The document describes John Archibald Wheeler's proposal for a quantum delayed-choice experiment (QDC). It discusses how a QDC could demonstrate that a photon simultaneously exhibits both particle-like and wave-like behavior. A QDC would do this by measuring these complementary aspects of the photon's behavior simultaneously, without needing to open or close the experimental apparatus after the photon interacts with it. The document provides historical context on wave-particle duality and delayed-choice experiments, and outlines some of the key developments and landmarks in experimental implementations of QDC experiments.

1. A
Quantum
Delayed-­‐Choice
(QDC)
Experiment

2. John
Archibald
Wheeler
1983
A
Quantum
Delayed-­‐Choice
(QDC)
Experiment

3. A
Quantum
Delayed-­‐Choice
(QDC)
Experiment

4. o Quantum
systems
exhibit
par$cle-­‐like
or
wave-­‐like
behaviour
depending
on
the
experimental
apparatus
that
they
are
confronted
with!
–
Delayed
Choice
experiment
(DC)
o Photon
is
forced
to
choose
a
behaviour
before
the
observer
decides
what
to
measure!
(DC)
o Quantum
delayed-­‐choice
experiment
(QDC)
–
parCcle
and
wave
behaviour
invesCgated
simultaneously!
o VerificaCon
of
the
quantum
nature
of
the
photon’s
behaviour
is
via
nonlocality
with
QDC,
replacing
the
delayed
choice
of
the
observer
in
DC.
A
QDC
Experiment
–
OVERVIEW
CLAIM:
“we
observed
strong
nonlocal
correla$ons,
which
show
the
photon
must
SIMULTANEOUSLY
behave
both
as
a
par$cle
and
a
wave”

5.
**KEY
DEVELOPMENT:
NO
LONGER
NECESSARY
TO
CLOSE/OPEN
INTERFEROMETER!**
(therefore
removing
the
role
of
the
observer/device!)
o QDC
scheme
based
on
Bell’s
inequality
(21)
–
can
test
the
most
general
classical
model
-­‐
device-­‐independent
“we
cer$fy
the
quantum
nature
of
the
photon’s
behaviour
by
observing
the
viola$on
of
a
Bell
inequality.
This
demonstrates
in
a
device-­‐independent
way
(without
making
assump$ons
about
the
func$oning
of
the
devices
–
that
no
local
hidden
variable
model
can
reproduce
the
quantum
predic$ons.”
A
QDC
Experiment
–
OVERVIEW

6. o Wave/par$cle
duality
-­‐-­‐-­‐-­‐àDESCARTES
1630
(waves)
NEWTON
1670s
(parCcles)
vs
HUYGENS
1678
(waves)
-­‐-­‐-­‐-­‐à
YOUNG
1803
(waves)
–
Double
Slit
-­‐-­‐-­‐-­‐à
MAXWELL
1865
(waves),
verified
by
HERTZ
1887
o NoCon
of
COMPLEMENTARITY
(Copenhagen
interpretaCon)
-­‐-­‐-­‐-­‐à
Appeal
to
hidden-­‐variable
models
o Wheelers
DELAYED
CHOICE
(DC)
gedankenexperiment
1980s
A
QDC
Experiment
–
LANDMARKS

7.
o Experimental
implementaCons
(1987
–
2000)
A
QDC
Experiment
–
LANDMARKS

8. A
DC
Experiment
–
WHEELER
John
Archibald
Wheeler
1983

9. A
DC
Experiment
–
WHEELER

10. A
DC
Experiment
–
WHEELER

11. Squint
to
see
a
‘complementary’
image!!!
J
A
DC
Experiment
–
WHEELER

12. Squint
to
see
a
‘complementary’
image!!!
J
A
DC
Experiment
–
WHEELER
o Describes
dialog
between
EINSTEIN
and
BOHR
between
EINSTEIN’S
arrival
in
Princeton
in
1933
and
his
death
in
1955.
o EINSTEIN
is
adament
that
an
observer
dependence
“IS
INCOMPATIBLE
WITH
ANY
REASONABLE
IDEA
OF
REALITY”
o BOHR’S
reply
“YOUR
CONCEPT
OF
REALITY
IS
TOO
LIMITED’

