Title slide

1
Title slide
Quantum information with photons and atoms from
tomography to error correction
C. W. Ellenor, M. Mohseni, S.H. Myrskog, J.K.
Fox, J. S. Lundeen, K. J. Resch, M. W. Mitchell,
and Aephraim M.
Steinberg Dept. of Physics, University of Toronto
2
Acknowledgments
U of T quantum optics laser cooling
group PDF Morgan Mitchell Optics
Kevin Resch (? Wien) Jeff Lundeen Chris
Ellenor (? Korea) Masoud Mohseni Reza Mir (?
Lidar) Atom Traps Stefan Myrskog Jalani
Fox Ana Jofre Mirco Siercke Salvatore
Maone Samansa Maneshi TBA Rob
Adamson Theory friends Daniel Lidar, Janos
Bergou, John Sipe, Paul Brumer, Howard Wiseman
3
OUTLINE

• Introduction
• Photons and atoms are promising for QI.
• Need for real-world process characterisation
• and tailored error correction.
• No time to say more.
• Quantum process tomography on entangled photon
  pairs
• - E.g., quality control for Bell-state filters.
• - Input data for tailored Quantum Error
  Correction.
• An experimental application of decoherence-free
• subspaces in a quantum computation.
• Quantum state (and process?) tomography on
• center-of-mass states of atoms in optical
  lattices.
• Coming attractions

4
Density matrices and superoperators
5
Two-photon Process Tomography
Two waveplates per photon for state preparation
Detector A
HWP
HWP
PBS
QWP
QWP
SPDC source
QWP
QWP
PBS
HWP
HWP
Detector B
Argon Ion Laser
Two waveplates per photon for state analysis
6
Hong-Ou-Mandel Interference
gt 85 visibility for HH and VV polarizations
HOM acts as a filter for the Bell state ??
(HV-VH)/v2
Goal Use Quantum Process Tomography to find the
superoperator which takes ?in ? ?out Characterize
the action (and imperfections) of the Bell- State
filter.
7
Measuring the superoperator
Coincidencences
Output DM Input

HH



16 input states
HV
etc.
VV
16 analyzer settings
VH
8
Measuring the superoperator
Superoperator
Input Output DM
HH
HV
VV
VH
Output
Input
etc.
9
Measuring the superoperator
Superoperator
Input Output DM
HH
HV
VV
VH
Output
Input
etc.
10
Testing the superoperator
LL input state
Predicted
Nphotons 297 14
11
Testing the superoperator
LL input state
Predicted
Nphotons 297 14
Observed
Nphotons 314
12
So, How's Our Singlet State Filter?
13
Model of real-world beamsplitter
Singlet filter
multi-layer dielectric
AR coating
45 unpolarized 50/50 dielectric beamsplitter
at 702 nm (CVI Laser)
birefringent element singlet-state
filter birefringent element
14
Model beamsplitter predicitons
Singlet filter
Best Fit
?1 0.76 p ?2 0.80 p
Predicted
15
Comparison to measured Superop
Observed
Predicted
Predicted
16
Performing a quantum computation in a
decoherence-free subspace
The Deutsch-Jozsa algorithm
Oracle
A
A
H
x
x
H
y
H
We use a four-rail representation of our two
physical qubits and encode the logical states
00, 01, 10 and 11 by a photon traveling down one
of four optical rails numbered 1, 2, 3 and 4,
respectively.
Photon number basis
Computational basis
1
1st qubit
2nd qubit
2
3
4
17
Error model and decoherence-free subspaces
Consider a source of dephasing which acts
symmetrically on states 01 and 10 (rails 2 and 3)
Modified Deutsch-Jozsa Quantum Circuit
H
x
x
H
y
y
f(x)
H
18
DJ experimental setup
Experimental Setup
1
2
1
3
4
23
2
Preparation
3
4
Oracle
3/4
B
Optional swap for choice of encoding
D
Phase Shifter
4/3
C
A
PBS
Detector
Waveplate
Mirror
19
DJ without noise -- raw data
Original encoding
DFS Encoding
C
B
C
C
C
B
B
B
20
DJ with noise-- results
21
Tomography in Optical Lattices
Part I measuring state populations in a lattice
22
Houston, we have separation!
23
Quantum state reconstruction
p
p
??x
???t
x
x
Initial phase- space distribution
Wait
Shift
p
Q(0,0) Pg
x
Measure ground state population
(More recently direct density-matrix
reconstruction)
24
Quasi-Q (Pg versus shift) for a 2-state lattice
with 80 in upper state.
25
Exp't"W" or Pg-Pe(x,p)
26
W(x,p) for 80 excitation
27
Coming attractions

• A "two-photon switch" using quantum enhancement
  of
• two-photon nonlinearities for
• - Hardy's Paradox (and weak measurements)
• - Bell-state determination and quantum dense
  coding(?)
• Optimal state discrimination/filtering (w/
  Bergou, Hillery)
• The quantum 3-box problem (and weak
  measurements)
• Process tomography in the optical lattice
• - applying tomography to tailored Q. error
  correction
• Welcher-Weg experiments (and weak measurements,
  w/ Wiseman)
• Coherent control in optical lattices (w/ Brumer)
• Exchange-effect enhancement of 2x1-photon
  absorption
• (w/
  Sipe, after Franson)
• Tunneling-induced coherence in optical lattices
• Transient anomalous momentum distributions (w/
  Muga)
• Probing tunneling atoms (and weak measurements)
• 
  et cetera

28
Schematic of DJ
Schematic diagram of D-J interferometer
1
2
3
4
Oracle
1
00
2
01
3
10
4
11
1
2
3
4
Click at either det. 1 or det. 2 (i.e., qubit 1
low) indicates a constant function each looks at
an interferometer comparing the two halves of the
oracle.
29
Quantum state reconstruction
Wait
Shift
Initial phase- space distribution
Measure ground state population
30
Q(x,p) for a coherent H.O. state
31
Theory for 80/20 mix of e and g