Measurements of General Quantum Correlations in
Nuclear Magnetic Resonance Systems
Eduardo Ribeiro deAzevedo
São Paulo
Brazil
UNIVERSITY OF SÃO PAULO - USP
• 75 years
• 240 courses
• 57.000 undergrad students
• ~200 Msc. and PHD programs
UNIVERSITY OF SÃO PAULO AT SÃO CARLOS
São Carlos City:
250.000 people.
5 universities:
1 Federal University (UFSCAR).
1 State Univesity (USP).
3 Private Univesities.
USP at São Carlos:
2 Campi, ~8.000 undergrad students
São Carlos Institute of Physics, USP, Brazil
www.ifsc.usp.br
Al
DC V
ETL
(ionomer)
OC1OC6 - PPV
ITO
glass
emitted
light
IFSC NMR group: Tito Bonagamba,
Eduardo R. deAzevedo
(Solid-State NMR, MRI)
First experiments done in São Carlos using quadrupolar nuclei
First thesis defence in NMR QIP (Fabio A. Bonk at IFSC) and (Juan Bulnes at CBPF)
2012 2010 2009 2007
2003
CBPF NMR group: Ivan Oliveira, Alberto
Passos, Roberto Sarthour, Jair C. C Freitas
(magnetism and magnetic materials)
2005
2002
NMR QIP in Brazil
Publication of the Book Quantum Information Processing by Elsevier
Gather with the quantum information theory group at UFABC – Lucas Celeri and Roberto
Serra.
CBPF NMR spectrometer start to operate.
Hiring of new researchers (Alexandre Souza-CBPF, Diogo Pinto IFSC, João Teles-UFSCAR,
Ruben Auccaise - UEPG ) tend to strenght this researche area.
PEOPLE INVOLVED
Experiments
Isabela Almeida
Ruben Auccaise
Alexandre Souza
Ivan S. Oliveira
Roberto Sarthour
Tito Bonagamba
Theory
Diogo S. Pinto
Lucas Céleri
Roberto Serra
Jonas Maziero
Felipe Fanchini
David Girolami
Gerardo Adesso
F. M. Paula
J. D. Montealegre
A Saguia
Marcelo Sarandy
NMR and the QIP
• Experimental demonstration of QIP procedures, including quantum
protocols, algorithms, quantum simulations etc.;
• Development of many useful tools for QIP, including quantum protocols,
algorithms, dynamic decoupling schemes, among others;
• NMR is also an excellent test bench for studies on open quantum
systems:
– efficient implementation and manipulation of the quantum states
(excellent control of the unitary transformations coming from the
radiofrequency pulses);
– presence of real environments, which can be described by phase
damping and generalized amplitude damping channels;
Quantum Computation
Entanglement
?
• In certain schemes of quantum computation where the quantum
bits are affected by noise, there seems to be a speed-up over
classical scenarios even in the presence of negligibly small or
vanishing entanglement.
Knill, E.; Laflamme, R. Power of one bit of quantum information. Physical Review Letters, v. 81, n. 25, p.
5672, 1998.
Datta, A.; Shaji, A. and Caves. C. M. Physical Review Letters 100, p.050502, 2008.
Modi, K., Paterek, T., Son, W., Vedral, V. and Williamson M. Unified View of Quantum and Classical
Correlations Physical Review Letters, v. 104, p.080501, 2010.
• A possible explanation for the speed up would be quantum
correlations different for entanglement.
General Quantum Correlations
How to detect
them?
Other types of correlations
Quantum Computation
Ollivier, H. & Zurek, W. H. Quantum discord: a measure
of the quantumness of correlations.Phys. Rev.
Lett. 88, 017901 (2001).
Entanglement
?
Merali, Z. Nature,
v. 474, p. 24, 2011.
Classification of Quantum and
Classical States
All Correlated
States
Separable
States
C
CQ
Entangled
States
Separable
 

p ij  i  
A
B
j
ij
Entangled
 

p ij  i  
A
B
j
ij
Classically
Correlated
 

p ij i
i  j
j
ij
 i  , j 
o rto n o rm a l b a s is .
Classification of Quantum and
Classical Two-Qubit States
All Correlated
States
Separable
States
C
CQ
Separable

p ij  i  
A
B
j
ij
Entangled
States
Entangled
 

p ij  i  
A
B
j
ij
Classically
Correlated
• Bell diagonal states:
1
  1 
4
 

 c j j   j 
j 1

 

