Telecommunication via ultra-weak signals

Atomic-S · « **on:** 10/12/2006 06:22:49 »

Can more than one bit be transmitted on a single photon?

lightarrow · « **Reply #1 on:** 10/12/2006 13:29:06 »

It's a quiz for us or you really don't know the answer?

syhprum · « **Reply #2 on:** 10/12/2006 13:56:59 »

I can visualise a synchronous system whereby a time frame is established between the transmitter and receiver and the bit value depends on the arrival time of the photon.
Would this annoy Mr Shannon?

Heliotrope · « **Reply #3 on:** 10/12/2006 18:48:28 »

You can encode many pieces of information within the parameters of a single photon.
Polarisation and frequency are just two things you can control to provide you with information.

Atomic-S · « **Reply #4 on:** 18/12/2006 05:09:50 »

Well, let's see; if in a 1 second interval a photon's arrival can be pinpointed to the nearest 1/1024th of a second, that would give 10 bits worth of information (2^10 = 1024) out of one photon.

syhprum · « **Reply #5 on:** 18/12/2006 07:00:25 »

Historical note

This is pulse phase modulation, first used in 1944 for military communications by the British command in France (number 10 set)

lyner · « **Reply #6 on:** 18/12/2006 23:59:09 »

There is a lot of information by virtue of the frequency / energy of the photon. We're effectively in the realms of FM transmission here.
lyner

syhprum · « **Reply #7 on:** 19/12/2006 06:48:16 »

The question referred to a "single photon" I fear an error has crept in in as much as we have been considering what infomation can be derived from a series of photons.
From a single photon we can derive its energy, its time of arrival and the direction from whence it comes.
now if we had some pre synchronisation with the source we could derive information about its time of arrival but does the question permit this?.
All we can learn is its energy and source so I suppose we can measure the energy within QM limits but I do not know how many bits this represents

lyner · « **Reply #8 on:** 20/12/2006 00:32:51 »

The answer to the original question has just got to be "yes" .
Remember, the concept of a 'bit' is not really very fundamental to communication theory.
What limits the information that a single photon would carry is the amount of noise or interference in the system - i.e. other photons around.
Lyner

Atomic-S · « **Reply #9 on:** 20/12/2006 05:10:08 »

Quote

now if we had some pre synchronisation with the source we could derive information about its time of arrival but does the question permit this?.

Actually, the question could be interpreted two ways: One, how much information can be obtained if confronted with a single photon and no other corresponding signals. This would be like if a particle detector registered the arrival of one gamma ray photon, and the question would be, under the most ideal design, how much could we learn from the photon? Two (and this was my more intended meaning): given a signal consisting of a stream of (relatively rare) photons, how much of a signal can be recovered from them? This would be like if attempting to telecommunicate via laser beam from Earth to some distant part of the galaxy, where the signal would be so weak that we could not necessarily assume that the photon rate at the receiver would be greater than the bit rate in the original signal, and the question is, can we still read an intelligible signal, and if so, by what technology?

syhprum · « **Reply #10 on:** 20/12/2006 08:56:30 »

The amount of information that can be carried by a communication channel depends solely on the signal to noise ratio (see Shahnnon et al).
If the transmitter is sending one high energy gamma ray photon each second and the natural source of such photons is about one each day the signal to noise ratio would be about 50db, modulation could be imparted onto this channel by varying the timing of the photons (phase modulation).
SETI have chosen to listen close to 1420MHz although the natural level of noise is high at this frequency this is chosen as it would be well understood by extra terrestials

Atomic-S · « **Reply #11 on:** 22/12/2006 04:54:25 »

Minimum photon requirements for pictures:

One can see an object only insofar as one receives light from it. Therefore it is generally assumed that one cannot take a meaningful picture without a certain minimum number of photons. This is considered the absolute limit of photography.

What is the minimum number of photons required? It depends upon how accurately the shades must be represented (let us consider only grayscale photography for now). If you want to distinguish 16 levels of lightness, then each pixel must receive from 0 to 15 photons.

Unfortunately, that analysis does not take into consideration the statistical nature of quantum mechanics. When light intensity equivalent to a number of photons reaches a detector, we do not have the certainty that that many will be detected, but only the probability that that many will be detected. The actual number detected may be different. In order to reliably produce a level of gray, the light intensity must be such that the level will not be deviated from, due to chance, by more than an acceptable margin.

