No-cloning and stimulated emission

  • #26
9,290
2,179
Right, but cloning just the spin (or polarization), and not the other properties, is already a violation of the no-cloning theorem. Cloning the entire photon is a violation, but so is cloning certain subsets of it. That's what I was objecting to. (I probably should have included your "It refers to an arbitrary state - not one parameter of that state ie its spin." part of the quote in my reply.)
Yes - you cant clone a subset either.

I also checked what I wrote just to refresh what I said and I couldn't locate your quote.

Thanks
Bill
 
  • #27
Strilanc
Science Advisor
588
210
Yes - you cant clone a subset either.

I also checked what I wrote just to refresh what I said and I couldn't locate your quote.

Thanks
Bill
Alright, sounds like we agree.

I pulled the quote from post #9 in this thread where you said:

Because that's not what the no cloning theorem says. It refers to an arbitrary state - not one parameter of that state ie its spin.
I think I may have simply misunderstood your "arbitrary" as meaning "entire".
 
  • #28
9,290
2,179
I have been investigating this a bit further.

I am not satisfied with the explanation in the article I linked to - I don't think it resolves it.

After searching I think I have finally got the correct answer:
http://www2.cruzio.com/~quanta/flash.html
'Shortly after publication of FLASH Wooters and Zurek published in Nature a paper entitled "A Single Quantum Cannot be Cloned" arguing that polarization-neutral laser amplifiers cannot be built. However Mandel a few weeks later published an explicit design for a polarization-neutral laser amplifier. Mandel in addition showed that such an amplifier would produce just enough noise that the polarization eigenstate of the input photon will be unmeasurable. For example when you put, say, an H photon into Mandel's device, two H photons come out--a single photon CAN be cloned--two times out of three. But one time out of three when an H photon goes in, an H and a V photon come out. This looks good--a signal-to-noise ratio of 2 to 1--but just this amount of noise exactly suffices to prevent you from discovering the difference between a random mixture of V, H photons (ZERO) and a random mixture of S, D photons (ONE). Thus Alice can send Boris a faster-than-light message but Boris cannot decode it.'

Interesting. I have only seen this FTL proposal with electrons and the no cloning theorem directly used to resolve it. Its not clear here with a laser how its resolved - it looked like a reasonably faithful amplifier. But really it isn't - and it not faithful hust enough to foul this up - interesting.

Thanks
Bill
 
  • #29
418
20
Thank you. I guess that's the "mechanism" I was looking for preventing FTL communication.

Unfortunately it doesn't go into detail much. So one time out of three stimulated emission produces a V photon from an H photon? Does this mean the textbook treatment of stimulated emission is only true in two out of three times?

And what about spontaneous emission? In the paper in #3 they say "it is spontaneous emission that limits the achievable quality of the quantum cloning and ensures that the no-cloning theorem is not violated", but the other link doesn't mention it in that context.
 
  • #30
9,290
2,179
So one time out of three stimulated emission produces a V photon from an H photon?
It mentions one time out of 3 a V and a H photon comes out. Thus one goes in - two comes out. This is QFT spontaneous emission which would seem the bottom line issue.

Thanks
Bill
 
  • #31
Demystifier
Science Advisor
Insights Author
10,577
3,327
So one time out of three stimulated emission produces a V photon from an H photon? Does this mean the textbook treatment of stimulated emission is only true in two out of three times?
Yes, that's probably the simplest way to understand why stimulated emission does not allow perfect cloning. In an attempt of cloning there is always some probability for an error, even if a very small one. But imperfect cloning which tollerates an error is, of course, possible.
 
  • #32
418
20
Do we need QFT to prove this? I guess so, since photons are described by QFT.

Interestingly though, the proof of the general no-cloning theorem only uses Hilbert space properties and doesn't need special relativity.
 
  • #33
9,290
2,179
Do we need QFT to prove this? I guess so, since photons are described by QFT.
I think its more that in QFT particle numbers are not fixed so its required to explain particle creation.

This is actually a deep requirement of combining relativity and QM. See:
https://www.amazon.com/dp/019969933X/?tag=pfamazon01-20

It has a chapter giving the gory mathematical detail - contour integration and all.

Thanks
Bill
 

Related Threads for: No-cloning and stimulated emission

Replies
3
Views
823
  • Last Post
Replies
4
Views
2K
  • Last Post
Replies
3
Views
2K
  • Last Post
Replies
7
Views
880
  • Last Post
Replies
1
Views
4K
Replies
20
Views
392
  • Last Post
Replies
4
Views
376
  • Last Post
Replies
6
Views
896
Top