p ij i
i  j
j
ij
 i  , j 
o rto n o rm a l b a s is .
3
Correlation Matrix:
 c1

C  0

0

0
c2
0
0

0

c 3 
 AB
 1  c3

0
 
 0

 c1  c 2
0
0
1  c3
c1  c 2
c1  c 2
1  c3
0
0
c1  c 2 

0

0 

1  c3 
Classification of Quantum and
Classical States
All Correlated
States
Separable
States
C
Entangled
States
CQ
Separable
1
  1 
4

 c j j   j 
j 1

3

p ij  i  
A
B
j
ij
Entangled
 

p ij  i  
A
B
j
ij
Classically
Correlated
• Bell diagonal states:
 
 

p ij i
i  j
j
ij
 i  , j 
o rto n o rm a l b a s is .
3
cj
1
 1

   
 i   j       
4


j 1 

 4
In this sense NMR seems to be the perfect tool for probing
quantum correlations of separable states and their
interaction with the environment;
NMR sensitive
part of the
density matrix
Quantum Discord
– Entropic Discord*: disturbance made in a system when a
measurement is applied.
Von Neumann Entropy
S (  )   T r (  lo g 2  )
S(ρA)
*Ollivier, H.; Zurek, W. Physical Review Letters, v. 88, n. 1, p. 017901, 2002.
S(ρAB)
S(ρB)
Quantum Discord
– Entropic Discord*: disturbance made in a system when a
measurement is applied.
Von Neumann Entropy
S (  )   T r (  lo g 2  )
S(ρA)
S(ρAB)
S(ρB)
• Mutual information: I   A : B   S   A   S   B   S   A : B 
*Ollivier, H.; Zurek, W. Physical Review Letters, v. 88, n. 1, p. 017901, 2002.
Quantum Discord
– Entropic Discord*: disturbance made in a system when a
measurement is applied.
Von Neumann Entropy
S (  )   T r (  lo g 2  )
S(ρA)
S(ρAB)
S(ρB)
• Mutual information: I   A : B   S   A   S   B   S   A : B 
• Classical Correlation: J Q   A : B   S   A   S
*Ollivier, H.; Zurek, W. Physical Review Letters, v. 88, n. 1, p. 017901, 2002.


B
j
 


A B
Quantum Discord
– Entropic Discord*: disturbance made in a system when a
measurement is applied.
Von Neumann Entropy
S (  )   T r (  lo g 2  )
S(ρA)
S(ρAB)
S(ρB)
• Mutual information: I   A : B   S   A   S   B   S   A : B 
• Classical Correlation: J Q   A : B   S   A   S


B
j
 


A B
• Quantum Discord: D   A B   I   A : B   m ax J Q   A : B 
 
B
j
*Ollivier, H.; Zurek, W. Physical Review Letters, v. 88, n. 1, p. 017901, 2002.
Quantum Discord
– For two-qubits Bell diagonal states*:
c  m ax  c1 , c 2 , c 3
D   AB   I   AB   C   AB 

1
4
  1  c1  c 2  c 3  lo g 2  1  c1  c 2  c 3 
  1  c1  c 2  c 3  lo g 2  1  c1  c 2  c 3 
  1  c1  c 2  c 3  lo g 2  1  c1  c 2  c 3 
  1  c1  c 2  c 3  lo g 2  1  c1  c 2  c 3  

1 c
2
lo g 2  1  c  
1 c
2
lo g 2  1  c 
*Luo, S. Quantum discord for two-qubit systems. Physical Review A, v. 7, n. 4, p. 042303, 2008.

Probing Quantum Correlations
What is required for probing discord and their degradation upon
interaction with the environment?
• To prepare states with different amounts of QCs .
• To perform a reliable read-out of the final states.
• To have a good description and characterization of the system
relaxation.
NMR has all that!!!!
Diogo sets a partnership do study quantum
discord by NMR
with Roberto Serra and Lucas Céleri ;
3/2 spins system
• NMR system.
Sample: Lyotropic Liquid Crystals -Sodium Dodecyl Sulfat
Sodium dodecyl sulfate in (SDS) - Heavy Water (D2O) - Decanol (C10H21OH)
water forming a lyotropic
Q
2
23


