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Quantum Cheshire Cats Y. Aharonov, S. Popescu, D. Rohrlich,
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Quantum Cheshire Cats
Y. Aharonov, S. Popescu, D. Rohrlich,P. Skrzypczyk (2012)
Quantum Cheshire Cats
H
Quantum Cheshire Cats
HRL
in2
H
Quantum Cheshire Cats
H
2
VRHLfin
HRL
in2
Quantum weak values
A pre- and post-selected ensemble:
The initial state is
The final state is
in
fin
Quantum weak values
A pre- and post-selected ensemble:
The initial state is
The final state is
in
fin
measure A “weakly”
Quantum weak values
If we measure A “weakly” on an ensemble of systems pre-selected in and post-selected in
, the result is the “weak value” :
Y. Aharonov, D. Albert and L. Vaidman, PRL 60 (1988) 1351
infin
wA
infin
infin
w
AA
Quantum Cheshire Cats
Quantum Cheshire Cats
Quantum Cheshire Cats
“Well! I've often seen a cat without a grin,” thought Alice; “but a grin without a cat! It's the most curious thing I ever saw in all my life!”
Quantum “grin” states
“grin +” (left circularly polarized)
“grin –”(left circularly polarized)
Quantum position states
L R
Quantum Cheshire Cats
H
2
VRHLfin
HRL
in2
Quantum weak values
VRHL
HRL
fin
in
. 1
infin
infin
w
LLLL
The weak value of is
LL
Quantum weak values
VRHL
HRL
fin
in
. 0
infin
infin
w
RRRR
The weak value of isRR
Quantum weak values
VRHL
HRL
fin
in
. 1
infin
infin
w
SS
The weak value of
is
VHHVS
Quantum weak values
So, is the Cat in the Left box?
It sure is!
Quantum weak values
So, is the Cat grinning?
It sure is!
Quantum Cheshire Cat
The Cat in the Left box, and the Cat is grinning. Hence it is obvious, dear Alice, that the Cat is grinning in the Left box!
Quantum Cheshire Cat
The Cat in the Left box, and the Cat is grinning. Hence it is obvious, dear Alice, that the Cat is grinning in the Left box!
Obvious but false: the weak value of
vanishes!
SLL
Quantum weak values
VRHL
HRL
fin
in
. 0
infin
infin
w
SLLSLL
The weak value of
is
VHHVLLSLL
Quantum weak values
VRHL
HRL
fin
in
. 1
infin
infin
w
SRRSRR
The weak value of
is
VHHVRRSRR
Quantum Cheshire Cat
The Cheshire Cat is in the Left box, but there is no net grin in the Left box. On the contrary, the only net grin is in the Right box.
Quantum Cheshire Cat