13. o EINSTEIN
could
not
reconcile
himself
to
the
fact
that
the
DOUBLE-­‐SLIT
experiment
could
be
made
to
demonstrate
WAVE-­‐LIKE
or
PARTICLE-­‐LIKE
behaviour.
o He
declared
it
to
be
“CLEARLY
OBVIOUS
THAT
QUANTUM
THEORY
IS
INCONSISTENT”
o BOHR
emphasised
that
there
in
fact
was
NO
INCONSISTENCY
o We
are
dealing
with
two
different
experiments,
BUT
IT
IS
IMPOSSIBLE
TO
DO
BOTH
EXPERIMENTS
SIMULTANEOUSLY
(unCl
the
QDC!!!)
o He
argued
one
can
observe
one
feature
of
nature,
or
its
complementary
feature.
BUT
NOT
BOTH
SIMULTANEOUSLY
(unCl
the
QDC!!)
A
DC
Experiment
–
WHEELER

14. A
DC
Experiment
–
BACKGROUND

15. A
DC
Experiment
–
BACKGROUND

16. A
DC
Experiment
–
BACKGROUND

17. o Decision
to
add
/
remove
half-­‐silvered
mirror
(BS2)
is
made
at
the
last
picosecond,
aher
the
photon
has
already
travelled
through
(most)
of
the
system
o “WE
HAVE
A
STRANGE
INVERSION
OF
THE
NORMAL
ORDER
OF
TIME”
(unCl
QDC!!)
o “WE
NOW…HAVE
AN
UNAVOIDABLE
EFFECT
ON
WHAT
WE
HAVE
A
RIGHT
TO
SAY
ABOUT
THE
ALREADY
PAST
HISTORY
OF
THAT
PHOTON”
o Argument
has
since
been
refined
with
the
DC
experiment
A
DC
Experiment
–
WHEELER

18. A
DC
Experiment
–
WHEELER
o DC
AT
THE
COSMOLOGICAL
SCALE!
o Distance
of
travel
in
a
Lab
split-­‐beam
experiment
~30m
o Time
of
travel
~
0.1
microseconds
o Distance
COULD
be
billions
of
light
years
o Consequently
an
observing
device,
configured
to
respond
a
specific
way
has
an
“IRRETRIEVABLE
CONSEQUENCE
FOR
WHAT
ONE
HAS
THE
RIGHT
TO
SAY
ABOUT
A
PHOTON
THAT
WAS
PRODUCED
LONG
BEFORE
THERE
WAS
ANY
LIFE
IN
THE
UNIVERSE”
o Two
astronomical
objects
(0957
+
561
A,B)

19. (Were
once
considered
to
be
two
disCnct
quasi-­‐stellar
objects
(or
‘quasars’)
as
they
are
seperated
by
6
seconds
of
arc.
Now
considered
to
be
two
disCnct
images
of
one
quasar
An
intervening
galaxy
has
been
found
1/4
of
way
from
us
to
the
quasar
(0957
+
561
A,B)
A
DC
Experiment
–
WHEELER

20. A
DC
Experiment
–
WHEELER

21. A
DC
Experiment
–
Experimental
RealisaCon

22. A
DC
Experiment
–
Experimental
RealisaCon

23. A
DC
Experiment
–
Experimental
RealisaCon

24. A
DC
Experiment
–
Experimental
RealisaCon

25. A
DC
Experiment
–
Experimental
RealisaCon
o University
of
Rochester
–
Emission
of
photon
pair
from
two-­‐down
conversion
crystals
o One
photon
passes
MZI,
second
photon
determines
whether
first
shows
interference
o THEREFORE
view
that
act
of
determining
parCcles
path
disturbs
interference
effects
is
UNTENABLE!
o KEY
FACTOR
=
whether
path
informaCon
is
available
or
not
(experiments
where
path
info
carried
by
second
parCcle
is
destroyed
aher
parCcle
registered
–
see
interference!)

