Experimental Issues in Quantum Measurement

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Experimental Issues in Quantum Measurement

• Today, 7.10.03 OVERVIEW
• a survey of some important situations in q.
  msmt. theory
• (why bother coming to these lectures?)
• 13.10.03 SOME TECHNICAL BACKGROUND
• introduction to standard quantum measurement
  theory
• (measurement postulate, collapse, von Neumann
  msmts,
• density matrices and entanglement,...)
• 20.10.03 THE QUANTUM ERASER
• Bohr-Einstein debates
• Scully, Englert, Walther complementarity vs
  uncertainty
• Two-photon experiments
• Alternate pictures (collapse vs correlations)
• 27.10.03 OTHER MODERN EXPERIMENTS...

Being a quantum physicist is like being an
alcoholic.
...the first step is to admit you have a problem.
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FIRST TOPIC Interruptions
MAKE THEM!
VALID REASONS TO INTERRUPT ME
Im going too fast. Im going too slow. You
want to correct my grammar. You disagree with
something I said. I seem to disagree with
something Ive said. You have a question about
something Ive said. You have a question about
something completely unrelated.
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Some references
I will not be following any particular textbook,
but for obvious reasons, will draw
disproportionately from experiments I myself have
worked on... Appropriate references will be
provide as the lectures progress. General
references on quantum mechanics Your favorite
QM text Shankars Principles of QM Background
on the quantum measurement problem Wheeler
Zureks Quantum Theory and Measurement Bells
Speakable and Unspeakable in Quantum Mechanics My
general perspective on these issues References
on my web page, http//www.physics.utoronto.ca/
aephraim/aephraim.html where slides from
these lectures will be too, eventually Speakabl
e and Unspeakable, Past and Future
http//lanl.arxiv.org/abs/quant-ph/0302003
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The Copenhagen Viewpoint
(Toronto description of)
Bohr, Heisenberg We must only discuss the
outcomes of measurements. An experiment
described to measure wave properties will
measure wave properties. An experiment described
to measure particle properties will measure
particle properties. In an experiment which
measures wave properties, a question about
particle properties is not a question about the
outcome of real measurements it is not a
proper question. Wave and particle
descriptions are complementary they
can never both be observed in a single
experiment.
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The Bohr-Einstein debates
Heisenberg microscope photons which allow you
to look at the particle bounce off it,
disturbing its momentum.
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Feynmans Rules for interference
If two or more indistinguishable processes can
lead to the same final event (particle could go
through either slit and still get to the same
spot on the screen), then add their
complex amplitudes and square, to find the
probability P A1A2 2 eikL1 eikL2 2
1 cos k(L1-L2) If multiple distinguishable
processes occur, find the real probability of
each, and then add P A12 A22 eikL1
2 eikL2 2 1
If there is any way even in principle to tell
which process occurred, then there can be no
interference (if you knew which slit the
particle came from, youd see a 1-slit pattern) !
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The quantum eraser
spin-up (?) particles
Still no interference because we could check
the spin of the particle, and discover which slit
it had traversed.
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Must there be a disturbance?
Bohr Measurement of X disturbs P et
cetera Measurement means amplification of a
quantum phenomenon by interaction with some
large (classical) device Msmt involves some
uncontrollable, irreversible disturbance We must
treat the measuring device classically.
Wigner Why must we? What will happen to us if
we dont?
Scully, Englert, Walther Complementarity is
more fundamental than uncertainty. We can use
information to destroy interference, without
disturbing the momentum.
Storey, Tan, Collett, Walls No. Any such
measurement always disturbs the momentum.
Wiseman ( Toronto experiment) Theyre both
right. And we can measure how much the momentum
is disturbed.
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The EPR Paradox and
superluminal signalling?
RECALL Spin-projections along different axes
are incompatible (cant be measured
simultaneously -- like X P) If you find Sz
1 (spin ?), and then measure Sx, Sx 1 (spin
?) and Sx 1 (spin ?) are equally likely. Then
if you find one of those, ? and ? become equally
likely. Bohr Heisenberg tell us we must
choose we can know Sz, but give up all
knowledge of Sx... or know Sx and give up all
knowledge of Sz...
Copenhagen no wave function has both those
properties defined and the wave function is
all you can possibly know. EPR are cheating,
discussing measurements they didnt do.
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Some important lessons
One of the more subtle ones You can extract
very limited information from a single
particle. In fact, to duplicate the particle,
you must destroy it information in QM is
never gained or lost.
NO CLONING!
(...and yet, recent quantum cloning
experiments...)
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Distinguishing the indistinguishable

