of
the information describing the system whether an observer can detect that
change or not. That are of course two different things, the information
describing the state of the system and the information an observer can learn
about the state of the system, but I see no conflict here.

 _No, you can 't. You're using colloquial English to reason about physics.
This is wrong. Physicists have a very specific definition for "information"
(as I already said, and you ignored). And in this case, no information is
exchanged._

If I measure a spin without prior knowledge of its state, I obtain one bit of
information, I guess that is the sense in which you want to understand
information, right? If I repeat the experiment with identical preparation over
and over again, then I can learn the wave function, maybe 30 % up, 70 % down.
If Alice and Bob do this with their entangled cards, then Bob can decide
between the case that Alice saw a red card in which case he will always see
his card blue and the case that Alice did not look at her card in which case
he will see his card as randomly red or blue. When Alice looks at her card she
must of course perform a post selection to get rid of the pairs where she saw
her card as blue.

I hope you notice that I am not trying to argue that you are wrong, I am just
trying to understand what you say, especially why one would consider the
result of a measurement as information but not consider the wave function as
information.

~~~
adekok
> But what about the wave function?

Looking at the wave function changes nothing. It's all the same physics, and
all the same concepts. You can't get different behavior from the physical
system by "looking at the wave function" instead of looking at the particles.

> If the wave function is spatially extended, then the change of the wave
> function has to propagate through space

... via _real particles_. Which can't go faster than the speed of light.

> And the wave function contains the information that fully describes the
> state of the system but one can not learn the wave function in general
> because some operators are not commutative.

That... doesn't make any sense from a physics point of view.

You're trying to understand which is good. But you're mangling the concepts.

> If I measure a spin without prior knowledge of its state, I obtain one bit
> of information, I guess that is the sense in which you want to understand
> information, right? If I repeat the experiment with identical preparation
> over and over again, then I can learn the wave function, maybe 30 % up, 70 %
> down

No. You're learning the _probability distribution_ of the wave function. i.e
the _statistical_ distribution of the wave function, taken over many
measurements.

> If Alice and Bob do this with their entangled cards,

... they learn that 50% of the cards are blue, and 50% of the cards are red.
_Which they already knew_.

> ... Bob can decide between the case that Alice saw a red card in which case
> he will always see his card blue and the case that Alice did not look at her
> card in which case he will see his card as randomly red or blue

I'm not even sure what that means. It's based on a misunderstanding of the
underlying concepts, so the sentence doesn't really make sense to me.

> I am just trying to understand what you say, especially why one would
> consider the result of a measurement as information but not consider the
> wave function as information.

I never said that.

The wave function is a probability distribution.

Information is exchanged via real particles.

You can learn new information through measurements... but not when the
underlying measurements are random. i.e. with entangled particles, all you
measure is that (in this case) half of the cards are red, and half are blue.
Which you already knew.

Since you already knew that half of the cards are red and half are blue, the
measurements give you no new information.

The concepts are really quite simple, once you throw away your "common sense"
understanding of what is going on.

~~~
danbruc
_Looking at the wave function changes nothing. It 's all the same physics, and
all the same concepts. You can't get different behavior from the physical
system by "looking at the wave function" instead of looking at the particles._

Alice hands Bob a particle that is either spin up or a superposition of spin
up and spin down. Bob can not distinguish those two cases with a measurement.
But if Bob would know the wave function he could tell the difference and Bob
could learn the wave function be repeating the experiment many times. So there
is a difference between looking at the outcome of a measurement and looking at
the wave function.

 _... via real particles. Which can 't go faster than the speed of light._

If Alice measures her particle of an entangled pair the wave function of Bobs
particle will change without any particle transporting any information from
Alice to Bob. Bob is unable to detect that change with a local measurement but
the wave function changed and no particle has been exchanged.

 _That... doesn 't make any sense from a physics point of view. You're trying
to understand which is good. But you're mangling the concepts._

What is wrong with that? The wave function fully describes the state of a
system but you can not learn that state in general because you would have to
perform several different measurements and those measurements do not commute
in general and change the state to an eigenstate of the measured observable.
Only in an experimental setup with repeated measurements on identically
prepared systems can you learn the wave function of the system.