26. A
DC
Experiment
–
Experimental
RealisaCon
o QDC
says
otherwise!!

27. A
DC
Experiment
–
Experimental
RealisaCon

28. A
DC
Experiment
–
Experimental
RealisaCon

29. A
DC
Experiment
–
Experimental
RealisaCon

30. A
DC
Experiment
–
Experimental
RealisaCon
o QDC
says
otherwise!!
(see
next
slide)

31. A
QDC
Experiment
–
Proposal

32. A
QDC
Experiment
–
Proposal

33. A
QDC
Experiment
–
Proposal

34. A
Quantum
Delayed-­‐Choice
(QDC)
Experiment

35. o Quantum
mechanics
most
consistent
and
accurate
physical
theory
we
have...
o HOWEVER,
makes
counter-­‐intuiCve
predicCons
o NoCon
of
WAVE-­‐PARTICLE
DUALITY
introduced
A
quantum
sytem
may
behave
as
a
parCcle
or
wave
depending
upon
the
experiment
o
COPENHAGEN
INTERPRETATION
–
parCcle
/
wave
behaviour
are
never
observed
simultaneously
o To
reconcile
quantum
predicCons
and
common
sense
it
has
been
suggested
that
quantum
parCcles
may
know
the
experiment
in
advance,
via
a
HIDDEN
VARIABLE
o Challenged
by
J.
A
Wheeler
in
DELAYED
CHOICE
gedankenexperiment
A
Quantum
Delayed-­‐Choice
(QDC)
Experiment

36. o Quantum
parCcle
sent
towards
MZI
o RelaCve
phase
between
the
two
MZI
arms
adjusted
so
parCcle
emerges
at
D’
with
certainty
(WAVE-­‐LIKE
BEHAVIOUR)
o BS2
can
be
removed
arbitrarily
–
meaning
a
WHICH
PATH
measurement
is
made.
o The
photon
is
detected
in
each
mode
with
an
equal
probability
of
1/2
(PARTICLE-­‐LIKE
BEHAVIOUR)
o BS2
can
be
removed/inserted
arbitrarily
aher
the
parCcle
has
entered
the
MZI
(aher
BS1)
o ParCcle
could
not
have
known
in
advance
(via
hidden
variables)
which
kind
of
experiment
it
would
be
confronted
with.
A
Quantum
Delayed-­‐Choice
(QDC)
Experiment

37. CONCEPTUALLY
DIFFERENT
STARTING
POINT:
o Recent
theoreCcal
proposal
of
QDC
using
a
quantum-­‐controlled
BS
(C(H))
which
can
be
in
a
superposiCon
of
PRESENT
and
ABSENT
o meaning
the
MZI
can
be
simultaneously
CLOSED
and
OPEN
–
tesCng
WAVE
and
PARTICLE
nature
of
the
photon
simultaneously!
o Used
a
reconfigurable
integrated
quantum
photonic
circuit
to
implement
a
MZI
with
a
quantum
BS
o Observed
CONTINUOUS
MORPHING
between
WAVE
and
PARTICLE
behaviour!
o (although
this
can
be
reproduced
by
a
simple
classical
model
–
weakness
in
proposal
and
recent
NMR
implementaCons)
A
Quantum
Delayed-­‐Choice
(QDC)
Experiment

38. o Observed
CONTINUOUS
MORPHING
between
WAVE
and
PARTICLE
behaviour!
o Therefore
experimentally
demonstrated
QDC
based
on
BELL
INEQUALITY
–
allowed
to
test
the
most
general
classical
model.
o ACHIEVED
STRONG
BELL
INEQUALITY
VIOLATIONS
–
the
delayed
choice
of
closing
the
MZI
or
not
is
no
longer
necesssary
–
instead
we
cerCfy
the
quantum
nature
of
the
photon’s
behaviour
by
observing
the
violaCon
of
a
Bell
ineuality
o Demonstrates
in
a
device-­‐independent
way
(without
making
assumpCons
about
the
funcConing
of
the
devices)
–
that
NO
LOCAL
HIDDEN
VARIABLE
model
can
reproduce
the
quantum
predicCons.
o “NO
MODEL
WHERE
PHOTON
KNEW
IN
ADVANCE
CAN
ACCOUNT
FOR
THE
OBSERVED
STATISTICS”
A
Quantum
Delayed-­‐Choice
(QDC)
Experiment

39. Classical
delayed-­‐choice
Equivalent
quantum
network
Delayed-­‐choice
with
quantum
beam
spliber
Biased
QRNG
A
Quantum
Delayed-­‐Choice
(QDC)
Experiment