• Non-orthogonal quantum states cannot be
  distinguished
• with certainty.
• This is one of the central features of quantum
  information
• which leads to secure (eavesdrop-proof)
  communications.
• Crucial element we must learn how to
  distinguish quantum
• states as well as possible -- and we must
  know how well
• a potential eavesdropper could do.

If it gets through an H polarizer, ...it could
still have been 45, and its too late to
tell. If it gets through a 45 polarizer, same
story.
BUT a clever measurement can tell with
certainty, 25 of the time. BUT BUT a
non-standard quantum measurement can do better!
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A 14-path interferometer for arbitrary 2-qubit
unitaries...
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Success!
"Definitely 3"
"Definitely 2"
"Definitely 1"
"I don't know"
The correct state was identified 55 of the
time-- Much better than the 33 maximum for
standard measurements ( everything in your
textbook).
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" Quantum seeing in the dark "

• (AKA The Elitzur-Vaidman bomb experiment)
• A. Elitzur, and L. Vaidman, Found. Phys. 23, 987
  (1993)
• P.G. Kwiat, H. Weinfurter, and A. Zeilinger, Sci.
  Am. (Nov., 1996)

Problem Consider a collection of bombs so
sensitive that a collision with any single
particle (photon, electron, etc.) is guarranteed
to trigger it. Suppose that certain of the bombs
are defective, but differ in their behaviour in
no way other than that they will not blow up when
triggered. Is there any way to identify the
working bombs (or some of them) without blowing
them up?
Bomb absent Only detector C fires
Bomb present "boom!" 1/2 C 1/4
D 1/4
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Quantum CAT scans
If you measure momentum P... you dont know
anything about X. If you measure position X...
you dont know anything about P. But in real
life, dont I know something about each? Dont I
also know that if a car left this morning and is
already in Budapest, its going faster than if
its still on Währingerstr.? Wigner function
W(x,p) is like the probability for a particle to
be at x and have momentum p. Its integrals
correctly predict P(x), P(p), and everything else
you want. Of course, you must study a large
ensemble of particles to get so much
information quantum state tomography
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The Wigner quasiprobability function for an atom
trapped in a light wave
P(0,0) lt 0 ?!
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Predicting the past ?

• Standard recipe of quantum mechanics
• Prepare a state igt (by measuring a particle to
  be in that state see 4)
• Let Schrödinger do his magic igt ? fgtU(t) igt,
  deterministically
• Upon a measurement, fgt ? some result ngt ,
  randomly
• Forget igt, and return to step 2, starting with
  ngt as new state.

Aharonovs objection (as I read it) No one has
ever seen any evidence for step 3 as a real
process we dont even know how to define a
measurement. Step 2 is time-reversible, like
classical mechanics. Why must I describe the
particle, between two measurements (1
4) based on the result of the first, propagated
forward, rather than on that of the latter,
propagated backward?
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Predicting the past...
What are the odds that the particle was in a
given box (e.g., box B)?
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Pick a box, any box...
Well see that applying similar logic here lets
us conclude P(A) 100 P(B) 100 and then,
necessarily P(C) 100 (?!) ....and that
real measurements agree (somehow!)
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Measurement as a tool KLM...
INPUT STATE
OUTPUT STATE
a0gt b1gt c2gt
a0gt b1gt c2gt
TRIGGER (postselection)
ANCILLA
special ?i gt
particular ?f gt
Knill, Laflamme, Milburn Nature 409, 46, (2001)
and others since. Experiments by Franson et al.,
White et al., Zeilinger et al...
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Summary the kinds of thingswell cover...

• Why does one thing happen and not another?
• When is a quantum measurement?
• Does a measurement necessarily disturb the
  system, and how?
• What can we say about an observable before we
  measure it?
• Does a wave function describe a single particle,
  or only an ensemble?
• Is a wave function a complete description of a
  single particle?
• Can we predict the past?