 _No. You 're learning the probability distribution of the wave function. i.e
the statistical distribution of the wave function, taken over many
measurements._

No, I said identically prepared systems, so the wave functions are identical
in every run of the experiment. I then obtain a distribution of the
eigenstates of the operator by repeating the experiment and that determines
the wave function up to the phase.

 _I 'm not even sure what that means. It's based on a misunderstanding of the
underlying concepts, so the sentence doesn't really make sense to me._

Alice prepares a set of entangled particle pairs. On two thirds of the sets
she measures her particle and sorts them by outcome. Now Alice has three sets,
unmeasured, measured up and measured down. Bob can determine which set is
which by measuring his particles, he gets 50/50 up and down, 100 % down and
100 % up respectively.

 _I never said that._

You did or at least I understood it that way. You say that information is what
an observer can learn about the state of a system by performing measurements
but there is also the information describing the state of the system, the wave
function, which is not necessarily accessible to an observer.

 _The wave function is a probability distribution._

It is not, it is a description of the state of the system. You can obtain a
probability distribution of eigenstates by repeatedly performing measurements
on identical wave functions and that distribution is determined by the
magnitude of the amplitude of the wave function but the wave function itself
is not a probability distribution.

 _You can learn new information through measurements... but not when the
underlying measurements are random. i.e. with entangled particles, all you
measure is that (in this case) half of the cards are red, and half are blue.
Which you already knew.

Since you already knew that half of the cards are red and half are blue, the
measurements give you no new information._

I did not dispute that, observers obtain information about the state of a
system by performing measurements, but that is not the same as the information
describing the state of the system. The later is the truth, the former is what
an observer knows about the truth.

~~~
adekok
Let's back up.

You're using colloquial English to reason about physics. This is wrong.
Physicists have _very_ specific definitions of the terms they use. Which are
sort of similar to the common ones, but differ in key points. Those key points
are what you're getting hung up on. And it's difficult to explain the
differences without explaining all pf physics.

On top of that, you've disagreed with the common definitions used by
physicists "I'm not sure that's correct". Well, it is. If you think that's
wrong, you either think you're smarter than all physicists alive, or you're
wrong. Pick one.

> ... But if Bob would know the wave function he could tell the difference ...

No. No. A thousand times no.

It just doesn't work like that.

> If Alice measures her particle of an entangled pair the wave function of
> Bobs particle will change without any particle transporting any information
> from Alice to Bob. Bob is unable to detect that change with a local
> measurement but the wave function changed and no particle has been
> exchanged.

That is a bunch of pseudo-physics words put together in a sentence.

>> You're trying to understand which is good. But you're mangling the
concepts. > What is wrong with that?

Everything. If you're not using the correct terms in the correct way, you
might as well be putting random words together in a sentence.

>> No. You're learning the probability distribution of the wave function. i.e
the statistical distribution of the wave function, taken over many
measurements. > No, I said identically prepared systems, so the wave functions
are identical in every run of the experiment.

So... you know better than the nuclear physicist.

This should set off alarm bells that you either don't understand the topic, or
you don't care to understand it.

> You did or at least I understood it that way. You say that information is
> what an observer can learn about the state of a system by performing
> measurements but there is also the information describing the state of the
> system, the wave function, which is not necessarily accessible to an
> observer.

<sigh> The observer can do multiple measurements to determine the wave
function.

>> The wave function is a probability distribution. > It is not, it is a
description of the state of the system.

Again, you're arguing with the nuclear physicist.

The probability distribution _is_ a description of the system.

>> Since you already knew that half of the cards are red and half are blue,
the measurements give you no new information. > I did not dispute that,
observers obtain information about the state of a system by performing
measurements,

Yes.

> but that is not the same as the information describing the state of the
> system. The later is the truth, the former is what an observer knows about
> the truth.

<sigh> I'm trying to educate you on physics, and you're arguing pseudo-
philosophical metaphysics.

Please stop. Your understanding of the terms is largely wrong. As a result,
your arguments are based on falsities, and therefore also wrong.

Please go read a popular book about QM before discussing this with anyone.

And stop arguing with the nuclear physicist. This is one situation where I can
appeal to authority without it being a logical fallacy. I've explained
repeatedly why you're wrong. You don't seem to understand.

