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Quantum-optics experiments in Olomouc
Palacký University & Institute of Physics of AS CR
Jan Soubusta, Martin Hendrych, Jan Peřina, Jr., Ondřej Haderka
Antonín Černoch, Miroslav Gavenda, Eva Kachlíková, Lucie Bartůšková
Radim Filip, Jaromír Fiurášek, Miloslav Dušek
Quantum identification system

M. Dušek et al, Phys. Rev. A 60, 149 (1999).
• QIS combines classical identification
procedure and quantum key distribution.
• Dim laser pulses as a carrier of
information.
830 nm
100kHz
Rate: 4.3 kbits/s
Error rate: 0.3%
Visibility >99.5%
Losses < 4.5dB
<1ph.pp
0.5 km
Experiments with entangled photons produced by downconversion in non-linear crystal pumped by Kr+laser




M. Hendrych et al, Simple optical measurement of the overlap and
fidelity of quantum states, Phys. Lett. A 310, 95 (2003).
J. Soubusta et al, Experimental verification of energy correlations in
entangled photon pairs, Phys. Lett. A 319, 251 (2003).
J. Soubusta et al, Experimental realization of a programmable
quantum-state discriminator and a phase-covariant quantum
multimeter, Phys. Rev. A 69, 052321 (2004).
R. Filip et al, How quantum correlations enhance prediction of
complementary measurements, Phys. Rev. Lett. 93, 180404 (2004).
Simple optical measurement
of the overlap and fidelity
of quantum states
V      
Tr V  A   B   Tr   A  B 
V    


Bipartite system:     1
Qubits:       



1

H
2
A
V
B
V
A
H
B

Simple optical measurement
of the overlap and fidelity
of quantum states
H 
2
  p V V  12p  X X  Y Y
A 

1
2
H
V

Experimental tests of energy and time
quantum correlations in photon pairs
Entangled state of two photons
produced by a non-linear crystal:
 =  d  ( ) 
1
0  
2
Experimental tests of energy and time
quantum correlations in photon pairs
2nd order interference.
Reduction of the spectrum induces
prolongation of the coherence length.
Geometric filtering (FWHM=5.3 nm).
Narrow band interference filter (FWHM
of 1.8 nm). Fabry-Perot rezonator.
4th order interference.
Hong-Ou-Mandel
interference dip
Programmable quantum-state discriminator
"Data":
d  a H d  b Vd
"Program":  p  a H p  b V p



1

HV  VH

2
1

HH  VV

2

- Our device can distinguish

- Our device cannot distinguish
Phase-covariant quantum multimeter
Quantum multimeters – measurement basis
determined by a quantum state of a “program
register”
Basis in the subspace of equatorial qubits:
   H  ei V
Program state  + determines basis
Phase-covariant multimeters – success
probability independent of 
 Programmable discriminator of unknown
non-orthogonal polarization states of photon
 Phase-covariant quantum multimeter
Programmable discriminator
Parameters of the polarization states: ellipticity tan  and
orientation 
  0
  24
d  a H d  b Vd
Phase-covariant quantum multimeter
How quantum correlations enhance prediction of
complementary measurements
The measurement on the one of two correlated particles give us the power of prediction of the
measurement results on the other one. Of course, one can never predict exactly the results of
two complementary measurements at once. However, knowing what kind of measurement we
want to predict on signal particle, we can choose the optimal measurement on the meter
particle. But there is still a fundamental limitation given by the sort and amount of correlations
between the particles. Both of these kinds of constraints are quantitatively expressed by our
inequality. The limitation stemming from mutual correlation of particles manifests itself by the
maximal Bell factor appearing in the inequality. We have proved this inequality theoretically as
well as tested it experimentally
K 2 ( M   S )  K 2 ( M   'S )  1
Bmax 

K ( M   S )  K ( M   S )  

 2 
2
2
'
'
Bmax  max Tr   n1  ˆ1  n2  ˆ 2 
n ,n
1
2
2
How quantum correlations enhance prediction of
complementary measurements
Polarization two-photon mixed states:
Werner states with the mixing parameter p.
p   
1 p

4
Theoretical
Bell factor:
Bmax  2 2 p
Theoretical
knowledge excess:
K  p cos(2  )
K '  p sin( 2 )
K ( )  K ' ( )  1
2
p  0.82
Bmax=2.36
p  0.45
Bmax=1.32
2
K ( )  K ' ( ' ) 
2
2
 
Bmax 2
2
Optical implementation of the encoding of two qubits
into a single qutrit
• A qutrit in a pure state is specified by four real numbers. The same
number of parameters is necessary to specify two qubits in a pure
product state.
qubits
qutrit
• Encoding transformation:
0
1
02 0
01121
11 12  2
• Any of the two encoded qubit states can be error-free restored but not
both of them simultaneously.
• Decoding projectors:
1  1 1  2 2 ,
1  0 0
 2  0 0  1 1 ,
 2  2 2
• States of qubits: 1 01

• State of qutrit:
f1f 2
T 1 2 001
 1 10
f1f 2 f 4
f1f 2
   2 01
 
 ( R  T )12 010
R  1/ 4,
• Additional damping factor:
f 3f 4
f1f 2 f 4
T  3/ 4
4  1/ 3
 2 10
f 3f 4


 R12 100
f1f 2 f 4
Observed fidelities of reconstructed qubit states forvarious input states.
Optical implementation of the optimal phase-covariant
quantum cloning machine
• Exact copying of unknown quantum states is forbidden by the linearity of
quantum mechanics.
•Approximate cloning machines are possible and many implementations for
qubits, qudits and continuous variables were recently designed.
• If the qubit states lie exclusively on the equator of the Bloch sphere, then
the optimal phase-covariant cloner exhibits better cloning fidelity than the
universal cloning machine.
Fidelity: Fj     in  j ,out  in ,
 in  cos

2
i
V  e sin

2
H
 fixed (equatorial qubits:  = /2)
j  1, 2
Optical implementation of the optimal phase-covariant
quantum cloning machine
RV TV  80 20
RH TH  20 80
V
psucc  1
V  ei H
3
F  85%
F1   , F2   [   / 2]
F1   , F2   [  0]
Psucc   [   / 2]
Another approach to optical implementation of
phase-covariant clonning
fiber
Polarization-dependent loses
Correction of noise and distorsions of quantum
signals sent through imperfect
Other cooperating groups
•
•
Experimental multi-photon-resolving detector using a single
avalanche photodiode
Study of spatial correlations and photon statistics in twin beams
generated by down conversion pumped by a pulsed laser
The End