H



I

3
I
liquid crystal – Na NMR
L Z
 z  I  I  1 1 
6
Anatoly K. Khitrin and B. M. Fung. The Journal of Chemical
Physics, 112(16):6963–6965, 2000.
Neeraj Sinha, T. S. Mahesh, K. V. Ramanathan, and Anil
Kumar. The Journal of Chemical Physics, 114(10):4415–4420,
2001.
Tools for NMR QIP using
quadrupolar Nuclei
• Strong Modulated Pulase (SMP)*:
k
U SM P 
 U 
n
, n , tn 
n 1
F   t arg et ,  SMP  
Tr   t arg et ,  SMP

 

Tr  t arg et Tr  SMP
2
2

*Fortunato, E.; Pravia, M.; Boulant, N.; Teklemariam, G.; Havel, T.; Cory, D. Design of modulating pulses to
implement precise effective hamiltonians for quantum information processing. Journal of Chemical Physics,
v. 116, n. 17, p. 7599, 2002. Nelder, J.A.; Mead, R. A simplex-method for function minimization. Computer
Journal, v. 7, n. 4, p. 308, 1965.
Single hard pulse
  11

 12
 
  13

  14
  11

 12
 
  13

  14
  11

 12
 
  13

  14
  11

 12
 
  13

  14
 12
 13
 14 
 22
 23
 23
 33
 24
 34


 34 

 44 
 12
 13
 14 
 22
 23
 23
 33
 24
 34


 34 

 44 
 12
 13
 14 
 22
 23
 23
 33
 24
 34


 34 

 44 
 12
 13
 14 
 22
 23
 23
 33
 24
 34
 24
 24
 24


 34 

 44 
 24
Pure quadrupolar
relaxation
+
Redfield Equations
Two Qubit System
• Generalized Amplitude Damping Channel (GAD):
– Longitudinal relaxation (T1)
E1 
E3 
p
1
2

L
2 k BT
1
p
 0

 , E2 
1   
 1 
1 p 
 0
 B  1 e
0
p
0
0
 2 CJ 1 t
0
 , E4 
1
 1 e

 0
p
 


0 
0

0 
t
T1 B
 A  1 e
 2 CJ 2 t
 1 e

t
T1 A
– Global phase damping channel (GPD);
E0 
  11

 12
 
  13

  14
 

2
1
1

0

1 
0

0
 12
 13
 22
 23
 23
 33
 24
 34
1 e
 C J 0t
0
0
1
0
0
1
0
0
0

0
, E 
1
0

1
1

0


0

0
0
0
1
0
0
1
0
0
0

0

0

1
 14 


 34 

 44 
 24

E 0  E 0  E1  E1
†


2

 2


 11
†
 2   1   12  2   1   13
 1   12
 22
 23
 1   13
 23
 33
 14
 2   1   24  2   1   34
 14


 2   1   24 
 2   1   34 

 44





X random
Monotonical
Decay
|
Different amount of
classical and correations
in each state
time (ms)
HOWEVER....
Sudden-Change Phenomena:
• Decoherence Process in Bell-diagonal States:
→ Local Phase Damping Channel:
Mutual Information
Classical Correlation
Entropic Discord
c 3  0   c1  0  e c 2  0 
c3  0   0
Time (s)
*Maziero, J. and et al. Physical Review A, v. 80, p. 044102, 2009.
c 3  0   c1  0  e ou c 2  0 
Sudden-Change Phenomena:
• Decoherence Process in Bell-diagonal States:
→ Phase Damping Channel:
Mutual Information
Classical Correlation
Entropic Discord
c 3  0   c1  0  e c 2  0 
Time (s)
c3  0   0
Time
(s)
*Maziero, J. and et al. Physical Review A, v. 80, p. 044102, 2009.
c 3  0   c1  0  e ou c 2  0 
Sudden-Change Phenomena:
• Decoherence Process in Bell-diagonal States:
→ Phase Damping Channel:
Mutual Information
Classical Correlation
Entropic Discord
c 3  0   c1  0  e c 2  0 
Time (s)
c3  0   0
Time
(s)
*Maziero, J. and et al. Physical Review A, v. 80, p. 044102, 2009.
c 3  0   c1  0  e ou c 2  0 
Time (s)
Sudden-Change Phenomena:
• Decoherence Process in Bell-diagonal States:
→ Phase Damping Channel:
Mutual Information
Classical Correlation
Entropic Discord
c 3  0   c1  0  e c 2  0 
Time (s)
c3  0   0
Time
(s)
*Maziero, J. and et al. Physical Review A, v. 80, p. 044102, 2009.
c 3  0   c1  0  e ou c 2  0 
Time (s)
• Two physical Qubits - NMR representation:
− 2 spins 1/2:
H    L I Z   L S Z  2 JI Z S z
A
B
• Generalized Amplitude Damping Channel:
– Longitudinal relaxation (T1)
E1 

