Therefore, Nick it is premature for you to claim that the full machinery of the Glauber coherent states, i.e. distinguishable over-complete non-orthogonality is not necessary for KISS to work. Let's not rush to judgement and proceed with caution. This technology, if it were to work is as momentous as the discovery of fire, the wheel, movable type, calculus, the steam engine, electricity, relativity, nuclear fission & fusion, Turing machine & Von Neumann's programmable computer concept, DNA, transistor, internet ...
On Feb 5, 2013, at 12:18 PM, Demetrios Kalamidas <dakalamidas@sci.ccny.cuny.edu> wrote:
Hi Nick,
And thanks much for your careful examination of my scheme....however, there appears to be a misunderstanding.
Let me explain:
"On page 3 you drop two r terms because "alpha", the complex amplitude of the coherent state can be arbitrarily large in magnitude."
I drop the two terms in eq.5b because they are proportional to 'r'....and 'r' approaches zero. However, the INITIAL INPUT amplitude, 'alpha', of each coherent state can be as large as we desire in order to get whatever SMALL BUT NONVANISHING AND SIGNIFICANT product 'r*alpha', which is related to the terms I retain.
In other words, for whatever 'r*alpha' we want, lets say 'r*alpha'=0.2, 'r' can be as close to zero as we want since we can always input a coherent state with large enough initial 'alpha' to give us the 0.2 amplitude that we want.
So, terms proportional to 'r' are vanishing, while terms proportional to 'r*alpha' are small but significant and observable.
You state:
"But on page 4 you reduce the magnitude of "alpha" so that at most one photon is reflected. So now alpha cannot be arbitrarily large in magnitude."
The magnitude of 'alpha' is for the INITIAL coherent states coming from a3 and b3, BEFORE they are split at BSa and BSb. It is this 'alpha' that is pre-adjusted, according to how small 'r' is, to give us an appropriately small reflected magnitude, i.e. 'r*alpha'=0.2, so that the "....weak coherent state containing at most one photon...." condition is reasonably valid.
Demetrios
On Feb 5, 2013, at 12:18 PM, Demetrios Kalamidas <dakalamidas@sci.ccny.cuny.edu> wrote:
Hi Nick,
And thanks much for your careful examination of my scheme....however, there appears to be a misunderstanding.
Let me explain:
"On page 3 you drop two r terms because "alpha", the complex amplitude of the coherent state can be arbitrarily large in magnitude."
I drop the two terms in eq.5b because they are proportional to 'r'....and 'r' approaches zero. However, the INITIAL INPUT amplitude, 'alpha', of each coherent state can be as large as we desire in order to get whatever SMALL BUT NONVANISHING AND SIGNIFICANT product 'r*alpha', which is related to the terms I retain.
In other words, for whatever 'r*alpha' we want, lets say 'r*alpha'=0.2, 'r' can be as close to zero as we want since we can always input a coherent state with large enough initial 'alpha' to give us the 0.2 amplitude that we want.
So, terms proportional to 'r' are vanishing, while terms proportional to 'r*alpha' are small but significant and observable.
You state:
"But on page 4 you reduce the magnitude of "alpha" so that at most one photon is reflected. So now alpha cannot be arbitrarily large in magnitude."
The magnitude of 'alpha' is for the INITIAL coherent states coming from a3 and b3, BEFORE they are split at BSa and BSb. It is this 'alpha' that is pre-adjusted, according to how small 'r' is, to give us an appropriately small reflected magnitude, i.e. 'r*alpha'=0.2, so that the "....weak coherent state containing at most one photon...." condition is reasonably valid.
Demetrios
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