   To calculate the margin of error associated with the arrival of photons at a pixel, we could divide the total number of photons for the whole scene by the number of pixels, and conclude that the resulting number represents the probable result, and then work on the basis that any photon may by chance arrive at any pixel, to calculate the deviation; however this model is unrealistic because each photon does not, in fact, have an equal chance at arriving at each pixel (otherwise the scene would be entirely blank!). Adjacent pixels will in general have markedly different probable numbers of photons. So we must approach the problem differently.

   Let us look at a single pixel, and state that for this pixel, certain photon detections may occur. We can regard each possibility of a photon detection as the toss of a die, some of whose faces are painted white (meaning detection) and others painted black (meaning non-detection). The number of white faces is the same on all dice, as is the number of black faces. These dice do not necessarily have 6 faces; each may in fact each have as many faces as we deem necessary, so long as the number of faces is the same for each. The fraction of faces on any one die that is white is the probability that a photon will be detected; and black that the photon will not be detected.

   The following quantities are still unknown: the fraction of faces on any one die which are white or black, and the number of dice being tossed. What we do know is that when they are tossed, the expected, i.e. most probable, outcome is that a certain number of white faces will show up, equal to the number of expected photons. However, if 1200 dice are tossed each of which has 1/12 of its faces white, then the probable outcome (100 white faces) is the same as if 120000 dice were tossed each of which had 1/1200 of its faces white. That means that we are free to adjust (with reason) these two numbers as we wish, and the results will be the same, so long as the expected number of white faces is kept equal to the expected number of photons.

   Let us choose the most convenient numbers. The simplest possible die has but 2 faces, one white and one black. I.e., a coin. The expected outcome of a toss of n coins is that n/2 will come up white. Thus, we set n/2 equal to the expected number of photons, and calculate the resultant statistics based upon the toss of n coins.

   As you know, the formula for coin-tossing tells us that if n coins are tossed, n being a large number, then there is an approximatley 95% chance that the number of whites will fall between n/2 - sqrt(n) and n/2 + sqrt(n). For small values of n, this formula is somewhat inaccurate but will be close enough for our purposes. Thus, if a pixel "ought" (based upon the classical physics of the situation) to receive 50 photons, then the number it actually will receive has a good chance of falling anywhere between 50 - sqrt(100) and 50 + sqrt(100), that is, between 40 and 60.

   Using this analysis, the following table of statistically adjacent and effectively non-overlapping intervals is constructed:


      Nominal      half-width       resultant
      number of   of uncertainty      boundaries of
      photons      (rounded to      this gray
            integer)      level

                     0
      2      2         
                     4
      7      3
                     10
      13      4
                     17
      22      5
                     27
      33      6
                     39
      46      7
                     53
      61      8
                     69
      78      9
                     88
      97      10
                     107
      118      11
                     129
      141      12      
                     153
      166      13
                     179
      193      14
                     207
      222      15
                     237
      253      16
                     269
      286      17
                     303

This table shows the minimum number of photons to photograph in 16 dependable shades of gray. The scale is somewhat nonlinear due to the expanding margins of error as the number of photons increases; but we may say, roughly, that to photograph a typical scene in 16 shades of gray, the detector must accumulate an average of about 140 photons per pixel (corresponding to average tone or middle gray) as an absolute minimum, in order to overcome quantum statistical noise.

Now let us consider transmitting this picture. How many photons do we need to transmit it? Well, each pixel is accurate to 1 of 16 levels, which can be sent as 4 bits. To send 4 bits requires how many photons? It was mentioned earlier in this thread that 10 bits, or even more, can be sent using one photon, if the system is correctly arranged. Let us say it is set up to send 12 bits per photon, by identifying the time of arrival of the photon to an accuracy of 1 part in 2^12 . With that, we can send THREE pixels with one photon.

But it took about 140 photons to record one pixel.

This sounds like a violation of the conservation of something.

It is generally thought that it is not possible to send a message containing 140 units of information using a channel having capacity of only 1/3 of a unit. If that be possible, then the original message would be considered highly redundant and compressible.

But as we have just observed, the original message is already photon limited -- the least use of photons possible to take the picture.