 , E2 
1   
0
 1 
1 p 
 0
E3 
p
1
p
 0
1
2

L
0
 , E4 
1
 
2 k BT
1
2
0
p
0


0 
 0
p
 
1  e
 t T1
Energy exchange
between system
and environment
0

0 

• Phase Damping Channel:
Loss of coherence
without loss of energy
- Transversal relaxation (T2):
E1 
1
 
0
0
 , E2 
1
1
1  
0
0 

 1

1
  1  e
2
t
2 T2





1 0
 
2 0

0
0
0

0
0

0
0
0

0

0


  

1 0
 
2 0

   
0
0
 
  
  
 
0
0
   

0

0 

  
c 3  0   c1  0  e c 2  0 
c 3  0   c1  0  e ou c 2  0 
Mutual information
Mutual information
Classical correlation
Classical correlation
Quantum correlation
Quantum correlation
Geometric Discord
Hilbert-Schmidt distance between the state and the
nearest classical state;
E
D G     2 m in   
 C
ρ
S
2
D
2
Diogo sets a partneship with
Gerardo Adesso
C
*Dakic, B.; Vedral, V.; Brukner, C. Necessary and sufficient condition for nonzero quantum discord.
Physical Review Letters, v. 105, n. 19, p. 190502, 2010. Girolami, D.; Adesso, G. Observable
measure of bipartite quantum correlations. Physical Review Letters, v. 108, n. 15, p. 150403, 2012.
Modi, K. and et al. Unified view of quantum and classical correlations. Physical Review Letters, v.
104, n. 8, p. 080501, 2010.
• 2 q-bits:
1
  1  1 
4
3
 x
i
i 1
D G     2  T r  S   k 1 
3
i
1

i 1

y i 1   i   C ij i   j 
i , j 1

3
• 2 q-bits:
1
  1  1 
4
3
 x
i
3
i
1
i 1
i 1
D G     2  T r  S   k 1 
S 
1
4
xx  C C
t

t

y i 1   i   C ij i   j 
i , j 1

3
• Para um sistema de 2 q-bits:
1
  1  1 
4
3
 x
i
3
i
1
i 1

i 1
D G     2  T r  S   k 1 
k1 
S 
1
4
xx  C C
t
t

y i 1   i   C ij i   j 
i , j 1

3
Tr  S 
3

6T r  S
2
  2T r  S 
3
2
 
cos  
3
• 2 q-bits:
1
  1  1 
4
3
 x
i
3
1
i
i 1

i 1
D G     2  T r  S   k 1 
k1 
1
S 
xx  C C
t

y i 1   i   C ij i   j 
i , j 1

3
Tr  S 

6T r  S
2
3
  2T r  S 
2
3
 
cos  
3
t
4

3

2
3
  arccos  2T r  S   9T r  S  T r  S   9T r  S 



x i  T r     i  1    i  1
y i  T r    1   i   1   i

c ij  T r    i  
j

 
2
 3T r  S
2
i 
  Tr S 

j
2

3





 4 Ii  I j
• Direct Measurement Method:
1
  1  1 
4
3
 x
i
3
i
1
i 1

3
yi1   i 
i 1

i 1

c ij  i   j 

x i  T r     i  1    i  1
NMR Observables
y i  T r    1   i   1   i

c ij  T r    i  
j
 
i 
j
 4 Ii  I j
Convert into a local measurement:
Zero and Double
Quantum
Coherences
and anti-phase
magnetizations
• Direct Measurement Method:
1
  1  1 
4
3
 x
i
3
i
1
i 1

3
yi1   i 
i 1

i 1

c ij  i   j 

x i  T r     i  1    i  1
NMR Observables
y i  T r    1   i   1   i

c ij  T r    i  
j
 
i 
 4 Ii  I j
j
Convert into a local measurement:

T r   i  
j
  T r  
i
Zero and Double
Quantum
Coherences
and anti-phase
magnetizations
 1   ij 
 ij  U ij  U ij , onde U ij  C N O T A  B R ,   ij 
†
i
j
 ij  U ij  U ij , onde U ij  C N O T A  B R ,   ij 
†
i
j
1  x  2  z  3  y
Θ
j/i
1
2
3
1
0
3π/2
π/2
2
3π/2
π/2
- π/2
3
π/2
- π/2
π/2
– Negativity of Quantumness (QNA)*:
Minimum amount of entanglement created between the system
and its measurement apparatus in a local measurement;
Geometric measurement (trace norm);
J. D. Montealegre, F. M. Paula, A. Saguia, and M. S. Sarandy, Phys. Rev. A 87, 042115 (2013).
T. Nakano, M. Piani, and G. Adesso, Phys. Rev. A 88, 012117 (2013).
– Negativity of Quantumness (QNA)*:
Minimum amount of entanglement created between the system
and its measurement apparatus in a local measurement;
Geometric measurement (trace norm);
QN
A
  AB 
1
 m in    ij
B A 2
 i, j
1

 1

• Bell diagonal states:
J. D. Montealegre, F. M. Paula, A. Saguia, and M. S. Sarandy, Phys. Rev. A 87, 042115 (2013).
T. Nakano, M. Piani, and G. Adesso, Phys. Rev. A 88, 012117 (2013).
– Negativity of Quantumness (QNA)*:
Minimum amount of entanglement created between the system
and its measurement apparatus in a local measurement;
Geometric measurement (trace norm);
QN
A
  AB 
1
 m in    ij
B A 2
 i, j
• Bell diagonal states:
QN
A
  AB  
c int
1

 1

1
  1 
4
3
c
j

j

j 1
2
J. D. Montealegre, F. M. Paula, A. Saguia, and M. S. Sarandy, Phys. Rev. A 87, 042115 (2013).
T. Nakano, M. Piani, and G. Adesso, Phys. Rev. A 88, 012117 (2013).
j



• Freezing phenomenon:
– Initial state condition*:
 0  3  1  2 e   0   3   1   2   0
ou  0 1   2  3 e
  0  1    3   2   0
– Eg.: c1 = 1, c2 = -0.2, c3 = 0.2 (λ0 = 0, λ1 = 0, λ2 = 0.6, λ3 = 0.4)
*You, B.; Cen, L-X. Physical Review A, v. 86,
p. 012102, 2012.
• Freezing phenomenon:
c1  t   e
– Initial state condition*:
c2  t   e
 0  3  1  2 e   0   3   1   2   0
ou  0 1   2  3 e
 t
c1  0 
 t
c2  0 
c3  t   c3  0 
  0  1    3   2   0
T2  T2
A
 
B
A
– Eg.: c1 = 1, c2 = -0.2, c3 = 0.2 (λ0 = 0, λ1 = 0, λ2 = 0.6, λ3 = 0.4)
2 DG
DG
*You, B.; Cen, L-X. Physical Review A, v. 86,
p. 012102, 2012.
B
T2 T2
Time (s)
• Generalized Amplitude Damping Channel:
c1  t  
1 a
1   b c1  0 
c2  t  
1 a
1   b c2  0 
c 3  t   1   a  b   a   b  c 3  0 
  1 e
t
T1
• 2 qubits system represented by 2 coupled spins ½:
– Sample: 100 mg of 13C-labeled CHCl3 dissolved
in 0.7 mL CDCl3
– Spectrometer: Varian Premium
Shielded – 11 T
H – 500 MHz, T1 = 9 s, T2 = 1.2 s
C – 125 MHz, T1 = 25 s, T2 = 0.18 s
Acoplamento J – 215.1 Hz
– Initial State: c
1
 0 .5, c 2  0 .0 6 , c 3  0 .2 4
c 3  0   c1  0  e
ou c2  0 
Fidelity = 0.993
• 2 qubits system represented by 2 coupled spins ½:
– Sample: 100 mg of 13C-labeled CHCl3 dissolved
in 0.7 mL CDCl3
– Spectrometer: Varian Premium
Shielded – 11 T
H – 500 MHz, T1 = 9 s, T2 = 1.2 s
C – 125 MHz, T1 = 25 s, T2 = 0.18 s
Acoplamento J – 215.1 Hz
– Initial State: c
1
 0 .5, c 2  0 .0 6 , c 3  0 .2 4
c 3  0   c1  0  e
ou c2  0 
– 1º State:
c1  c 2  c 3  0 .2
c 3  0   c1  0  e c 2  0 
Fidelity = 0.994
– 2º State:
c1  0 .5, c 2  0 .0 6, c 3  0 .2 4
c 3  0   c1  0  e ou c 2  0 
Fidelity = 0.993
• Geometric Discord:
Direct Measurement
Time (s)
Time (s)
Tomography
Theoretical
Time (s)
Time (s)
• Negativity of Quantumness:
(Theoretical)
Time (s)
Time (s)
Time (s)
Time (s)
(Theoretical)
Freezing Universality
(a) Discord (b) Geometric Discord
(c) Trace Distance (d) Bures Distance
Aaronson, B.; Lo Franco, R.; Adesso,
G. Physical Review A, v. 88, p. 012120, 2013.
Preliminary Results
Relaxation Process
Decoherence Channels:
Phase Damping (PD)
Generalized Amplitude Damping (GAD)
• Phase Damping Channel:
Loss of coherence
without loss of energy
Two Qubit System
- Transversal relaxation (T2):
E1 
1
 