~~~
danbruc
Unfortunately I have not enough time for a full reply right now, but I will
come back over the weekend.

Wave function and probability distribution. You repeatedly insisted on precise
language, that is why I objected your statement that the wave function is a
probability distribution. And I still do, nuclear physicist or not. A wave
function is complex-valued, a probability distribution is usually defined by a
real-valued probability density function or a real-valued cumulative
distribution function. The state 1/sqrt(2)(|0> \+ |1>) has probability
amplitudes of magnitude 1/sqrt(2) for both states, the probability
distribution you obtain when you repeatedly measure particles in that state
has probability 1/2 for both states, the square of the magnitude of the
amplitude. The wave function certainly defines a probability distribution but
it is not itself one.

 _< sigh> I'm trying to educate you on physics, and you're arguing pseudo-
philosophical metaphysics. Please stop. Your understanding of the terms is
largely wrong. As a result, your arguments are based on falsities, and
therefore also wrong. Please go read a popular book about QM before discussing
this with anyone. And stop arguing with the nuclear physicist. This is one
situation where I can appeal to authority without it being a logical fallacy.
I've explained repeatedly why you're wrong. You don't seem to understand._

I haven't read everything again but most of your responses, especially in your
last comment, simply state that I am wrong without pointing out why or
providing a supposedly correct point of view. It is of course not you job to
teach me physics, but simply stating that I am wrong is only of limited help
to overcome misunderstandings. Besides that we are discussing a topic that has
not been definitely settled and where there is disagreement even among
professional physicists, so maybe we should not be too surprised about a
certain amount of disagreement.

I would very much appreciate if we could continue this discussion a bit once I
had time for a full reply - and I agree, we have to back up quite a bit, the
discussion got fragmented pretty quickly - but I won't blame you if you
declare me a lost case.

------
tim333
The author "makes it simple" by using a crappy get out for explaining the
seeming faster than light influence in quantum entanglement:

>This “spooky action at a distance,” as Einstein called it, might seem to
require transmission of information — in this case, information about what
measurement was performed — at a rate faster than the speed of light.

>But does it? Until I know the result you obtained, I don’t know what to
expect. I gain useful information when I learn the result you’ve measured, not
at the moment you measure it. And any message revealing the result you
measured must be transmitted in some concrete physical way, slower
(presumably) than the speed of light.

The thing is when the results are obtained you can write them down or similar.
Unless you are presuming the written results and other records change as you
mail them to each other you are left with the faster than light type paradox.
I'm with Einstein on that one in that something odd is happening.