How is this possible?

syhprum · « **Reply #12 on:** 22/12/2006 07:23:27 »

The number of bits of information that can be derived from the reception of one photon depends on the degree to which the accuracy of some characteristic of this photon can be determined.
If we are to determine the timing accurately the communication channel must have a wide bandwidth and hence the probability of letting though unwanted photons i.e noise.
On a completely noise free channel there is no limit to the amount of information that can be carried by a single photon

Atomic-S · « **Reply #13 on:** 23/12/2006 01:37:30 »

Well, then in theory, the entire picture could be transmitted on a single photon.

Be that as it may, it is clear that the number of photons needed to transmit the picture may well be considerably fewer than the minimum number required to take it in the first place, and therein lies the enigma: it suggests that the information content that is recorded during taking is considerably less than the information capacity of the photons used in the photography, even under the most stringent conditions. That seems strange.

syhprum · « **Reply #14 on:** 23/12/2006 06:11:26 »

I remember a science fiction story where the this idea was taken to an impossible but logical end.
The alien visitor had a metallic rod on which two line were inscribed which he claimed carried all the infomation from all the libraries on his planet.
by measuring the distance between these marks with sufficient accuracy the digital number required to encode this length could as a data stream carry all this information.
What you are describing is data compression taken to its ultimate limit which of course cannot be done in real time

Atomic-S · « **Reply #15 on:** 29/12/2006 04:57:50 »

I am unfamiliar with that story; sounds interesting. In any case, admittedly transmitting an entire picture on one photon is somewhat impractical; but transmitting 3 pixels on one photon is entirely reasonable. Returning to the enigmatic puzzle -- why it should be possible to transmit a picture using substantially fewer photons than the minimum thought necessary to form it, thereby seemingly violating the conservation of photon information capacity, remains somewhat of a queer concept. One suspects it could have something to do with the fact that the photons used in trasmission must be under a high degree of control to accomplish this; whereas those used in the taking are not particularly controlled, although they are utilized to the maximum extent that conventional thinking about photography permits. Raising the possibility of unconventional thinking about photography. Might there be any way to take the picture using quite a bit fewer photons than normally thought necessary?

While we are on this subject, let us consider radio reception. A radio signal consists of certain sidebands and possibly the carrier within a bandwidth. Quantum mechanically, this represents a diversity of frequencies and therefore a diversity of photon energies. What happens as the distance from the transmitter increases very greatly? We can think of microwaves beamed into space, and after many light years of travel they would become weaker and weaker till the energy level would be comparable or less than the photon count. What does such a signal look like? Can such a signal be received?

syhprum · « **Reply #16 on:** 29/12/2006 14:49:11 »

When I was involved with press picture transmission working for Muirhead in the early 70,s the normal method of picture transmission via telephone lines was either straight AM on a 1300 HZ carrier or FM plus or minus 300 HZ deviation.
It was investigated whether digital transmission could be used as the modems of that time could send 9600 bits/sec by sending 2400 pulse's/sec of 16 different amplitudes.
This was never implemented as the company went out of business and we were overtaken by the computer age and by some miracle modems have been coaxed up to 56K bits/sec

Heliotrope · « **Reply #17 on:** 29/12/2006 19:51:11 »

Quote from: syhprum on 22/12/2006 07:23:27

The number of bits of information that can be derived from the reception of one photon depends on the degree to which the accuracy of some characteristic of this photon can be determined.
On a completely noise free channel there is no limit to the amount of information that can be carried by a single photon

There is alimit to the amount of information encoded in a single photon.
And you've mentioned it in the first line of your post.

You start to run up against the Heisenberg Uncertainty Principle when you have many different things encoded.
You want information out of the wavelength, the phase, the polarisation, the spin etc...
These properties cannot be measured with infinite precision.
You can have some of all, or all of one, but not all of all.

Heliotrope · « **Reply #18 on:** 29/12/2006 19:52:56 »

I'm actually wondering if it's possible to modulate the envelope of a single quanta.
A single quanta has a certain number of wavelengths inside it dependent upon the energy of the photon.
I wonder if it's even theoretically possible to shape the envelope of the quanta ?

syhprum · « **Reply #19 on:** 30/12/2006 13:24:51 »

I did of course appreciate this point but thank you for pointing it out all the same

Telecommunication via ultra-weak signals

Atomic-S (OP)

Atomic-S (OP)

lyner

lyner

Atomic-S (OP)

Atomic-S (OP)

Atomic-S (OP)

Atomic-S (OP)