Computational and Nonlinear Quantum Optics CNQO at Strathclyde

1
Computational and Nonlinear Quantum Optics CNQO
at Strathclyde
http//cnqo.phys.strath.ac.uk
Graeme McCartney Kieran Hunter Eng-Kian (Peter)
Tan Nick Whitlock Erika Andersson Sonja
Franke-Arnold Damia Gomila-Villalonga Gordon
Robb Andrew Scroggie Roberta Zambrini Patrik
Ohberg John Jeffers Francesco Papoff Steve
Barnett Willie Firth Gian-Luca Oppo Alain Aspect
(Carnegie prof.)
Quantum information
students
BEC and cold gases
postdocs
Optical angular momentum

Quantum images
lect.
Visiting profs Rodney Loudon, Essex Simon
Phoenix, BT David Pegg, Griffith, Aus Maxi San
Miguel, Palma
prof.
2
Orbital angular momentum of light
OAM detection, mode sorter
OAM for quantum communication
Uncertainty relation for angular momentum and
angular position, minimum-uncertainty states
Sonja Franke-Arnold, Roberta Zambrini, Erika
Andersson, Steve Barnett At Glasgow Uni Jonathan
Leach, Johannes Courtial, Eric Yao, Miles
Padgett, Les Allen
3
(No Transcript)
4
(No Transcript)
5
(No Transcript)
6
BEC and cold gases

• Slow light

• Low-dimensional
• cold gases

• Quantum information
• with cold atoms
• slow light

• Matter flux

• Quantum Hall effect
• in cold gases

• Coherence

• Solitons in BECs

..
Nick Whitlock, Sonja Franke-Arnold, Patrik
Ohberg, John Jeffers, Steve Barnett, Willie
Firth, Alain Aspect, Luis Santos (Hannover)
Experimental First Scottish condensate,
MacBEC, June 24!
http//www.photonics.phys.strath.ac.uk
Craig Garvie, Aidan Arnold, Erling Riis
(Photonics)
7
Quantum images
Optical patterns in non-linear media
Cavity solitons
Optical sprinklers
Control of spatial and temporal disorder in
optical devices
Quantum imaging
Graeme McCartney, Damia Gomila Villalonga, Gordon
Robb, Andrew Scroggie, John Jeffers, Francesco
Papoff, Steve Barnett, Willie Firth, Gian-Luca
Oppo, Maxi San Miguel (Palma de Mallorca)
8
Quantum information
Retrodiction
Generalised measurements
Quantum coding, communication
Implementations of quantum information theory
Experimental realisation of POM measurements!
Non-Markovian master equations
Kieran Hunter, Eng-Kian (Peter) Tan, Erika
Andersson, Andrew Scroggie, John Jeffers,
Stephen Barnett, Erling Riis (exp) Collaborators
and visitors Jim Cresser (Macquarie, Aus), Igor
Jex (Prague), David Pegg (Griffith, Aus), John
Vaccaro and Tony Chefles (Hertfordshire),
Masahide Sasaki (CRL, Japan)
9
Simultaneous measurements of spin, signal
locality, and uncertainty
Erika Andersson, Steve Barnett, and Alain Aspect
University of Strathclyde, Glasgow
Thanks EPSRC, Scottish Executive Education and
Lifelong Learning Department, EU Marie Curie
scheme, Carnegie
Talk in Oxford (Thursday) on quantum
comparison 10
Entanglement and signal locality
EPR-Bohm paradox
Singlet
1 2
-
1 2
Y ( - - - ) ( -
- - )
z z z z
x x x x
L R L R
L R L R
Right and left measurement results
correlated, but this cannot be used to
communicate.
p () 1/2, p (-)1/2.
Measurement on the left particle
L L
1 2
x