My guess is that quantum mechanics is the fundamental nature of the universe
and the appearance of space and time are a resulting epiphenomenon. As a
result of that the particles appear far apart but are in some ways are still
connected.

~~~
pwendelboe
As I understand it though, because the result is random you can't actually
transmit meaningful information faster than light. You can know what the other
measurement was but because it was random it's rather useless information. But
I don't know maybe I have it wrong...

------
cousin_it
> _The interesting effects, which EPR considered paradoxical, arise when we
> make measurements of both members of the pair. When we measure both members
> for color, or both members for shape, we find that the results always agree.
> Thus if we find that one is red, and later measure the color of the other,
> we will discover that it too is red, and so forth. On the other hand, if we
> measure the shape of one, and then the color of the other, there is no
> correlation. Thus if the first is square, the second is equally likely to be
> red or to be blue._

That's not paradoxical, that's just two objects with the same random shape and
the same random color. Quantum entanglement is stranger than that, it can't be
explained by hidden correlated information about both objects.

Here's an example of quantum entanglement. Imagine that Alice and Bob live far
from each other and can't communicate. There are three possible yes/no
questions you can ask them, but each person can only answer one question.
These facts are known:

1) If you ask Alice and Bob the same question, they always give opposite
answers.

2) If you ask Alice question 1 and ask Bob question 2, the probability that
both will say yes is 5%.

3) If you ask Alice question 2 and ask Bob question 3, the probability that
both will say yes is 5%.

4) If you ask Alice question 1 and ask Bob question 3, the probability that
both will say yes is 20%.

Under classical assumptions, there's no way for Alice and Bob to prepare a
strategy beforehand that would lead to such probabilities. The reason is that
case 4 is completely covered by cases 2 and 3, but has higher probability than
the two of them combined. Here's a proof:

    
    
        (4)
        => A1Y and B3Y
        => A1Y and B3Y and (A2N or A2Y)                    // tautology
        => A1Y and B3Y and (B2Y or A2Y)                    // by (1)
        => (A1Y and B2Y and B3Y) or (A1Y and A2Y and B3Y)  // logical operations
        => (A1Y and B2Y) or (A2Y and B3Y)                  // logical operations
        => (2) or (3)
    

Now, as strange as it sounds, in a quantum world Alice and Bob can defeat that
proof and prepare a strategy beforehand. When you ask Alice a question, she
will consult her prepared photon in a box, and measure it in a way that
depends on which question you asked. The measurement will mess up the photon's
state, so you don't get to ask another question. Elsewhere, Bob will do the
same with his photon. The two photons were prepared together, but are
completely separated at the time of the game.

Before you ask, it's provable that such tricks cannot be used to send
information faster than light. Quantum "spooky action" is somehow more
powerful than hidden correlations, but less powerful than outright
communication. It's pretty subtle and most popular accounts don't get it
right.

~~~
BrandonSmithJ
I don't quite follow your proof on the last two steps; would you mind
explaining? You say it's by logical operations, but I'm missing something
because I see:

(A && B && C) || (A && D && C) == (A && B) || (D && C)

~~~
cousin_it
It's =>, not ==. We need to show that (4) is contained in the union of (2) and
(3).

~~~
mh-cx
I think you misunderstood his question. I have the same problem.

How do you get from this line:

    
    
        (A1Y and B2Y and B3Y) or (A1Y and A2Y and B3Y) 
    

to this

    
    
        (A1Y and B2Y) or (A2Y and B3Y)
    

BrandonSmithJ just did some replacement to make it easier to read. Maybe he
shouldn't have used the same letters to avoid confusion.

Let's write it differently: Why are these terms equivalent?

    
    
       (u && v && w) || (u && x && w)
       (u && v)  || (x && w)

~~~
cousin_it
They are not equivalent. The former term logically implies the latter term.
That means the set of situations described by the former term is a subset of
the situations described by the latter term. That means the probability of the
former set should be less or equal than the probability of the latter set.

~~~
mh-cx
Ah, makes sense now. Thanks!

Now I also get your previous comment. I've read your => as arrows instead of
"equal or greater".

~~~
cousin_it
They are arrows, logical implications :-)

~~~
mh-cx
Argh. Right. After more thinking equal or greater than wouldn't make much
sense.

------
eternalban
I found this video [1] to be a remarkably engaging and informative (but Bohr
biased) overview of this topic.

Alain Aspect's comment regarding "if you just want answers you simply compute"
in context of "understanding" entanglement is spot on.

[1]: [https://youtu.be/-LklvINk_L4](https://youtu.be/-LklvINk_L4)

~~~
eternalban
This is a much better upload of the same film:
[https://youtu.be/BFvJOZ51tmc](https://youtu.be/BFvJOZ51tmc)

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fiatjaf

      > Entanglement arises in situations where we have partial knowledge of the state of two systems.
    

What happened to the notion that entangled states were about particles being
in many places at the same time?

~~~
lmm
Superposition is a necessary precondition for entanglement but not what
entanglement itself is about.

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acqq
A horrible article, it can only contribute to confusion than to present what
is known.

No, there are no squares and circles, and no cakes. It isn't simpler an
there's no insight to be gained by thinking about the cakes and squares and
circles.

Much better learning about what is. For example, to get some intuition for the
things you can't directly observe try considering what's going on in the
"simple" act of water drop forming and detaching.

[https://youtu.be/c4MUTij8f6I?t=120](https://youtu.be/c4MUTij8f6I?t=120)

It's waves all the way down.