40. Classical
delayed-­‐choice
Equivalent
quantum
network
o Second
beam
spliper
inserted/removed
randomly
once
the
photon
is
inside
the
MZI
(has
passed
BS1)
o HADAMARD
gates
act
as
BEAMSPLITTERS
o RED
LINE
=
ANCILLA,
iniCally
prepared
in
|0>,
then
|+>,
then
measured
–
acts
as
QRNG!
A
Quantum
Delayed-­‐Choice
(QDC)
Experiment

41. Delayed-­‐choice
with
quantum
beam
spliber
Equivalent
quantum
network
[Classical
control
acer
ANCILLA
measurement]
=
[quantum
control
before
ANCILLA
measurement
SECOND
BEAM
SPLITTER
NOW
IN
SUPERPOSITION
OF
PRESENT
/
ABSENT
(controlled-­‐Hadamard)
C(H)
o Have
a
quantum
BS
in
superposiCon
of
present
/
absent
o Interferometer
is
therefore
open
/
closed
o Forces
photon
to
be
in
a
superposiCon
of
parCcle
/
wave
(following
Wheelers
interpretaCon)
A
Quantum
Delayed-­‐Choice
(QDC)
Experiment

42. Delayed-­‐choice
with
quantum
beam
spliber
Biased
QRNG
o Can
also
bias
the
QRNG
by
preparing
the
ANCILLA
in
an
arbitrary
state
A
Quantum
Delayed-­‐Choice
(QDC)
Experiment

43.
QUANTUM
DELAYED
CHOICE
o BS2
in
now
a
quantum
BS
(represented
by
a
controlled-­‐Hadamard
operaCon)
–
can
be
set
into
a
superposiCon
of
present
and
absent
via
ANCILLA
photon
o Again,
a
single
photon
is
sent
through
the
MZI,
aher
the
first
Hadamard
a
superposiCon
of
the
two
spaCal
modes
is
created
(|+>)
o And
a
phase
shiher
modifies
the
relaCve
phase
A
Quantum
Delayed-­‐Choice
(QDC)
Experiment

44.
THE
PRESENCE
OF
BS2
DEPENDS
ON
STATE
OF
ANCILLA
o If
ancilla
is
prepared
in
the
state
|0>a
no
BS
is
present
o MZI
is
leh
OPEN
o Corresponds
to
IDENTITY
acCng
upon
the
state,
results
in:
o Final
measurement
in
the
computaConal
{|0>s,|1>s}
basis
reveals
the
PARTICLE-­‐NATURE
of
the
photon
as
a
WHICH-­‐PATH
measurement
is
made.
o Measured
intensiCes
in
both
output
modes
are
EQUAL
and
PHASE-­‐INDEPENDENT
ID’
=
ID’’
=
1/2
A
Quantum
Delayed-­‐Choice
(QDC)
Experiment

45.
THE
PRESENCE
OF
BS2
DEPENDS
ON
STATE
OF
ANCILLA
o If
ancilla
is
prepared
in
the
state
|1>a
the
BS
is
present
o MZI
is
CLOSED
o Corresponds
to
HADAMARD
acCng
upon
the
state,
results
in:
o Final
measurement
gives
informaCon
regarding
the
MZI
phase,
but
no
path
informaCon
o Measured
intensiCes
are
now
A
Quantum
Delayed-­‐Choice
(QDC)
Experiment

46. o Main
feature
of
QBS
is
that
it
can
be
in
a
superposiCon
of
present
and
absent
o If
ANCILLA
is
iniCally
in
a
superposiCon
the
global
state
of
the
system
evolves
into:
o The
SYSTEM
and
ANCILLA
photons
are
now
ENTANGLED
when
o Measured
intensiCes
are
now
A
Quantum
Delayed-­‐Choice
(QDC)
Experiment

47. A
Quantum
Delayed-­‐Choice
(QDC)
Experiment
-­‐
IMPLEMENTATION

48. A
Quantum
Delayed-­‐Choice
(QDC)
Experiment
–
(CHSH)
BELL
INEQUALITY

49. A
Quantum
Delayed-­‐Choice
(QDC)
Experiment
–
(CHSH)
BELL
INEQUALITY

50. A
Quantum
Delayed-­‐Choice
(QDC)
Experiment

51. A
Quantum
Delayed-­‐Choice
(QDC)
Experiment