| Subject: What, then, are Qbits good for?
Date: Mon, 22 Jul 2002 20:05:22 +0300 From: "Dimiter G. Chakalov" <dchakalov@surfeu.at> To: "N. David Mermin" <mermin@ccmr.cornell.edu> CC: Asher Peres <peres@photon.technion.ac.il>, G.Milburn@damtp.cam.ac.uk, shimony@bu.edu, kochen@math.princeton.edu, adler@ias.edu, jbub@carnap.umd.edu, a.steane1@physics.ox.ac.uk, adami@krl.caltech.edu, artur.ekert@qubit.org, tapster@falcor.dera.gov.uk, lkgrover@lucent.com, Pieter.Kok@jpl.nasa.gov, bennetc@watson.ibm.com, William.K.Wootters@williams.edu BCC: [snip] Dear David: Regarding your recent quant-ph/0207118 [Ref. 1]: How long it will take to realize that: 1. The normalization procedure, as explained in Footnote 12 [Ref. 1], refers to ONE single instant of time, as read with your good old wristwatch? 2. No error correction whatsoever [Ref. 1] could possibly cope with this generic problem recognized by Erwin Schrödinger in 1931, http://members.aon.at/chakalov/readme1st.html 3. The phrase "the states immediately before and immediately after the measurement" [Ref. 1] is an oxymoron? I think Qbits are good for intellectual exercise only, http://members.aon.at/chakalov/right.html#Note_2 http://members.aon.at/chakalov/Milburn.html What you are looking after is right above your neck: your brain. There are very real and very serious challenges out there, http://news.bbc.co.uk/hi/english/sci/tech/newsid http://news.bbc.co.uk/hi/english/world/americas/newsid Let's get serious, okay? It's about time. I extend this offer to your colleague Asher Peres as well, http://members.aon.at/chakalov/Peres.html I hope that all my email messages send to you in the past three years have been safely received. You can read this email at http://members.aon.at/chakalov/Mermin.html Needless to say, my web site will be included in my forthcoming CD ROM "Physics of Human Intention". Regards, Dimi
Reference [Ref. 1] N. David Mermin. From Cbits to
Qbits: Teaching computer scientists quantum mechanics. Fri,
19 Jul 2002 16:15:09 GMT,
"First, a quantum computer -- or, more accurately, the
abstract quantum computer that one hopes some day to be able to realize
-- is an extremely simple example of a physical system.
"The best physicists have an extraordinary intuition for
what features of the actual phenomena are essential and must be represented
in the abstract model, and what features are inessential and can be ignored.
It takes years to develop such intuition. Some never do.
"So in a general multi-Qbit state each individual Qbit
has no state of its own. This is the first major way in which Qbits differ
from Cbits.
"It looks as if the extension from Cbits to Qbits opens
up an enormously richer landscape of computational possibilities. While
the state of one Cbit is specified by a single bit of information, to specify
the state of one Qbit requires an infinite amount of information: two complex
numbers constrained only by the normalization condition (29).
"But there is a catch! Qbits suffer from a major limitation which does not afflict Cbits. Although their state contains vast amounts of information, given n Qbits in some state |psi> there is nothing you can do to the Qbits that enables you to learn what |psi> is. There is thus no way to extract anything like the huge amount of information contained in the amplitudes [alfa]_x. "What, then, are Qbits good for? How can we exploit their
greater flexibility to do anything useful at all?
"VI. Measurement: how to squeeze information out of Qbits." (Footnote 14, p. 12: "The condition that the states be unit vectors is thus the condition that the sum of the probabilities of all the possible measurement outcomes should be 1.") "The postmeasurement state contains no trace of the information
present in the premeasurement state |psi> and is nothing
more than the classical state associated with the value of x
indicated by the measuring device.
"The conservative way to put
it is simply to state the relation between the states immediately before
and immediately after the measurement, in a way that suggests no mechanism
for the change of state, confers no objective status on it, and makes no
commitment to what (if anything) a change in state implies about what (if
anything) has happened to the Qbits themselves.
"There is no way to reconstruct the input from the output.
Measurement is, however, the only irreversible operation on Qbits. All
other operations are unitary.
"A Qbit in a superposition of classical-basis states is
distinctly different from a Qbit that is in one of those classical states
with a probability given by the squared modulus of the corresponding amplitude.
Superpositions have no classical interpretation. They are sui generis,
an intrinsically quantum-mechanical construct, whose meaning derives only
from the rules that characterize the reversible operations (unitary) that
can be performed on them and the available means (measurement) for extracting
information from them.
"People have been arguing about the meaning of the quantum
state ever since the concept first appeared, with no indication that we
are getting any closer to a consensus. These conceptual issues are unimportant
for an understanding of quantum computation which only requires one to
know how states are built up from other states (by appropriate unitary
transformations) and how information can be extracted from Qbits in a given
state (by measurement, according to the Born rules).
"Another pitfall of taking their state to be an objective
property of the Qbits is that one can then succumb to the temptation to
believe that the application of a series of unitary transformations to
the Qbits implements a physical computation of all the resulting amplitudes
[alfa]_x . The clue that this has not been accomplished lies in the fact,
noted above, that given the Qbits there is nothing whatever you can do
with them to reveal the values of those amplitudes.
"But unfortunately there is a small amount of unintended coupling between the two sets of Qbits -- unitary transformations whose action is not restricted to either the relevant or irrelevant Qbits -- whose disruptive action on the relevant Qbits it is the task of error correction to undo." =============== Note: Recently N. David Mermin wrote a paper on the occasion of the 60th birthday of Charles H. Bennett, entitled "Copenhagen Computation: How I Learned to Stop Worrying and Love Bohr", quant-ph/0305088. He quoted his fabulous "From Cbits to Qbits" [Ref. 1], which has been published in American Journal of Physics 71, 23-30 (2003), and posed a very interesting question:
"Why did my bare-bones, no-nonsense,
pedagogically motivated, minimalist introduction to quantum mechanics come
out sounding so Copenhagen? I think there are several reasons: I think it is very difficult to find a better answer. These kids studying computer science at Cornell should read much more about error correction, not only from N. David Mermin but also from Andrew Steane, to decide whether should invest time and efforts in reinventing the wheel, as known since 1931. Kids have the right to know the whole truth, not just bits and pieces assembled with the magic conjuration "our knowledge of the system". I'm sure one day Professor Mermin will tell them the whole truth. The sooner, the better. The countdown has begun: Monday, 19 May 2003, day 1. Watch this space! Dimi Chakalov Day 18: I haven't heard yet
from Prof. Mermin. Maybe he's too busy. Day 33: Dark and
somber silence. Well, it rarely happens that Saul
becomes Paul. ================ Subject: What,
then, are Qbits good for? John S. Bell
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