quantum entanglement - Univerza v Ljubljani

University of Ljubljana
Faculty of Mathematics and Physics
QUANTUM ENTANGLEMENT
Seminar
Jure Koncilija
Mentor: doc. dr. Irena Drevenšek - Olenik
Abstract
Quantum entanglement is a physical resource, like energy, associated with the peculiar
nonclassical correlations that are possible between separated quantum systems.
Entanglement can be measured, transformed, and purified. A pair of quantum systems in
an entangled state can be used as a quantum information channel to perform
computational and cryptographic tasks that are impossible in classical systems. In this
seminar I will describe two and multi particle entangled states and the possibilities that
this states bring to quantum information technologies.
September 2005

Contents
1. Introduction 3
2. Quantum information 4
2.1. Quantum superposition 4
2.2. Qubit 4
2.3. Single-Qubit transformations 5
2.4. Entanglement 6
2.5. The EPR argument and Bell's inequality 7
3. Quantum entanglement 9
3.1. Entangled pair 9
3.2. Producing quantum entangled states 9
3.3. Generation of correlated photon pairs in type-II parametric down-conversion 10
3.4. Multi photon entanglement 12
4. Quantum dense coding 13
4.1. Quantum dense coding protocol 13
4.2. Experimental dense coding with qubits 14
5. Conclusion 16
6. References 17
2

1. Introduction
One hundred years ago Albert Einstein introduced the concept of the photon.
Although in the early years after 1905 the evidence for quantum nature of light was not
compelling, modern experiments, especially those using photon pairs, have beautifully
confirmed its corpuscular character. Research on the quantum properties of light
(quantum optics) triggered the evolution of the whole field of quantum information
processing, which now promises new technology, such as quantum cryptography and
even quantum computers [1].
Although Einstein was one of the creators of quantum theory, he never liked all of
its implications. In particular, he simply could not accept the idea that randomness should
be an inherent principle of nature. He felt that the theory did not and could not explain
why quantum effects should appear random to us. He revealed all his doubts in a paper
written together with B. Podolsky and N. Rosen entitled "Can quantum-mechanical
description of physics reality be considered complete?" In their paper, EPR argued that
description of nature should obey the following two properties. First, anything that
happens here and now can influence the result of a measurement elsewhere, but only if
enough time has elapsed for a signal to get there without traveling faster than the speed of
light. Second, the result of a measurement is predetermined, particularly if one can
predict it with complete certainty (in other words a result is fixed even if we do not carry
out the measurement itself). Afterwards they examined what impact would these two
conditions have on observations of quantum particles that had previously interacted with
one another. They concluded that such particles would exhibit correlations that lead to
contradictions with Heisenberg's uncertainty principle.
In the same year of 1935 Erwin Schrödinger published a response to the EPR
paper, in which he introduced the notion of "entanglement" to describe such quantum
correlations. He said that entanglement was the essence of quantum mechanics and that it
illustrated the difference between the quantum and classical worlds in the most
pronounced way. Schrödinger realized that two entangled particles have to be seen as a
whole, rather than as two separate entities. [2]
After that the studies of entanglement paused for thirty years until John Bell's
reconsideration and extension of the EPR argument [1]. Bell looked at entanglement in
simpler systems, matching correlations between two-valued dynamical quantities, such as
polarization or spin, of two separated systems in an entangled states. His investigation
generated an ongoing debate on the foundations of quantum mechanics. One important
feature of this debate was confirmation that entanglement can persist over long distances.
[2] But it was yet in the 1980s that physicists, computer scientists and cryptographers
began to regard the non-local correlations of entangled quantum states, which have
become an important part of quantum information processing and quantum computations.
Physicists nowadays are making great efforts to entangle as many particles as possible
and in 2004 a group of scientist lead by Jian Wei Pan succeeded in entangling five
photons [5]. Although four photons had been entangled before, this was a great
breakthrough because five is the minimum number needed for universal error correction
in quantum computation [4].
3

