Re: Quantum communication might be possible?
- From: Greg Egan <gregegan@xxxxxxxxxxxxxxx>
- Date: Sun, 22 Jan 2006 22:00:38 +0000 (UTC)
In article <dqm70h$d8t$1@xxxxxxxxxxxxxxxxxxxx>, nmm1@xxxxxxxxxxxxx (Nick
Maclaren) wrote:
> In article <20060118010542.E99924B58A@xxxxxxxxxxxxxxxxxxxx>,
> Greg Egan <gregegan@xxxxxxxxxxxxxxxxxxxxx> wrote:
[snip]
> >Quantum communication
> >---------------------
> >
> >Alice and Bob receive sequences of photons which are correlated as above.
>
> So this is either an entangled CHANNEL or the number of bits transferred
> is fixed? I am not sure how an entangled channel of photons would
> work, and I was definitely told that the number of bits was indefinite
> (see below).
What I am describing is simply the production and transmission of as
many individual pairs of entangled photons as required to fulfill the
purpose at hand. The number of bits available is unlimited because the
number of photon pairs you can create and distribute is unlimited. This
is not the most efficient scheme, but it's conceptually the simplest, so
it's worth understanding what's happening here before considering all
the various permutations and refinements.
If you want to create and distribute a *single* entangled system, and
then use it for applications involving an indefinite number of bits,
that's a more complicated matter -- and it would always require the
parties to keep on sending things to each other; they can't just share a
finite entangled system and then expect to communicate an indefinite
number of bits, without any further physical exchanges taking place.
For example, there's a sophisticated scheme for quantum key distribution
<http://arxiv.org/abs/quant-ph/9911025> in which a finite entangled
system is created once only, and then two of its qubits (out of a total
of six) are repeatedly passed back and forth between Alice and Bob to
allow a random key of arbitrary length to be created and shared
securely.
> > Alice and Bob randomly choose between two directions, V and W, which are
> >45 degrees from each other. After they have collected a large number of
> >measurements, they publish their choices of directions; this allows them
> >then to know when they made measurements along the same direction. Their
> >polarisation results when their directions coincided are known only by
> >them, and will agree, so they can use this sequence of bits as a secure
> >key.
>
> And it is safe from snooping because, if Cecil does snoop, he will
> destroy the entanglement and Alice's and Bob's keys will not match.
> That is a critical characteristic - without it, quantum communication
> is no advance on distributing two copies of a one-time pad.
Yes, and that's exactly what I'm talking about below. Sorry if I
confused you by referring to "statistics about the data"; I was using
the word "data" generically, not to refer to a message as distinct from
a key.
> >Any eavesdropper/data-corrupter will not know the choices of direction
> >made by Alice and Bob, and so will be forced to make his own choices. If
> >Alice and Bob publish some further statistics about the data, it's
> >possible for them to verify that no eavesdropping or corruption of the
> >data has taken place.
The point I was trying to make was, if Alice and Bob end up with
different keys because of the intervention of an eavesdropper, how do
they establish that fact? They can't publish their entire keys, so it's
a matter of judiciously publishing statistics.
> Eh? At most, that will enable them to say that about the key (and
> my previous remark addresses that). All of the papers and talks have
> sworn that snooping on the DATA is also impossible, because at least
> some of it is transferred by the entangled channel.
Literally dozens of different schemes have been proposed, and what's
practical and advantageous will vary from context to context. You can
distribute a key by a secure entanglement-based method and then send all
the encrypted data classically if you like ... or you can use various
quantum methods for everything. The possibilities are endless, but I
was trying to outline the most basic version from which the principles
can be understood.
The first simple schemes that were envisaged involved the kind of thing
I've been discussing -- generating lots of entangled pairs -- whereas
more recently people have got excited about various schemes that swap
entanglement from one pair of particles to another, an example of
"quantum teleportation".
In general, what happens with teleportation is that Alice and Bob first
receive particles 1 and 2 which are members of an entangled pair. Alice
can then perform a *joint measurement* on the combined state of
particles 1 and 3, where 3 is in an unknown state. She then sends the
result of this measurement as 2 bits of classical data to Bob, and he
can use it to perform an operation on particle 2 that will put it in
exactly the quantum state that particle 3 originally possessed.
This includes the possibility that particle 3 was entangled with some
other particle, 4, in which case particle 2 rather than particle 3 will
now be entangled with particle 4. Hence we have a case of "entanglement
swapping".
My understanding of what's meant by the phrase "entangled channel" in
the literature is the ability to take one entangled system and swap the
entanglement around from system to system. So rather than just having a
specific entangled system, what we have is a certain "amount" of
entanglement that we can (at least in principle) shuffle around between
different physical systems. This is probably more important for quantum
computing than for quantum cryptography.
The crucial point is that an "entangled channel" shouldn't be mistaken
for some kind of quantum walkie-talkie that you can pump information
through without having other means of communication. If you give Alice
and Bob an entangled channel but otherwise isolate them from each other
completely, they won't be able to communicate anything.
Greg Egan
Email address (remove name of animal and add standard punctuation):
gregegan netspace zebra net au
.
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