# [ExI] simulation

Gary Miller aiguy at comcast.net
Mon Dec 17 11:05:57 UTC 2007

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Eugene said:

>> We'll think of interpretations when we have observations violating
Einstein's dictum (no superluminal information transfer). So far, there are
none, zilch, zero. >>

http://en.wikipedia.org/wiki/Quantum_cryptography

Wikipedia does say that in their article on Quantum Cryptography in the
second protocol method they describe that the Keys are transmitted as
quantum information.  And that the receiver can deduce their key with above
50% probability (error rate 20% April 2007) from their measurement.  So the
key is information.  It is a collection of measurements that evaluate to a
string used to decode the longer textual message.  So why not just transmit
textual message several times each with 20% errorrate and compare the
results to eliminate the errors not for encryption but data transfer.  The
article says that the errorrate is caused by imperfections in the
transmission line and detectors.  If this is correct then it should just
require additional error correction protocol engineered (TCP/IP) into the
hardware or software to ensure that error free information emerges.  I know
this sounds too simple so I must be missing something.  But anything above
50% should be real data and it sounds like they can get 80% as of April
right?

The current reconciliation method that they use to correct for errors in key
values is complex, but the probably do this on purpose to preserve the
property of the encryption that makes someone attempting to listen to the
encrypted channel detectable.

Gary

Wikipedia >>

 Entangled photons - Artur Ekert (1991)
The Ekert scheme uses entangled pairs of photons. These can be made by
Alice, by Bob, or by some source separate from both of them, including
eavesdropper Eve, although the problem of certifying them will arise. In any
case, the photons are distributed so that Alice and Bob each end up with one
photon from each pair.

The scheme relies on three properties of entanglement. First, we can make
entangled states which are perfectly correlated in the sense that if Alice
and Bob both test whether their particles have vertical or horizontal
polarizations, they will always get opposite answers. The same is true if
they both measure any other pair of complementary (orthogonal)
polarizations. However, their individual results are completely random: it
is impossible for Alice to predict if she will get vertical polarization or
horizontal polarization.

Second, these states have a property often called quantum non-locality,
which has no analogue in classical physics. If Alice and Bob carry out
polarization measurements, their answers will not be perfectly correlated,
but they will be somewhat correlated. That is, there is an above-50%
probability that Alice can, from her measurement, correctly deduce Bob's
measurement, and vice versa. And these correlations are stronger - Alice's
guesses will on average be better - than any model based on classical
physics or ordinary intuition would predict.

Third, any attempt at eavesdropping by Eve will weaken these correlations,
in a way that Alice and Bob can detect.

Privacy amplification and information reconciliation
The quantum cryptography protocols described above will provide Alice and
Bob with nearly identical shared keys, and also with an estimate of the
discrepancy between the keys. These differences can be caused by
eavesdropping, but will also be caused by imperfections in the transmission
line and detectors. As it is impossible to distinguish between these two
types of errors, it is assumed all errors are due to eavesdropping in order
to guarantee security. Provided the error rate between the keys is lower
than a certain threshold (20% as of April 2007[2]), two steps can be
performed to first remove the erroneous bits and then reduce Eve's knowledge
of the key to an arbitrary small value. These two steps are known as
information reconciliation and privacy amplification respectively, and were
first described in 1992[3].

Information reconciliation is a form of error correction carried out between
Alice and Bob's keys, in order to ensure both keys are identical. It is
conducted over the public channel and as such it is vital to minimise the
information sent about each key, as this can be read by Eve. A common
protocol used for information reconciliation is the cascade protocol,
proposed in 1994 [4]. This operates in several rounds, with both keys
divided into blocks in each round and the parity of those blocks compared.
If a difference in parity is found then a binary search is performed to find
and correct the error. If an error is found in a block from a previous round
that had correct parity then another error must be contained in that block;
this error is found and corrected as before. This process is repeated
recursively, which is the source of the cascade name. After all blocks have
been compared, Alice and Bob both reorder their keys in the same random way,
and a new round begins. At the end of multiple rounds Alice and Bob will
have identical keys with high probability, however Eve will have gained