Quantum-optics experiments in Olomouc

Jan Soubusta, Martin Hendrych, Jan Peřina, Jr., Ondřej Haderka

Radim Filip, Jaromír Fiurášek, Miloslav Dušek

Antonín Černoch, Miroslav Gavenda, Eva Kachlíková, Lucie Bartůšková

Palacký University & Institute of Physics of AS CR

Quantum identification system M. Dušek et al, Phys. Rev. A 60, 149 (1999).

830 nm100kHz

Visibility >99.5%Losses < 4.5dB

Rate: 4.3 kbits/sError rate: 0.3%

<1ph.pp0.5 km

• QIS combines classical identification procedure and quantum key distribution.• Dim laser pulses as a carrier of information.

Experiments with entangled photons produced by down-conversion 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

Tr Tr

Bipartite system: 1

Qubits:

1

2

A B A B

A B A B

V

V

V

H V V H

Simple optical measurement of the overlap and fidelity of quantum states

2H

YYXXVVp p 2

1

VHA 2

1

Experimental tests of energy and time quantum correlations in photon pairs

01 2

Entangled state of two photons

produced by a non-linear crystal:

= d ( )

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":

"Program":

1 - Our device can distinguish

21

- Our device cannot distinguish2

d d d

p p p

a H b V

a H b V

HV VH

HH VV

Phase-covariant quantum multimeter

+

Basis in the subspace of equatorial qubits:

Program state determines basis

iH e V

Quantum multimeters – measurement basis determined by a quantum state of a “program register”

Phase-covariant multimeters – success probability independent of

Programmable discriminator of unknown non-orthogonal polarization states of photon

Phase-covariant quantum multimeter

0

24

ddd VbHa

Programmable discriminatorParameters of the polarization states: ellipticity tan and

orientation

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

1 2

2

ma

1 2

x

1 2max,

2

2 2

2 ' '

'( ) ( ) 1

ˆ

( ) ( )2

ˆ max Tr

M S M

M S M S

S

n n

B

n nB

K K

K K

How quantum correlations enhance prediction of complementary measurementsPolarization two-photon mixed states:Werner states with the mixing parameter p.

41 p

p

pB 22max

Theoretical knowledge excess:

)2sin('K

)cos(2K

p

p

TheoreticalBell factor:

p 0.82 0.82BBmaxmax=2.36=2.36

2222 max)'('K)(K B 1)('K)(K 22

p 0.45 0.45BBmaxmax=1.32=1.32

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.

• Encoding transformation:

• Any of the two encoded qubit states can be error-free restored but not both of them simultaneously.

• Decoding projectors:

1 2

1 2

1 2

0 0 0

0 1 1

1 1 2

qubits qutrit

1 1

2 2

1 1 2 2 , 0 0

0 0 1 1 , 2 2

• States of qubits:

• State of qutrit:

• Additional damping factor:

1/ 4, 3 / 4R T

1 2 1 2 1 21 2 4 1 2 4 1 2 4001 ( ) 010 100

f f f f f f f f fT R T R

1 1 2 21 2 1 2 3 4 3 401 10 01 10

f f f f f f f f

4 1/ 3

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. ,

2 2

Fidelity:

fixed (equatorial qubits: = /2)

, 1, 2

cos sin

j in j out in

iin

F j

V e H

Optical implementation of the optimal phase-covariant quantum cloning machine

iV e HV

8020

2080

HH

VV

TR

TR

succ1

385%

p

F

[ / 2]succP 1 2, [ / 2]F F

1 2, [ 0]F F

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