2. Quantum information
2.1. Quantum superposition
The superposition principle plays the most central role in all considerations of
quantum information. The essential experiment to describe the superposition is the
double-slit experiment. It is composed of a source, a double-slit assembly, and an
observation screen on which we observe the interference fringes. The interference fringes
may easily be understood on the basis of assuming a wave property of the particles
emerging from the source.
Figure 1: The double slit experiment [3]
Quantum mechanically, the state is the coherent superposition:
1
ψ = ( ψa + ψb
) (1)
2
where ψ a and ψ b describe the quantum state with only slit a or slit b open. The
interesting feature in quantum double-slit experiment is the observation that the
interference pattern can be collected one by one (one particle interferes with itself), and
that it is impossible of knowing which of the two slits a particle really takes in the
experiment. Any kind of experiment determining this information (we would need to
interact with the particle) would lead to decoherence - loss of interference.
2.2. Qubit
The most fundamental entity in information science is the bit. This is a system
that carries two possible values: "0" and "1", which determine two distinguished states.
No spontaneous transition can occur between the two states.
The quantum analog of a bit, the qubit, therefore also has to be a two-state system
where the two states are simply called 0 and 1 . Basically any quantum system that
has at least two states can serve as a qubit 1 . The most essential property of quantum
1 A two-state quantum system, that can be used as a qubit is for example spin. We distinguish to opposite
spin states: up ↑ and down ↓ .
4

states, when used to encode bits, is the possibility of coherence and superposition, the
general state being:
Q = α 0 + β 1
(2)
with
probability
2 2
α + β = 1.
This means that if we measure the qubit, we will find it with
2
2
α to carry the value "0" and with probability β to carry the value "1". It
is important to know that eq. (2) describes a coherent superposition rather than incoherent
mixture between "0" and "1". For a coherent superposition there is always a basis in
which the value of the qubit is well defined (as shown in further example), while for an
incoherent mixture it is a mixture whatever way we choose to describe it. Let us consider
a specific state
1
Q′ = ( 0 + 1 ) (3)
2
This clearly means that with 50% probability the qubit will be found to be rather "0" or
"1". Interestingly in basis rotated for 45 in Hilbert space the value of the qubit is well
defined. One of the most basic transformations in quantum information science is
Hadamard transformation ( ):
°
ˆH
ˆ 1 ˆ 1
H 0 0 1 , H 1 0
2 2
→ ( + ) → ( − )
1 (4)
Applying this to the qubit Q′ above, results in ˆ HQ′ = 0 , a well defined state, which
is never possible with an incoherent mixture.
2.3. Single-Qubit transformations
Insight of some basic experimental procedures in quantum information physics
can be gained by investigating the action of a simple 50/50 beamsplitter. Let us
investigate the case of just two incoming modes and two outgoing modes.
Figure 2: The 50/50 beamsplitter [3]
The effect of such a BS (beamsplitter) on an ingoing - incident state Q = 0 is the
in in
final state Q = 1
2 ( 0 + 1 ), and on an ingoing state Q = 1 the final state is
out
in in
5

(
Q = 1 0 − 1
2 ). For a 50/50 BS, a particle incident either from above or from
out
below has the same probability of 50% of emerging in either output beam, above or
below. The beamsplitter is non-absorbing. A very simple way to describe the action of a
beamsplitter is by the Hadamard transformation eq. (4). The incident state is in general
Q = α 0 + β 1 . Then the action of the beamsplitter results in the final state:
in in in
1
Q = Hˆ Q = ( ( α + β) 0 + ( α − β)
1
out in out out ) (5)
2
where ( α + β ) is now the probability amplitude for finding the particle in the outgoing
upper beam and (α − β ) is the probability amplitude for finding it in the lower beam. It is
interesting and instructive to consider sequences of such beamsplitters because they
realize sequences of Hadamard transformations. The double application of Hadamard
Q = Hˆ Hˆ Q = Q .
transformation is the identity operation ( )
out in in
Another important quantum gate besides the Hadamard gate is the phase shifter,
which is introduced into the double beamslitter sequence:
Figure 3: Double beamslitter sequence including a phase shifter in one of the two beams [3]
Its operation is simply to introduce a phase change ϕ to the amplitude of one of the two
beams. The action can be described as: Φ ˆ i
0 = e 0 , Φ ˆ 1 = 1 . The output qubit can be
ϕ
calculated as: Q = HˆΦ ˆ Hˆ Q . For example let us take the input qubit ( α = 1, β = 0 )
out in
Q = 0 . The final state becomes:
in
ˆ ˆ ˆ 1 iϕ iϕ
HΦ H 0 = ( ( e + 1) 0 + ( e − 1) 1 ) (6)
2
This means that the phase shift is able to switch the output qubit between "0" and "1".
For instatnce, if one arranges ϕ = π then the state 0 is transferred to in ( − 1 out ) .
2.4. Entanglement
Let us consider a source which emits a pair of particles such that one particle
emerges to the left and the other to the right . The source is such that the particles are
emitted with opposite momenta.
6

