The Classical Channel

Q: N-th Level Entangled Systems Generalization

3:17 AM

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I have seen qubits, qutrits & entangled bits (e-bits) a decent amount. I have also seen qunits/qudits for n-th level qubits. What I am trying to wrap my head around is the differences between n-th level e-bits vs n-th level qunits. What are the similarities? Differences? What generalizations ex...

Anonymous

3:33 AM

@Mithrandir24601 My issue with the answer isn't as much that it isn't perfect - rather I'm worried about the pretence going on there. Heather clearly threw around a few buzzwords and phrases like "quantum field theory", "quantum gravity", "complete", "Bell's inequality", "determinism" without understanding their implications in an answer.

Anonymous

It is usually good advice that one should not make claims about any theory (like "completeness") until they understand that theory (quantum field theory) well enough. Afaik quantum gravity isn't even well defined as of now.

Anonymous

Secondly, Heather clearly quotes my Hadamard state for single qubit and mentions that the difference with classical coins is "not satisfying Bell's inequality". That sentence itself made me extremely sceptical.

Anonymous

If at least (s)he mentioned quantum interference or something i'd leave it. (S)he once again tried to evade that one by saying (s)he is giving a "general idea" which sounds like a smart way to escape conversation to me. This is a very specific reason why I in particular mentioned a single qubit state in the question and not.

Anonymous

I have absolutely no idea how Bell's inequality is applicable to that one. And when I asked heather for a mathematical proof, (s)he tried to dodge that again. I can identify pretence when I see it, as I have done that before (pretended to be knowledge about something I'm not), myself, but I think it is a very bad habit. I personally would like to be pointed out if any of my answers sound like pretence. I'd immediately delete them.

Anonymous

Anyhow, got to follow up on SemiC's conversation today

Anonymous

3:37 AM

I'm very much interested in the transition matrix formulation of Bell's inequality and interference

Semiclassical

one typo in my conversation, which I'll mention here: I should've had tr[(UH+V)^T(UH+V)] (UH+V not UH-V)

and then V=-UH as the condition for equality

the upper bound I got was right, tho

Quantum Entanglement & Spooky Action at a Distance

4:03 AM

@Blue uh, what? I've been trying to engage you whenever you had a comment. that's not evading conversation. if i wanted to envade conversation, i wouldn't answer. and yeah, i mentioned quantum field theory and quantum gravity because i wanted to point out that quantum mechanics isn't "done" - there's bits we don't understand still. if you want me to remove that i will. i know quantum gravity isn't defined, i was giving the OP things to google, starting points.

that's half the battle, knowing what to google. determinism is not just a term i threw around, i discuss it in a large portion of the answer. further i didn't give a mathematical proof because a. what you were asking for didn't make sense and b. i didn't say anything that required a proof. i'm giving a general idea because that's what the OP asked for, not because i'm trying to evade conversation. yes, i quoted your comment, and the reason i quoted it was to set up that section of the answer.

i don't know everything there is to know about quantum computing, not even close. i'm not trying to pretend to.

i'm just trying to sketch out my understanding for the OP because I understand that it's really difficult learning from a wall of equations because I've been trying to figure stuff out from sources like that.

i've been trying to update and improve my answer based on your comments, and several of them have been really helpful, and i appreciate them.

so please don't accuse me of trying to be evasive and pretentious, that's the exact opposite of what i'm trying to do.

Anonymous

5:55 AM

@heather Fair enough. To avoid making accusations about you, I'll speak objectively (which I agree, I should have):

Anonymous

1. So anyway, we got this new set of laws, quantum mechanics. And the development of those laws is complete, though not completely correct (see quantum field theories, quantum gravity) but the history of their development is kind of interesting.

Anonymous

What is meant by "complete" here?

Anonymous

And what is meant by "completely correct" here?

