Experimental Realization of Quantum Teleportation of arbitrary two-qubit state using four qubit cluster state.

1. QUANTUM
TELEPORTATION OF TWO
QUBIT STATE USING FOUR
QUBIT CLUSTER STATE
Guided by:
Prof. P. K. Panigrahi
Rajiuddin Sk
18RS014
Email: rs18rs014@iiserkol.ac.in

2.  Introduction
 What Teleportation is ?
 Need for teleportation
 Cluster state
 Quantum circuit for Teleportation
 Results for Teleportation of different states
 Fidelity calculation
 Advantages of QT
 References
CONTENTS

3. Introduction
In 1993, the idea of teleportation moved out of the realm of
science fiction and into the world of theoretical possibility. The idea
was first expounded by Charles Bennett and his co-workers from
IBM. They confirmed that quantum teleportation was possible, but only
if the original object being teleported was destroyed.
The procedure for teleportation in science fiction varies from
story to story but generally goes as follows:
A device scans the original object to extract all the information
needed to describe it.
A transmitter sends the information to the receiving station to
obtain an exact replica of the original

4. But it fails..?
It violated the Heisenberg’s Uncertainty Principle, according to
which one can’t perform a perfect scan of the object to be teleported.
Because the more accurately an object is scanned, the more it is
disturbed by the scanning process, until one reaches a point where the
object’s original state has been completely disturbed, still without having
extracted enough information to make a perfect exact replica
Therefore, it would seem that a perfect copy cannot be made.

5. Entanglement
In 1998, physicists at the California Institute of Technology
(CalTech ) turned the IBM ideas into reality by successfully teleporting
a photon, a particle of energy that carries light, using a phenomenon
known as
ENTANGLEMENT or EINSTEIN-PODOLSKY-ROSEN (EPR)
EFFECT.
In an entangled state, both particles remain part of
the same quantum system so that whatever you do to
one of them affects the other one in a predictable way.

6. What Teleportation is..??
QUANTUM TELEPORTATION, OR ENTANGLEMENT-ASSISTED
TELEPORTATION, IS A PROCESS BY WHICH A QUBIT (THE BASIC
UNIT OF QUANTUM INFORMATION) CAN BE TRANSMITTED EXACTLY
FROM ONE LOCATION TO ANOTHER, WITHOUT THE QUBIT BEING
TRANSMITTED THROUGH THE INTERVENING SPACE. IT INCLUDES
MAKING AN OBJECT DISINTEGRATE IN ONE PLACE WHILE A
PERFECT REPLICA APPEARS SOMEWHERE ELSE.

7. Need For Teleportation
Various forms of transportation require us to cross a physical
distance, which can take anywhere from minutes to many hours.
Telecommunication
+
Transportation
=
Teleportation

8. Cluster state
In general a N qubit cluster state is represented as,
A four qubit cluster state acting as a quantum channel between
Alice and Bob is as follows,

9. ¤ Quantum circuit of four qubit Cluster state
A cluster state is
highly entangled
state and it is
robust against
decoherence.
A cluster state is
highly entangled
state and it is
robust against
decoherence.

10. Quantum circuit for
Teleportation
The actual quantum circuit used for the teleportation of an arbitrary two-
qubit state using four qubit cluster state in IBM QE processor is shown in
given figure.

11. Teleportation of Bell state
0
10
20
30
40
50
60
|00> |11>
IBM QASM IBM 16
If the unknown state is bell state 1/√2( |00 > +|11 >) which Alice
Wants to send Bob , then the probability of the outcomes measured
by Bob is shown ( in percentage) in given figure

12. Outcomesfor different unknown states
IBM qasm simulator IBM 16 Melbourne
State |00> |01> |10> |11> |00> |01> |10> |11>
|00> 1 0 0 0 0.37 0.27 0.22 0.14
|01> 0 1 0 0 0.22 0.25 0.25 0.28
0 0.46 0.54 0 0.30 0.27 0.23 0.20
|10> 0 0 1 0 0.34 0.23 0.26 0.17
0.46 0 0 0.54 0.37 0.20 0.22 0.21
|11> 0 0 0 1 0.21 0.25 0.24 0.29
Probablity

13. Fidelity
In quantum mechanics notably in quantum information theory,
fidelity is a measure of the "closeness" of two quantum states. It
expresses the probability that one state will pass a test to identify as
the other.
The fidelity is calculated from Bhattacharya coefficient
The Bhattacharyya coefficient is an approximate
measurement of the amount of overlap between two
statistical samples. The coefficient can be used to determine
the relative closeness of the two samples being considered.

14. ¤ Fidelity for different unknown states
State Fidelity
|00> 60.8
|01> 50
|10> 51
70.7
|11> 53.8
74.93

15. Transmission at higher rates.
Secure data transmission.
Can detect eavesdropping.
Transportation becomes much easier.
Reduced cost of transportation.
Accidents will be completely absent.
Faster transportation.
Advantages

16. References
1. Teleportation of two particle state via cluster state, Li Da-Chuang and
Cao Zhuo-Liang, communications in Theoritical physics, volume 47, number 3
2. Z. L. Cao and W. Song , Teleportation of a two particle entangled state via
W class state, Physica A 347, 177(2005)
3. http: research.ibm.com
4. M. Nielsen, and I. Chuang: Quantum Computation and Quantum
Information, Cam-
bridge University Press, 2000.