A document about quantum teleportation is summarized in 3 sentences: Sender Alice wishes to teleport an unknown quantum state to receiver Bob without sending the original particle. This is done by Alice and Bob initially sharing an entangled pair of particles. Alice performs a joint measurement on the unknown state particle and her entangled particle, sends the results to Bob, who uses it to perform a unitary transformation on his particle and recreate the original state. The protocol allows transfer of quantum information between particles in a non-classical way using entanglement and classical communication.

1. Quantum
Teleportation
:- Theory and
experiment
Chithrabhanu
P
Introduction
Quantum
Teleportation
Quantum Teleportation :
Theory and Experiment
Chithrabhanu P
chithrabhanu@prl.res.in
THEPH, PRL

2. Quantum
Teleportation
:- Theory and
experiment
Chithrabhanu
P
Introduction
Quantum
Teleportation
Quantum bits
Bit :- Fundamental unit of classical information {0,1}
Qubit :-Quantum analog to bit.
|ψ = α|0 + β|1 (1)
The state of the qubit is a vector in an two-dimensional
complex vector space. Qutrit, qudit :- 3 and higher
dimensions respectively.
|0 , |1 :- Computational basis states forming orthonormal
basis of the vector space. |α|2 :- Probability that system is
in |0 ; |β|2 :- Probability that system is in |1
Example of qubit states:- Two polarization states { |H ,
|V }, spin states { | ↑ ,| ↓ } etc.

3. Quantum
Teleportation
:- Theory and
experiment
Chithrabhanu
P
Introduction
Quantum
Teleportation
Entanglement
Non local quantum correlation between particles.
A two particle entangled state cannot be written as
product of two single particle states.
Ψ12 = φ1 ⊗ ξ2 (2)
Bell states :- Maximally entangled state of two qubits.
|Ψ±
=
1
√
2
(|0 |1 ± |1 |0 ) (3)
|Φ±
=
1
√
2
(|0 |0 ± |1 |1 ) (4)

4. Quantum
Teleportation
:- Theory and
experiment
Chithrabhanu
P
Introduction
Quantum
Teleportation
Quantum gates
Basic unit of a quantum circuit.
NOT gate { X }
X (α|0 + β|1 ) → α|1 + β|0 (5)
Z gate
Z (α|0 + β|1 ) → α|0 − β|1 (6)
Hadamard gate {H}
H (α|0 + β|1 ) = α
|0 + |1
√
2
+ β
|0 − |1
√
2
(7)
CNOT gate :- Two qubit state. Flips the second qubit
(target) if the first qubit (control) is 1. Similar to XOR
|A, B → |A, B ⊕ A

5. Quantum
Teleportation
:- Theory and
experiment
Chithrabhanu
P
Introduction
Quantum
Teleportation
Quantum gates cont..
Hadamard and CNOT operation to prepare Bell states.
x, y are |0 or |1 logic. βxy - Bell states.
In case of polarization; a half wave plate (HWP), can
perform many single qubit operations by keeping its fast
axis at different angle with respect to the incident
polarization. { 0 → ˆZ, π
4 → ˆX, π
8 → ˆH }
Polarization CNOT :- not trivial. Requires interaction of
two qubits (Zhao et al., PRL 2005; Bao et al., PRL 2007).

6. Quantum
Teleportation
:- Theory and
experiment
Chithrabhanu
P
Introduction
Quantum
Teleportation
Quantum Teleportation
VOLUME 70 29 MARCH l993 NUMBER 13
Teleporting an Unknown Quantum State via Dual Classical and
Einstein-Podolsky-Rosen Channels
Charles H. Bennett, ~ ) Gilles Brassard, ( ) Claude Crepeau, ( ) ( )
Richard Jozsa, ( ) Asher Peres, ~4) and William K. Wootters( )
' IBM Research Division, T.J. watson Research Center, Yorktomn Heights, ¹mYork 10598
( lDepartement IIto, Universite de Montreal, C.P OI28, Su. ccursale "A", Montreal, Quebec, Canada HBC 817
( lLaboratoire d'Informatique de 1'Ecole Normale Superieure, g5 rue d'Ulm, 7M80 Paris CEDEX 05, France~ i
l lDepartment of Physics, Technion Israel In—stitute of Technology, MOOO Haifa, Israel
l lDepartment of Physics, Williams College, Williamstoivn, Massachusetts OIP67
(Received 2 December 1992)
An unknown quantum state ]P) can be disassembled into, then later reconstructed from, purely
classical information and purely nonclassical Einstein-Podolsky-Rosen (EPR) correlations. To do
so the sender, "Alice," and the receiver, "Bob," must prearrange the sharing of an EPR-correlated
pair of particles. Alice makes a joint measurement on her EPR particle and the unknown quantum
system, and sends Bob the classical result of this measurement. Knowing this, Bob can convert the
state of his EPR particle into an exact replica of the unknown state ]P) which Alice destroyed.
PACS numbers: 03.65.Bz, 42.50.Dv, 89.70.+c
The existence of long range correlations between
Einstein-Podolsky-Rosen (EPR) [1] pairs of particles
raises the question of their use for information transfer.
Einstein himself used the word "telepathically" in this
contempt [2]. It is known that instantaneous information
transfer is definitely impossible [3]. Here, we show that
EPR correlations can nevertheless assist in the "telepor-
tation" of an intact quantum state from one place to
another, by a sender who knows neither the state to be
teleported nor the location of the intended receiver.
Suppose one observer, whom we shall call "Alice, " has
been given a quantum system such as a photon or spin-&
particle, prepared in a state ]P) unknown to her, and she
wishes to communicate to another observer, "Bob," suf-
ficient information about the quantum system for him to
make an accurate copy of it. Knowing the state vector
a perfectly accurate copy.
A trivial way for Alice to provide Bob with all the in-
formation in [P) would be to send the particle itself. If she
wants to avoid transferring the original particle, she can
make it.interact unitarily with another system, or "an-
cilla, " initially in a known state ~ap), in such a way that
after the interaction the original particle is left in a stan-
dard state ~Pp) and the ancilla is in an unknown state
]a) containing complete information about ~P). If Al-
ice now sends Bob the ancilla (perhaps technically easier
than sending the original particle), Bob can reverse her
actions to prepare a replica of her original state ~P). This
"spin-exchange measurement" [4] illustrates an essential
feature of quantum information: it can be swapped from
one system to another, but it cannot be duplicated or
"cloned" [5]. In this regard it is quite unlike classical
A non classical transfer of an unknown quantum state
using entanglement.
Sender (Alice) knows neither the state to be teleported
nor the location of the receiver (Bob )

