🚀 go-pugleaf

Stephen Barnett in NATURE 362, 11 March 1993 p.113 commenting on experiments 
of Poizat and Grangier (Phys. Rev. Letters 70, 271-274, 1993) writes:

"With a QND detector for light we could measure any information encoded on 
the amplitude of a laser beam without degrading the the quality of the 
information left on the beam ... it allows us to tap into an optical signal 
and measure the amplitude modulation without changing the signal ... 

Poizat and Grangier's quantum optical tap works by the nonlinear optical 
effect of cross-phase modulation ... In a sodium cell .. the index change 
will be proportional to the intensity of the light, so it leads to an 
intensity dependent phase modulation.

It is this phase modulation that is responsible for the production of 
solitons (self-sustaining wave packets) in optical fibres. When two beams 
are present, the intensity-dependent modification of the refractive index 
induced by one beam can produce a modulation of the phase in the second 
beam. This cross-modulation means that the phase change of one beam is 
proportional to the intensity of the other, so by monitoring the phase of 
the 'meter' beam which has interacted with the signal beam we can infer the 
intensity of the signal.

.. the signal is not absorbed .. Poizat and Grangier in fact measure the 
signal by conventional means after the QND measurement. Their comparison of 
these two measurements shows that the signal does not become appreciably 
depleted, and that the signal and meter beams are correlated so that the 
measurement carried out on the meter tells us something about the signal 
amplitude. This new experimental arrangement has achieved the sensitivity 
required to push the nondemolition measurement into the quantum regime where 
the signal degradation is lower and the correlation between the the meter 
and signal beams is stronger than could be achieved in any classical 
arrangement."

This is a new test for quantum nonlocality. The strong correlation here is 
like the strong correlation in the photon pair polarizations that violate 
Bell's locality inequality.

"A conventional measurement would either have to degrade the signal more to 
achieve the same degree of accuracy in the measurement, or sacrifice 
accuracy in order to leave the signal intact.

Measurement of the amplitude scrambles the phase of the signal beam. The 
nonlinear interaction between the meter and signal beams, causing a 
correlation between the signal intensity and the meter phase, also 
correlates the signal phase and the meter intensity. In monitoring the meter 
phase we discard information about the meter intensity and hence introduce 
additional uncertainty into the signal phase."

Roughly speaking, in second quantization, n = a*a is canonically conjugate 
to the phase @ where

a = n^1/2 e^i@

aa* - a*a = 1

A rigorous treatment is complicated and we cannot really use @ but need
things like cos@ operators. There's a lot of published literature on this 
problem. I did some of the original work on this as a graduate student with 
Lenny Susskind and Jonathan Glogower back at Cornell in 1963.  I introduced 
the problem to Susskind. It grew out of a paper I published in Nuovo 
Cimento. 

The question is, can we use this as a communication device? That is, can the 
choice to monitor or not monitor the meter phase transmit a bit to the 
signal beam?  Thus, suppose we do not monitor the meter phase, then the 
signal phase stays stable and with the proper interferometer splitting the 
signal beam we can see fringes. On the other hand, if we monitor meter phase 
we randomize the signal phase to that when it recombines with the signal 
reference beam the fringes are destroyed. 

Thus

Fig.1 Cross-phase modulation communicator gedankenexperiment (my invention)


                         cross-phase modulator           phase detector
 meter                       _____
 ---------------------------|     |--------------------------|   | S  
                            |     |                       transmitter
                /-----------|_____|-----------\
                |                             |
                |                             |
                |                             |
                |                             |
                |                             |
                |                             |
                |                             |
                |                             |
                |                             |
 signal         |        reference            |
----------------/-----------------------------\------------- R1
                                              |
                                              |
                                              |
                                              |      receiver
                                              |
                                              |
                                              | R2

If the phase detector at S is switched "on" it randomizes the phase in the 
upper signal sub-beam relative to the reference beam. Therefore, counters R1 
and R2 click at equal rates. On the other hand, if the phase detector at S 
is not switched "on", the relative phase in the split signal sub-beams is 
stable. Since there is an i unitary reflection phase shift at each splitter, 
using phase plates, we can arrange destructive interference at R1 and 
constructive interference at R2, allowing the observer at the receiver to
infer whether or not a phase measurement was made at S. This is local 
decoding. The spacetime interval between the phase measurement event at S 
that transmits the bit, and the counter clicks at R that decode the bit can 
be spacelike. We can even arrange R to be in the timelike future of R.

So where is the error?

"In an interesting variation on the QND theme, Grangier and colleagues also 
used a nonlinear optical crystal to produced two amplified copies of the 
information contained in one quadrature component of an input signal (Phys. 
Rev. Lett 70, 267-270, 1993)."

This shoots to hell the significance of the famous Wooters-Zurek result that 
Bennet assumes in his "quantum teleportation" scheme. You may not be able to 
clone a single-photon eigenstate, but, apparently there is no problem 
cloning Glauber and squeezed states.

"Thus an amplitude modulated signal is converted into two beams, each more 
intense than the original and carrying the same amplitude modulation. 
Observation of the amplitude of one beam reveals the modulation carried by 
its partner."