Figure 4: A two particle interferometer verification:
source S emits two qubits in an entangled state [3]
If the particle emerging to the left, which we call particle 1, is found in the upper beam,
then the particle 2 traveling to the right is always found in the lower beam and vice versa.
In qubit language we would say that the two particles carry different bit values. Quantum
1 i
0 1 e 1 0
2 χ
+ .
mechanically this is a two-particle superposition state of the form ( )
The phase χ is determined by the internal properties of the source and we assume for
simplicity 0
χ = . The entangled state is therefore described as:
1
Φ = ( 0 1 + 1 0 ) (7)
2
Interesting property is that neither of the two qubits carries a definite value, but what is
known from quantum state is that as soon as one of the two qubits is subject to a
measurement, the result of this measurement being completely random, the other one will
immediately be found to carry the opposite value. This phenomenon represents the
quantum non-locality, since the two qubits could be separated by arbitrary distances at
the time of the measurement.
2.5. The EPR argument and Bell's inequality
Immediately after the discovery of modern quantum mechanics, it was realized
that it contains novel, counterintuitive features. While Einstein initially tried to argue that
quantum mechanics is inconsistent, he later reformulated his argument towards
demonstrating that quantum mechanics is incomplete. In the seminal paper, EPR consider
quantum systems consisting of two particles such that, while neither position nor
momentum of either particle is well defined, the sum of their positions (that is the centre
of mass) and the difference of their momenta (that is their individual momenta in the
centre of mass system) are both precisely defined. It then follows that a measurement of
either position or momentum performed on, say, particle 1 immediately implies a precise
position or momentum, respectively, for particle 2, without interacting with that particle.
Assuming that the two particles can be separated by arbitrary distances, EPR suggests
that a measurement on particle 1 cannot have any actual influence on particle 2 (locality
condition); thus the property of particle 2 must be independent of the measurement
performed on particle 1. It follows that both position and momentum can simultaneously
be well defined properties of a quantum system [3].
7

In 1951 David Bohm introduced spin-entangled systems and in 1964 John Bell
showed that, for such entangled systems, measurements of correlated quantities should
yield different results in the quantum mechanical case to those expected if one assumes
that the properties of the system measured prior to, and independent of, the observation.
Let us briefly present the line of reasoning that leads to an inequality equivalent to
the original Bell inequality. Consider a source emitting two qubits in the polarisation
entangled state eq. (7). Such a state can be obtained from a decaying atom of cesium,
which emits two photons in opposite directions. The photons are circularly polarised one
right and the other left. The emitting process therefore conserves both the momentum and
the angular momentum of the cesium atom.
Figure 5: Correlation measurement experiment [3]
One qubit is sent to Alice (to the left in Fig. 5), the other is sent to Bob (to the right). On
both sides the polarisation measurements are made using polarising beamsplitter with two
single-photon detectors in the output ports. Alice will obtain the measurement result "0"
or "1", corresponding to the detection of a qubit by detector D1 or D2 respectively, each
with equal probability. This statement is valid in whatever polarisation basis she decides
to perform the measurement, the actual results being completely random. Yet, if Bob
chooses the same basis as Alice, he will always obtain the same result as Alice.
Following the first step of EPR reasoning, Alice can predict with certainty, what Bob's
result will be. The second step employs the locality hypothesis - the assumption that no
physical influence can instantly go from Alice's apparatus to Bob's, therefore his
measured result should only depend on the properties of his qubit and on the apparatus he
chose. Combining the two steps, J. Bell investigated possible correlations for the case that
Alice and Bob choose detection bases which are at oblique angles. For three arbitrary
angular orientations α, βγ , (used by Alice and Bob in different combinations) the
following inequality must be fulfilled:
N(1 ,1 ) ≤ N(1 ,1 ) + N(1
, 0 )
(8)
α β α γ β γ
N0
2
where N(1 α,1 β) = cos ( α − β )
2
2 is the quantum-mechanical prediction for the number
of cases where Alice obtains "1" with her apparatus at orientation α and Bob achieves
"1" with orientation β and N0
is the number of pairs emitted by the source. The
inequality is violated by the quantum-mechanical prediction if we choose, for example
2 The first value in the brackets always belongs to Alice's measurement and the second to Bob's
measurement.
8