• (

x x x x
R RR RR
1 2
z
(
z z z z
RR RR R
r is the same no matter what is done at L!
R
11
Signal locality
Ghirardi, Rimini and Weber, Lett. Nuov. Cim. 27,
293 (1980).
B
U
A
V
L observable independent
of of A only what is done to B.
A
A
No local operation acting on only one of a pair
of systems can change the reduced density matrix
of the other system.
This can be used to derive bounds on quantum
operations!
QM
Signal locality
Bruss, DAriano, Macchiavello, Sacchi PRA 62,
062302 (2000).
12
Simultaneous measurements of spin
Measuring two non-commuting observables at the
same time gives increased uncertainty.
.
.
Measure both A a s and B b s of a S1/2
particle
2 2 2
2 2
DA - 1 - a
s s s
2 2 2
2 2
S1/2
DB - 1 - b
s s s
Reduction in expectation values. Largest possible
a, b?
13
Measurement bound using locality
1 2
-
Singlet
Y ( - - - )
L R L R
On L, measure both A and B .
s s
On R, measure either C or D.
p(A B ) and p(A -B ) have to be independent
of whether C or D is measured to the right.
s s s s
p(A B )p(A B C) p(A B -C)
s s s s s
s
p(A B C) - p(A B -C)
s s s s
1 2
E(A ,C) E(B ,C), where E(A,B)AB.
s s
1 2
Similarly p(A -B ) E(A ,D) - E(B ,D).
s s s s
14
Measurement bound using locality
Adding these two inequalities, we obtain
E(A ,C) E(B ,C) E(A ,D) - E(B ,D) 2.
s s s
s
Very similar to Bell inequality! This is because
we have demanded that probabilities for triples,
e.g. p(A B C), exist.
s s
.
Use E(As,C) - a a c for singlet to obtain
.
.
(a a b b) c (a a - b b) d 2.
Choose c and d to maximise LHS
Final bound
a a b b a a - b b 2.
15
Measurement bound using locality
a a b b a a - b b 2
a a

• diagonals 2
• a, b

b b
The bound has been derived before with POMs
P. Busch, PRD 33, 2253 (1986). P. Busch, M.
Grabowski and P. J. Lahti, Operational Quantum
Physics, Springer-Verlag, Berlin, 1995.
Here we have assumed nothing about how to
describe the measurement!
16
Measurement operators
17
Uncertainty relation

• D2AsD2Bs (1- a22) (1- b22)
• (1-a2) (1-b2) (1-a2) b2(1-2)
• (1-b2) a2(1-2) a2 b2 (1-2) (1-2)

(1-2), (1-2) internal uncertainties
(1-a2) , (1-b2) external
measurement uncertainties
a
a a b b a a - b b 2 can be rewritten as
q
b
(1-a2) (1-b2) a2b2 sin2q .
This is a tight bound on the external
measurement uncertainty!
18
Uncertainty relation
Total uncertainty relation
D2AsD2Bs a2 b2 sin2q (1)2
This is stronger than the Arthurs-Goodman
relation
(PRL 1988)
D2AsD2Bs a2 b2 2 4 a2 b2 sin2q
2.
The difference is that we used a tight bound for
the external measurement uncertainty. The
Heisenberg uncertainty relation is not always
tight!
19
Three observables
a a b b g c a a b b - g c a
a - b b g c a a - b b - g c 4
g c

• diagonals 4
• a, b, g

a a
b b
.
Can also be written
a2 b2 g2 1 a2 b2 (a b)2 ...
If a x, b y, c z, then a2 b2 g2 1.
This means 2 2 2 1/3
for a simultaneous measurement with x,y,z
equally dizzy.
20
Summary

• The locality principle can be used to derive
• bounds on quantum measurements.

• Bound on simultaneous spin measurements
• without measurement operators.

• Uncertainty relations for simultaneous
• measurements of spin tight bound for
• external measurement uncertainty.

Barnett and Andersson, PRA 65, 044307 (2002) for
bound on discrimination between non-orthogonal
states. quant-ph/03? for simultaneous spin
measurements.
Thanks EPSRC, Scottish Executive Education and
Lifelong Learning Department, EU Marie Curie
scheme, Carnegie
Talk in Oxford (Thursday) on quantum
comparison
21
Various bits