THE STRUCTURE OF A WORLD
(WHICH MAY BE) DESCRIBED
BY QUANTUM MECHANICS
A. J. LEGGETT
Department of Physics, University of Illinois at Urbana-Champaign
Institute for Quantum Computing, University of Waterloo
Support: John D. and Catherine T. Macarthur Foundation John
Templeton Foundation
QCrypt 2013, Waterloo, Canada, Aug. 9 2013
The structure of a world described by quantum mechanics
1
Theoretical account of the world given by quantum mechanics (QM) is very bizarre.
But, a theory is only as good as the experiments which support it.
So:
What can we infer about the nature/structure of the physical world
a) from existing experiments which test QM
b) on the assumption that all future experiments will confirm predictions of QM?
Two major areas of experimentation:
1) EPR-Bell
2) Schrödinger’s cat
Both (may) involve in their interpretation the concept of realism.
So: what do we (can we) mean by “realism” in physics?
“Realism” in the simplest case: a two state system
2
(Microscopic) example: photon polarization
Single (heralded) photon
Detector
Polarizer with
transmission axis
‖ to a
Macroscopic
events
“Question” posed to photon:
Are you polarized along a? (“A = +1”)
Or perpendicular to a? (“A = -1”)
Experimental fact:
For each photon, either counter Y clicks (and
counter N does not) or N clicks (and Y does not).
Natural “paraphrase”:
When asked, each photon answers either
“yes” (A = +1) or “no” (A = -1).
But: what if it is not asked?
(no measuring device…)
Single (heralded) photon
Macroscopic counterfactual definiteness (MCFD)
3
Suppose a given photon is directed “elsewhere”.
What does it mean to ask “does it have a definite
value of A?”?
A possible quasi-operational definition:
Suppose photon had been switched into measuring
device:
Then:
Proposition I (truism?): It is a fact that either counter Y
would have clicked (A = +1) or counter N would have
clicked (A = -1).
“Elsewhere”
Single (heralded) photon
Switch
⇓?
Proposition II (MCFD): Either it is a fact that counter Y
would have clicked (i.e. it is a fact that A = +1) or it is
a fact that counter N would have clicked (A = -1).
Microrealism ⇒ MCFD
⇒
DO COUNTERFACTUAL STATEMENTS HAVE TRUTH VALUES?
(common sense, legal system…assume so!)
The EPR-Bell experiments (idealized)
4
CHSH inequality: all objective local theories (OLT’s)
satisfy the constraints
AB + A¢B + AB¢ - A¢B¢ £ 2
atomic source
randomly
activated
switch
(
, etc.)
(✱) is violated by predictions of QM, and by
experimental data.
(⬆: “loopholes” – individually blocked except for
“collapse locality” loophole: at what point is a
definite outcome “realized”?)
(✱)
The EPR-Bell experiments (cont.)
5
Thus, modulo “loopholes”, all OLT’s are refuted by
experiment.
Maybe in future: long-baseline EPR-Bell experiment.
Defining postulates of an OLT: conjunction of
1) Induction
( @ standard “arrow of time”)
2) Einstein locality
(no superluminal causality)
Nb: 2) ⇒ 1)
in SR but not
necessarily in
more general
theory
3) Microrealism/MCFD
Can we do without 3)? (i.e. are 1) and 2) alone
sufficient to prove CHSH theorem?)
Involves v. delicate questions concerning definition of
probability…
Anyway, irrespective of this, existing experiments prima
facie imply at least one of 1) – 3) has to go.
⬆: What about “collapse locality” loophole?
Until then, what can we say about the process (?) of
“collapse” (“realization”)?
Note existence of alternative (non-QM) scenarios
(CSL, Penrose…)
⇒ Can we build Schrödinger’s Cat in the lab?
Can we prove CHSH theorem without invoking realism/MCFD?
6