0
0
 , E2 
1
1
1  
0
0 

 1

1
  1  e
2
*Souza, A.M. and et al. Quantum Information Computation, v. 10, p. 653, 2010.
t
2 T2



• Phase Damping Channel:
Loss of coherence
without loss of energy
Two Qubit System
- Transversal relaxation (T2):
E1 
1
 
0
0
 , E2 
1
- Global Phase Damping (spin 3/2 system)*:
1

0

E0  1  
0

0
1
CJ t
  1  e

2
0
0
1
0
0
1
0
0
0

0
, E 
1
0

1
1

0


0

0
0
0
1
0
0
1
0
0
0

0

0

1
0
*Souza, A.M. and et al. Quantum Information Computation, v. 10, p. 653, 2010.
1
1  
0
0 

 1

1
  1  e
2
t
2 T2



• Phase Damping Channel:
Loss of coherence
without loss of energy
Two Qubit System
- Transversal relaxation (T2):
E1 
1
 
0
0
 , E2 
1
0
0
0
1
0
0
1
0
0
0

0
, E 
1
0

1
1

0


0

0
0
0
1
0
0
1
0
0
0

0

0

1
0 

 1

1
  1  e
2
- Global Phase Damping (spin 3/2 system)*:
1

0

E0  1  
0

0
1
CJ t
  1  e

2
1
1  
0
  11


 12
  13

  14
*Souza, A.M. and et al. Quantum Information Computation, v. 10, p. 653, 2010.
 12
 13
 22
 23
 23
 33
 24
 34
t
2 T2



 14 

 24

 34 

 44 
• Phase Damping Channel:
Loss of coherence
without loss of energy
Two Qubit System
- Transversal relaxation (T2):
E1 
1
 
0
0
 , E2 
1
0
0
0
1
0
0
1
0
0
0

0
, E 
1
0

1
1

0


0

0
0
0
1
0
0
1
0
0
0

0

0

1
0 

 1

1
  1  e
2
- Global Phase Damping (spin 3/2 system)*:
1

0

E0  1  
0

0
1
CJ t
  1  e

2
1
1  
0
  11


 12
  13

  14
*Souza, A.M. and et al. Quantum Information Computation, v. 10, p. 653, 2010.
 12
 13
 22
 23
 23
 33
 24
 34
t
2 T2



 14 

 24

 34 

 44 
Emergence of the Pointer Basis:
The pointer basis
emerges when
classical correlation
between S and A
becomes constant!*
Decoherence
S
A
Measurement
Collapse of A in some
classical state which is not
altered by decoherence!
Time (s)
J. D. Montealegre, F. M. Paula, A. Saguia, and M. S. Sarandy, Phys. Rev. A 87,
042115 (2013).
E
• Phase Damping Channel:
– 2 spins ½ system
• Generalized Amplitude Damping Channel:
– 3/2 spins system
– Sample: Lyotropic Liquid Crystals
• Sodium Dodecyl Sulfate (SDS)
• Heavy Water (D2O)
• Decanol (C10H21OH)
– Spectrometer: Varian Inova – 8 T
Na – 92 MHz
νQ = 10.4 kHz
AB
T1

1
2C J 1 2 
 11.3 m s
Conclusion
• Differences between representing two qubit systems
with two spins 1/2 coupled and one spin 3/2.
• Effects of phase damping and generalized amplitude
damping channels.
• Experimental observation of Sudden-change,
Freezing, Double Sudden-Change phenomena and the
emergence of Pointer Basis.
Acknowledgments