( α − β) = ( β − γ)
= 30
. The violation implies that at least one of the assumptions
entering Bell's inequality must be in conflict with Quantum mechanics. This is usually
viewed as evidence for non-locality [3].
3. Quantum entanglement
3.1. Entangled pair
Quantum entanglement is a physical resource, like energy, associated with the
peculiar nonclassical correlations that are possible between separated quantum systems.
Entanglement can be defined on any two-valued dynamical quantity that a par of particles
posses. The most common is the entanglement on the level of spin or polarization. There
are many natural sources of entangled pairs. A very simple example is a pion which has
no spin. When the pion decays it splits into two photons that shoot away in opposite
directions. These two photons have spin. If we measure the spin value of one photon we
instantaneously know the spin value of the other because their spin has to add up into no
spin - that pion has in the first place. Such pairs of photons or other particles are called
entangled pairs.
3.2. Producing quantum entangled states
In order to understand both the nature of entanglement and ways of producing it,
one has to realize that in states of form eq. (7) we have a superposition between product
states. As we know, superposition means that there is no way to tell which of the two
possibilities forming the superposition actually pertains. This rule must also be applied to
1
Ψ = 0 1 + 1 0
the understanding of quantum entanglement. In the state ( )
2
12 1 2 1 2
there is no way of telling whether qubit 1 carries the value "0" or "1" and likewise
whether qubit 2 carries value "0" or "1". Yet, if one qubit is measured the other one
immediately assumes a well-defined quantum state.
To produce entangled quantum states, one has various possibilities. First, one can
create a source which, through its physical construction, is such that the quantum states
emerging already have the indistinguishibility feature discussed above. This is realized,
for example, by the decay of a spin-0 particle into two spin- 1 2 particles under
conservation of the internal angular momentum. In this case, thee two spins of the
emerging particles have to be opposite and, if no further mechanism exist which permits
us to distinguish the possibilities right at the source, the emerging quantum state is:
where
( )
1
Ψ = ↑ ↓ − ↓ ↑ (9)
12 1 2 1 2
2
↑ means particle 1 with spin up. This state has the remarkable property that it is
1
rotationally invariant: the two spins are anti-parallel along whichever direction we choose
to measure.
9

A second possibility is that a source might actually produce quantum states of the
1
form of the individual components in the superposition Ψ = 12 ( 0 1 + 1 0
1 2 1 2 ) .
2
But the states might still be distinguished in some way. This happens, for example, in
type-II parametric down-conversion 3 (see reference [9] for detailed description), where
along a certain chosen direction the two emerging photon states are H V and
1 2
V H . That means that either photon 1 is horizontally polarized and photon 2 is
1 2
vertically polarized, or vice versa. Because of the different speeds of light for the H and
V polarized photon inside down-conversion crystal, the time correlation between the two
photons is different in the two cases. However the entaglement can be produced by
shifting the two photon-wave packets after their production relative to each other such
that they become indistinguishable on the basis of their position in time. The entangled
state for this case can be written as:
1
iϕ
Ψ = 12 ( H V + e V H
1 2 1 2 ) (10)
2
A third means of producing entangled states is to project a non-entangled state
onto an entangled one. Consider a source producing the non-entangled state 0 1 . 1 2
Suppose this state is now sent through filter described by the projection operator
P =Ψ 12 Ψ , where 12 Ψ is in the state of eq. (7):
12
( 0 1 )
P =
1 2
1
= ( 0
2
1 + 1 0 )( 0 1 + 1 0 ) 0 1
1
= ( 0 1 2
1 + 1 2 1 0 2)
1 2 1 2 1 2 1 2 1 2
The state is no longer normalized to unity because the projection procedure implies a loss
of qubits.
3.3. Generation of correlated photon pairs in type-II parametric downconversion
Most commonly used way to produce entangled pairs is parametric down
conversion. The basic optical configuration used for this process is shown in Fig. 6.
3
type-II parametric down-conversion: a nonlinear crystal splits incoming photons into pairs of photons
of lower energy whose combined energy
and momentum is equal to the energy and momentum of the
original photon: k = k + k
ω = ω + ω . "Parametric" refers to the fact that the state of the
ω ω
in
1
ω and
2 in 1 2
crystal is left unchanged in the process, which is why energy and momentum are conserved. Type-II means
that the phase-matching condition is noncolinear.
=
(11)
10