Anonymous

It's kind of vague to me

Anonymous

Anonymous

5:59 AM

2. That portion which is circled above is again extremely vague to me. The "general" idea (in your words) which you're trying to give, doesn't sound general to at all if it can't even explain a 1-qubit system

Anonymous

@Blue there is no need for mathematical proof. Step back a minute. I'm using the idea of Bell's inequality to point out that, firstly, measurement is fundamentally different in quantum mechanics, and secondly, that quantum mechanics is not deterministic. Both of these points mean that any quantum system, including a qubit, is going to be fundamentally different from any classical system. — heather ♦ 9 hours ago

Anonymous

You even say that it is the "defining" difference!

Anonymous

It would be nice if you can elaborate on that part, after doing some more research. If you're interested I'm thinking of starting a fresh Q&A thread on exactly this issue.

Anonymous

3. This portion can be left as it is if you're sufficiently satisfied. No need to change this. However, I personally find determinism to be a very subtle issue. Maybe I'll ask about this on Physics SE because I do well understand the implications of determinism in different interpretations.

Anonymous

6:08 AM

Anonymous

"For a while, there was debate. Hidden variable theories came up, where it wasn't just probability - there was a way the particle "knew" what it was going to be when measured; it wasn't all up to chance."

Anonymous

From here, what the idea behind "Hidden variable theory" even is, is opaque to me.

Anonymous

Why is it "hidden"? What is it called a "variable"?

Anonymous

"where it wasn't just probability - there was a way the particle "knew" what it was going to be when measured"

Anonymous

This sentence again is quite vague

Anonymous

6:13 AM

►

Anonymous

If you want to give a beginner level overview of hidden variable theory, I think that Veritasium video does a really nice job. It would be great to have that kind of an explanation in an answer.

Anonymous

4. I appreciate that underlined sentence. Thanks for that

Anonymous

I'm at least happy that you think that your answer can be improved, which is exactly why I tried to point out the opacities in your answer and not for the other's in that thread (surely I didn't even attempt to, for this one and this one as the authors of those answers hardly respond well to constructive feedback - speaking from past interactions with them)

Anonymous

James Wotton's answer, however, looks fine to me, although it doesn't cover as many points as yours.

Anonymous

6:22 AM

5. It would be nice if you could mention a bit about infinite dimensional spaces and operators in your answer. Linear algebra doesn't describe the infinite-dimensional cases in QM. Those fall in the domain of functional analysis (which I'm only a beginner in) apart from other things. A lot of linear algebra results aren't valid in those cases, unlike what introductory quantum computing textbooks seem to convey.

Anonymous

Fwiw, there isn't any need to hurry. However, at some point in time, it would be good if you can address these in your answer.

Anonymous

Meanwhile, I'll see if I can frame a fresh question regarding the Bell's inequality.

Anonymous

For now, I've deleted the comments from your answer, as they were making the comment section unnecessarily long. I think I've pretty much conveyed what I wanted to.

6:59 AM

@Blue the development of the laws of QM is far from 'complete', I'd argue...

@Blue At least, I'm assuming that 'complete' means 'finished', but it could also mean something like 'we now have a set of laws which is now self-consistent', which would make more sense

Or it could be a historical account, where 'complete' means 'fixed the issues with classical physics that were around at the time'

Anonymous

@Mithrandir24601 Yes, I agree with that. Which is why I mentioned that that usage is vague, to say the least

@Blue Depends on context, which I haven't read yet :P

Anonymous

Yup, surely context matters. But I was speaking about that answer in particular ;)

Yeah, I haven't read that answer yet

Anonymous

@Mithrandir24601 You know any source/reference for "multi-qubit controlled" gates and how to decompose them into standard gate sets?

Anonymous

7:08 AM

Nielsen and Chuang doesn't seem to cover it very well

@Blue If you can't simply decompose it into tensor/Kronecker products, Solovay Kitaev might be the way to go

Anonymous

I don't know Solovay-Kitaev :/ Would you recommend me to read the original paper?