7. Quantum
Teleportation
:- Theory and
experiment
Chithrabhanu
P
Introduction
Quantum
Teleportation
Teleportation protocol
Alice and Bob initially share a pair of entangled particles
(say 2 & 3).
Alice receives the particle with unknown state (say 1) .
Alice does a joint Bell operator measurement on the
unknown state particle and her entangled particle.
Projective measurement. 1 & 2 gets destroyed due to the
measurement.
Alice sends the outcome of her measurement to Bob
through a classical channel.
Bob does a unitary transformation on his particle (particle
3) with respect to Alice’s measurement results.

8. Quantum
Teleportation
:- Theory and
experiment
Chithrabhanu
P
Introduction
Quantum
Teleportation
How teleportation works?
Initially, the unknown state and entangled pair are given by
|φ1 = α|0 + β|1 ; |Ψ−
23 =
1
√
2
(|01 − |10 ) (8)
Total wave function
|Ψ123 = 1√
2
(α|0 + β|1 ) ⊗ (|01 − |10 ) (9)
It can be written as
|Ψ123 = 1√
2
(α|00 12|1 3 − α|01 12|0 3 +
β|10 12|1 3 + β|11 12|0 3) (10)

9. Quantum
Teleportation
:- Theory and
experiment
Chithrabhanu
P
Introduction
Quantum
Teleportation
How teleportation works?
From the Bell states (Eq.3 & Eq.4), we can have
|00 = |Φ+ +|Φ−
√
2
; |11 = |Φ+ −|Φ−
√
2
(11)
|01 = |Ψ+ +|Ψ−
√
2
; |10 = |Ψ+ −|Ψ−
√
2
(12)
Substituting in Eq.10 and rearranging the terms
|Ψ123 =
1
2
{ |Ψ−
12 (−α|0 3 − β|1 3) +
|Ψ+
12 (−α|0 3 + β|1 3) +
|Φ−
12 (α|1 3 + β|0 3) +
|Φ+
12 (α|1 3 − β|0 3)
} (13)

10. Quantum
Teleportation
:- Theory and
experiment
Chithrabhanu
P
Introduction
Quantum
Teleportation
How teleportation works?
Outcome Unitary operator
Ψ− ˆσ0
Ψ+ ˆσ3
Φ− ˆσ1
Φ+ ˆσ3 ˆσ1
In polarization case
ˆσ0 −→ Free space propagation
ˆσ3 −→ HWP in 00
ˆσ1 −→ HWP in π
4

11. Quantum
Teleportation
:- Theory and
experiment
Chithrabhanu
P
Introduction
Quantum
Teleportation
Quantum circuit for teleportation
Single/double lines :- classical/quantum channels.
ˆH ˆCNOT :- Bell state preparation; ˆCNOT
ˆH :- Bell state
projection/detection

12. Quantum
Teleportation
:- Theory and
experiment
Chithrabhanu
P
Introduction
Quantum
Teleportation
Experimental teleportation
Bouwmeester et al.(Nature 1997) demonstrated quantum
teleportation using photons.
Figure: Experimental teleportation- Bouwmeester et al.(1997)

13. Quantum
Teleportation
:- Theory and
experiment
Chithrabhanu
P
Introduction
Quantum
Teleportation
Experimental teleportation
Entangled pair :- parametric down converted photons
Bell projection :- beam splitter and detectors
Figure: Experimental teleportation- Bouwmeester et al.(1997)

14. Quantum
Teleportation
:- Theory and
experiment
Chithrabhanu
P
Introduction
Quantum
Teleportation
Experimental teleportation
Only particles with anti symmetric wave function ( |Ψ− )
will emerge from both ends of beam splitter (Loudon, R.
Coherence and Quantum Optics VI).
Coincidence in detectors f1&f2 only when state is |Ψ−
12 .
Unitary operation :- free space propagation.
Initial state is prepared in +45 (-45) polarization states .
ie 1√
2
(|H ± |V )
PBS differentiate +45 & -45 polarization. Detector on
each port (d1&d2)
A delay is given in photon 2 path.
Delay = 0 - no mixing - f1f2 coincidence 50% - f1f2d1 &
f1f2d2 coincidence 25%

15. Quantum
Teleportation
:- Theory and
experiment
Chithrabhanu
P
Introduction
Quantum
Teleportation
Teleportation results
initial state +45.
Delay 0 - f1f2 coincidence 25% - f1f2d1 coincidence 25% -
f1f2d2 coincidence 0%
Figure: Bouwmeester et al.(1997)
The absence of coincidence corresponding to zero delay
confirms the teleportation.

16. Quantum
Teleportation
:- Theory and
experiment
Chithrabhanu
P
Introduction
Quantum
Teleportation THANK YOU