Figure 6: left: geometrical arrangement for type-II parametric down-conversion [9]
right: the two rings of type-II down-conversion as seen through a narrow-band filter[3]
A pump beam enters a nonlinear optical crystal as an extraordinary beam, and is partially
converted into pairs of photons, obeying energy and momentum conservation. The two
photons in a pair created in this process using the type-II phase-matching condition are
always orthogonally polarised [9]. At certain angles between the pump-beam and the
optical axis of the conversion crystal the phase-matching conditions will be such that the
photons are emitted along cones, which do not have common axis (as illustrated in fig. 6)
One of the cones is ordinarily polarised (idler) and the other extraordinarily (signal). This
cones will in generally intersect along two directions where the emitted light is
unpolarised, because we cannot distinguish whether a certain photon belongs to one or
the other cone. Yet this is not exactly true, because in the crystal the e-polarised and opolarised
photons will propagate with different velocities, so in principle we can
distinguish the two cases by the order of their detection times. It is however possible to
compensate for that "walkoff", by inserting identical crystals of half the thickness rotated
by 90 in each of the two beams. This procedure completely erases any velocity and
arrival time differences and we have a true polarisation-entangled state which can be
described by eq.(10). Further more we can use these compensator crystals to change the
phase
χ between the two components of the entangled state. If we use an additional halfwave
plate in one of the two beams we can also produce states:
± 1
Φ = ( V V ± H H
12
1 2 1 2)
(12)
2
11

Now we have become acquainted with all four maximally entangled two-qubit
states or Bell states:
± 1
Φ = ( x x ± y y
1 2 1 2)
12 2
(13)
± 1
Ψ = ( x y ± y x
1 2 1 2)
12 2
This is a general expression, where x and y represent qubit values. For spin entanglement
the values of x and y are written as ↑ and ↓ and for polarisation entanglement as H and
V.
3.4. Multi photon entanglement
The method to entangle more than two photons was suggested by a group of
scientists Greenberger-Horne-Zeilinger and is therefore called GHZ entanglement. We
start by two polarization-entangled photon pairs (1-2 and 3-4) which are in the first Bell
+
state Φ :
+
Φ =
12
1
2
+
+
Φ =
34
1
2
+
( H H V V )
1 2 1 2
( H H V V )
3 4 3 4
where H denotes horizontal polarization and V vertical. One photon out of each pair
(photon 2 and photon 3) is then steered to a polarizing beam-splitter (PBS) 4 as shown on
figure 7:
Figure 7: The scheme of the GHZ entanglement method for four photons
The path lengths of each photon have to be adjusted such that they arrive simultaneously
on the splitter. Because the PBS transmits H and reflects V polarization, coincidence
detection between the two outputs of PBS, implies that either both photons, 2 and 3, are
H polarized or both V polarized. After PBS the renormalized state corresponding to a
fourfold coincidence is:
4 A polarising beam-splitter is an optical element composed of two prisms, that reflect horizontal
polarization and transmit vertical polarization of the incoming light beam.
(14)
12