Anonymous

I especially thinking about the decomposition of the $R(\lambda^{-1})$ gate in HHL

@Blue It should be explained in good lecture notes - Preskill might(?) have it. It's in Ashley Montanaro's notes to some level of detail and much more detail in Andrew Child's lecture notes

@Blue I have to read the most recent question of yours on that as well yet

Mithrandir

(psst. everyone should keep "assume good faith" in mind.)

Anonymous

7:15 AM

Okaies, I'm checking the lecture notes. Let's see if I can find something useful

Anonymous

@Mithrandir In my opinion, there's a subtle trade-off involved between being honest and assuming good faith. I'm really happy to have heather around, however, I feel they have a long way to go in terms of "maturity" (and so do I), otherwise we'll never be able to become the high quality site we aim to be. Ugh, that tone was a bit patronizing, but conveyed the point I guess!

Anonymous

MStern's words still sting me everyday and I'm working on improving.

Anonymous

"While the other nominees are highly motivated, their answers and questions sometimes show, that they do not see the big picture, yet."

7:46 AM

@Blue I'm reading this along the lines of 'we have [the Copenhagen interpretation of] quantum mechanics, which has a full set of self consistent laws but there are other issues to be sorted out, such as QFT and quantum theories of gravity'

Although there is a slight ambiguity, yeah

8:08 AM

to be fair, it's a bit more than just 'violation of Bell inequalities' and it involves e.g. sub-poissonian statistics and negative 'quasi-probabilities' of the Wigner function which allow for correlations, one example of which are Bell-type inequalities (Bell, CHSH etc.)

Q: How to show an N-Level System is Entangled

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How do I show that a two-qubit state is an entangled state? includes an answer which references the Peres–Horodecki criterion. This works for 2x2 and 2x3 dimensional cases; however, in higher dimensions it is "inconclusive." It is suggested to supplement with more advanced tests, such as those ba...

quantum-entanglement qubit-state qudit

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Q: Is "probabilitistic,universal, fault tolerant quantum computation" possible with continuous values?

It seems to be a widely held belief within the scientific community that it is possible to do "universal, fault-tolerant" quantum computation using optical means by following what is called "linear optical quantum computing (LOQC)" pioneered by KLM (Knill, Laflamme, Milburn). However, LOQC uses ...

optical-quantum-computing continuous-variable

Although these are, in a sense, equivalent statements - you might e.g. show a HOM dip with a source of a pair of photons. This isn't a Bell inequality violation, but the same source could be used to show a Bell violation

Or rather, the state produced in a (variant of a) HOM dip can then be used to violate a Bell inequality

Q: 3 qubits vs. 2 qutrits vs. 1 six level qunit

8:34 AM

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What is the difference between 3 qubits, 2 qutrits and a 6th level qunit? Are they equivalent? Why / why not? Can 6 classical bits be super-densely coded into each?

quantum-entanglement qudit qutrit matrix-representation

Quantum Computing Meta

9:14 AM

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Q: Links to Nielsen & Chuang's exercise questions

Where can an aspiring student find answers to their deepest, darkest questions the exercises in Nielsen & Chuang's Quantum Computation and Quantum Information (10th Anniversary Edition) textbook?

discussion

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Q: Jobs in Quantum Computing

Stack Overflow has a jobs page. Would that be possible to implement here? If yes, awesome! If no, alternative suggestions?

feature-request

Q: When can we expect the quantum internet?