(e.g. N. Gisin, Found. Phys. 42, 80 (2012))
“state of universe”
p ( a, b|x, y ) = ò d l r ( l ) p ( a|x, l ) p ( b|x, l )
measured correlation
“probability of Alice’s outcome a
given setting x and state Y”
⇒ CHSH inequality
⬆: Problem: What does p(a|x,Y)l actually mean?
e.g. if Y
l represents a standard “hidden variable”:
if values of Y
l are discrete and finite in number, can use “frequentist” df.:
p ( a|x, l ) º
N ( a : x, l )
But: what if Y
l is a continuous variable/state description?
N ( x, l )
Macroscopic quantum coherence (MQC)
7
Example: “flux qubit”
Supercond.
ring
time
“Q = +1”
Josephson
junction “Q = +1”
“Q = -1”
ti
macroscopically distinct states
tint
tf
“Q = -1”
Existing experiments: if raw data interpreted in QM
terms, state at tint is quantum superposition (not
mixture!) of states (+) and (--).
⬆: how “macroscopically” distinct?
How “macroscopically distinct” are (notionally) superposed
states of flux qubit?
8
Well, maybe…
+I
dust particle
–I
Q: What is W?
Korsbakken et al. (EPL 89, 30003 (2010)):
Q: How many single electrons do we need to
displace to go from +I to –I? (ans. = “W”)
Ans.: for all flux-qubit expts. to date, WFQ £ 5, 000
“not macroscopic or even mesoscopic”.
A: If we work in terms of indl. “elementary”
particles (inc. nucleons not nuclei!), WDP £ 1, 500 < WFQ .
If we consider nuclei as “elementary”, then WDP ~
105. However, if we do so, then in the flux qubit
case we should consider Cooper pairs as
“elementary” ⇒ WFQ ~ 106 – 107
⇒ either way, states of flux qubit are more
“macroscopically distinct” than those of dust particle!
MQC (cont.)
9
Analog of CHSH theorem for MQC:
Any macrorealistic theory satisfies constraint
In this case, unnatural to assert 2) while denying 3).
2) macrorealism (Q(t) = +1 or -1 for all t)
techniques (and arguable whether states
macroscopically distinct).
NIM cannot be explicitly tested, but can make
Q(t1)Q(t2 ) + Q(t2 )Q(t3 ) + Q(t3 )Q(t4 ) - Q(t1)Q(t4 ) £ 2 “plausible” by ancillary experiment to test whether,
when Q(t) is known to be (e.g.) +1, a noninvasive
which is violated (for appropriate choices of the ti)
measurement does or does not affect subsequent
by the QM predictions for an “ideal” 2-state system
statistics. But measurements must be projective (“von
Definition of “macrorealistic” theory: conjunction of
Neumann”).
1) induction
Existing experiments use “weak-measurement”
3) noninvasive measurability (NIM)
NIM:
measuring
device
If Q = +1, throw away
If Q = -1, keep
Conclusions
10
1. From existing EPR-Bell experiments, must either
a) reject at least one of
induction
locality
MCFD macroscopic counterfactual
definiteness
b) invoke collapse locality loophole.
2. If future long-baseline experiment verifies QM
predictions,
3. If a future MQC experiment with v. N.
measurements verifies QM predictions, must
reject at least one of
induction
macrorealism
NIM non-invasive measurability
4. If result of 3. is QM’l but that of 2. not, raises
question:
Are human “observers” special?
(Wigner’s friend: UIUC experiment)
b) is unviable.
A final thought: is induction (“arrow of time”)
sacred?
QM of human vision
11
Methods:

Two conditions
o Superposition condition: N photons at
(L)
L +(R)
+ R state
L +R
L or R
R
o Mixed condition: N photons each at (L)
L or (R)
with equal probability

Observer judges whether a light was present on
Left and on Right separately

Data analysis
o If the detection rates at L and/or R in the
superposition condition is statistically
different from that of the mixed condition,
then QM is violated.
Superposition condition
Mixed condition