🚀 go-pugleaf

Nearly a month ago, I asked whether a central premise of quantum
cryptology---that measurements on a single photon could only yield
grossly incomplete information on the photon's polarization---couldn't
be undermined by amplifying the photon and making many separate
measurements on the copies. This posting summarizes what I learned
from responses and from subsequent library work.

I wish to thank the handful of readers who gave me helpful pointers,
and particularly those who were thoughtful enough to compose their
missives without using the word "crackpot". I understand, now, that
to many workers close to this field, I have committed a sin analogous
to proposing a perpetual-motion machine.

An article by R. J. Glauber [1], who has a Harvard address and I gather
is a highly respected authority in the field of quantum coherence theory,
deals with exactly the question I asked. He quotes N. Herbert as proposing
in 1982 [2] that a "laser gain tube" be used to "clone" the photon, making
many duplicates identical to the original, thereby permitting detailed
measurements. Glauber, after many pages of assertions and equations
whose rigor and applicability I am not qualified to judge, but which
are all explained down to a level tantalizingly close to intelligible,
concludes that the amplifier will inevitably introduce just enough
noise (from such things as spontaneous emission) to make sure I get no
more information than I could have gotten from the original photon.

(A much shorter itinerary to the same destination can be found in [3].)

Physicists' interest in this question derives not from cryptology but
from the discomforting suggestion that if detailed polarization information
could be extracted from a single photon, then faster-than-light
communication could be effected by something like the hypothetical
Einstein-Podolsky-Rosen (EPR) experiment [4]. Faster-than-light communication
is held incompatible with special relativity, because there would
always exist an inertial reference frame in which the message arrived before
being sent.

Further interesting articles, from the quantum cryptologist's perspective,
are in [5,6].

This is probably as far as it's worth taking this subject on sci.crypt,
though I'm still dissatisfied with the final package. Quantum mechanics
seems to require that information travel faster than light from one end
of an EPR experiment to the other. Special relativity---completely
unrelated---forbids communicating that fast. To reconcile these two,
we have to invoke amplifier noise and spontaneous emission---nit-picky
details not obviously basic to either major theory---to make sure you
can't transmit useful information this way. Smells like a pretty
gross kluge to me. (Does God follow this news group?)


[1] R. J. Glauber, Amplifiers, Attenuators, and the Quantum Theory of
    Measurement, p. 534 in Frontiers of Quantum Optics, edited by E. R. Pike
    and S. Sarkar (Adam Hilger, Ltd., Bristol, 1986).

[2] N. Herbert, Found. Phys. 12, 1171 (1982).

[3] R. J. Glauber, Quantum Devices and Measurements, p. 126 in Laser
    Spectroscopy VIII, Proceedings of the Eighth International Conference,
    edited by W. Persson and S. Svanberg, (Springer-Verlag 1987).

[4] A. Einstein, B. Podolsky, and N. Rosen, Physical Review 47, 777 (1935).
    The "EPR paradox" is also well described in [1], and is no doubt
    discussed to death on sci.physics.

[5] C. H. Bennett et al., Quantum Cryptology Without Bell's Theorem,
    Phys. Rev. Letters 68, 557 (1992).

[6] C. H. Bennett, Phys. Rev. Letters 68, 3121 (1992).
-- 
pearson6@llnl.gov