10:01 AM

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This article from 2017 predicts 2030. Is this accurate? What are the biggest bottlenecks in the realization of the quantum internet?

quantum-computer quantum-information quantum-internet

I like the idea of a series with the N&C exercises. Should we have a tag for that? It would be an efficient way to collect all of them together without having to go to the meta post (that many won't even know exists anyway)

@heather that answer is becoming huge. Honestly, I believe that at a certain point when an answer is too long it defeats the purpose of stackexchange. If I have to read an entire treatise I may as well go read one of the countless introductions around the internet

it's also harder to do quality control when it's so long. Most people that know what you are talking about probably won't read it as it would take too long

maybe you could try to shorten it instead of expanding it? There are plenty of questions/answers around physics.SE about many aspects of that. If you could find some of those good posts and link them where due maybe it would improve the quality of the overall answer

@heather I also have to say that I disagree with the spirit of the first part. I don't think the fact that a qubit has a continuum of possible states qualifies as what makes it "quantum"

Finally, I'm unhappy with this sentence "And the development of those laws is complete, though not completely correct (see quantum field theories, quantum gravity) but the history of their development is kind of interesting" just as I was with its previous version. "Not completely correct" gives the wrong message here. While as in any theory there is always more work to do and something could happen to prove the theory wrong, I don't think there is anything in the current formalism of (...)

... QM that makes it "not completely correct". QM is perfectly self-consistent. There still are debated points regarding the measurement problem and such, yes, but honestly I think you are better off avoiding to mention that altogether.

Mithrandir

10:48 AM

(oh, @heather, when you have a couple minutes, can you ping me in /rooms/58064/?)

Q: Nielsen & Chuang Exercise 2.2 - “Matrix representations: example”

1:31 PM

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Reproduced from Exercise 2.2 of Nielsen & Chuang's Quantum Computation and Quantum Information (10th Anniversary Edition): Suppose $V$ is a vector space with basis vectors $|0\rangle$ and $|1\rangle$, and $A$ is a linear operator from $V$ to $V$ such that $A|0\rangle = |1\rangle$ and $A|1\ran...

quantum-gate matrix-representation

Q: Are Absolutely Maximally Entangled states maximally entangled under all entanglement monotones?

1:47 PM

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In Ref. [1] absolutely maximally entangled (AME) states are defined as: An $\textrm{AME}(n,d)$ state (absolutely maximally entangled state) of $n$ qudits of dimension $d$, $|\psi\rangle \in \mathbb{C}^{\otimes n}_d$, is a pure state for which every bipartition of the system into the sets $B$ ...

quantum-entanglement quantum-state

Q: Quantum Networks and Broadcasting

2:52 PM

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Quantum networks or quantum internet are terms that can be found when reading about quantum computation and information nowadys, but still I they are pretty vague concepts that are still in development. I was wondering about the fact that this networks or internet would be pretty limited in comm...

quantum-computer quantum-internet

3:14 PM

do we really need the quantum-internet tag? I think quantum-networks would do just fine for these questions

oh, I see that tag also doesn't exist. Maybe we can have a general quantum-communication tag then?

4:51 PM

@Mithrandir24601 that's what i was intending

@Blue thank you for that comprehensive list of points. I'll work through those as I have time.

@glS yeah, it's getting kinda long. I'll look through and see what is unnecessary/trimmable. As @Blue and @Mithrandir24601 also pointed out, yeah, that sentence is vague, and I'll be sure to fix that.

@glS finally, could you elaborate a bit on the "i'm unhappy with the first part" complaint? I'm a little unsure of what you mean there, sorry.

(could you quote the relevant sentence, perhaps?)

@Blue ouch =P

8:04 PM

That looks like 9 questions asked today! Nice! :)

@glS Considering that every question tagged quantum-internet could also be tagged quantum-networks, I'd be inclined to say no

8:19 PM

@Mithrandir24601 wow that's good

If we can keep this up, we'll hopefully be out of public beta in no time :)

8:31 PM

yup =)

man, i need a break

i've spent the last hour or so learning techniques for solving differential equations

@Mithrandir24601 I'm suggesting using quantum-networks instead of quantum-internet. I don't think quantum internet really needs a tag of its own. There is just two questions with that tags its not a lot of work to change now

@glS Yeah, exactly (I'm saying that we don't need the quantum-internet tag, to be clear)

Just tried my first (rather small) tag merge, so hopefully that's worked now...