1
Φ = 1234 ( H H H H + V V V V
1 2 3 4 1 2 3 4 )
(15)
2
which exhibits four-photon GHZ entanglement.
To generate five-photon entanglement (five is the highest number of entangled
photons achieved to this day) we further prepare one more photon in the state
1
( H V 1
2 + 1 ) from a single photon source. The scheme of the experiment is shown on
figure 8:
Figure 8: The scheme of the GHZ entanglement method for five photons [5]
As shown on figure 2, two PBS are needed: PBS12 to entangle photon 1 from the single
photon source with photon 2 of the entangled pair 23, and PBS34 to entangle photon 3
from the first pair and photon 4 from the second pair of entagled photons. The path
lengths of the photons 1,2,3 and 4 must be carefully adjusted such that they arrive
simultaneously at the designated PBS. After the photons pass through the two PBS, the
state corresponding to a fivefold coincidence is given by:
1
Φ = 12345 ( H H H H H + V V V V V
1 2 3 4 5 1 2 3 4 5 ) (16)
2
This is exactly a five-photon GHZ state.
Multiphoton entanglement is needed to realizing quantum computations, quantum
teleportation and building quantum computers.
4. Quantum dense coding
4.1. Quantum dense coding protocol
The scheme for quantum dense coding utilises entanglement between two qubits,
each of which individually has two orthogonal states 0 and 1 . Quantum mechanics
allows one to encode information superpositions of states of two or more entangled
particles. The most convenient basis in which to represent such states is formed by
maximally entangled Bell states - eq.13. Identifying each Bell state with different
13

information we can encode two bits of information by manipulating only one of the two
particles.
This is achieved in the following quantum communication scheme. Initially, Alice
+
and Bob each obtain one particle of an entangled pair, let us say, in the state of Ψ
given in eq. 13. Bob then performs one out of four possible unitary transformations on his
particle alone. The four such transformations are:
1. Identity operation (not changing the original two-particle state
+
Ψ )
12
2. State change ( 0 → 1 and 1 → 0 ; changing the two-particle state to
2 2
2 2
3. State-dependent phase shift (differing by π for 0 and 1 ; transforming to
2
2
4. State change and phase shift together (giving the state
−
Φ )
12
+
Φ )
12
12
−
Ψ )
12
Since the four manipulations result in the four orthogonal Bell states, four distinguishable
messages, 2 bits of information, can be sent via Bob's two state particle to Alice, who
finally reads the encoded information (see fig.9) by determining the Bell state of the two
particle system.
4.2. Experimental dense coding with qubits
A quantum-optical demonstration [3] of the quantum dense coding scheme
described in previous section requires three distinct parts; EPR source, Bob's station of
encoding the messages by a unitary transformation of his particle and Alice's Bell-state
analyser to read the signal sent to Bob (fig.9). The polarisation entangled photons (EPR
source) can be produced by type-II parametric down-conversion.
Figure 9: Experimental setup for quantum dense coding [3].
14

One particle of entangled state
+
Ψ is directed to Bob's encoding station, the
other directly to Alice's analyser.
For polarisation encoding, the necessary transformation of Bob's particle is
performed using a half-wave retardation plate for changing the polarisation and a quarterwave
plate to generate the polarisation dependent phase shift. The beam manipulated in
this way then combined with the other beam at Alice's Bell-state analyser. It consisted of
a single 50/50 beamsplitter followed by two-channel PBS polarisators in each of its
outputs and a proper coincidence analysis between four single photon detectors.
−
Since only the state Ψ has an antisymmetric spatial part, only this state will be
registered by coincidence detection between the different outputs of the beamsplitter
(coincidence between H D and V D ′ , or between H D ′ and DV
). For the remaining three
states both photons exit into the same output port of the beamsplitter. The state
+
Ψ can
easily be distinguished from the other two due to the different polarisations of the two
photons, giving behind the two channel polariser a coincidence between detectors H D
and DV or H D ′ and D V ′ . The two states
−
Φ and
+
Φ cannot be distinguished. The
following table gives an overview of the different manipulations and detection
probabilities of Bob's encoder and Alice's receiver.
Bob's setting
λ λ
2 4
0 0
0 90
45 0
45 90
State sent Alice's registration events
+
Ψ
−
Ψ
+
Φ
−
Φ
coinc. between D H and DV or H D ′ and V D ′
coinc. between H D and V D ′ or H D ′ and
2 photons in either D H , DV , H D ′ or
2 photons in either D H , DV , H D ′ or
To characterize the interference observable at Alice's Bell-state analyser, the path length
difference ∆ of the two beams is varied with the optical trombone. For ∆ c no
interference occurs and one obtains classical statistics for coincidence count rates at the
detectors. For optimal path length tunning (
l
∆ = 0 ), interference enables one to read the
encoded information.
D V ′
D V ′
DV
15

(a) (b)
Figure 10: coincidental rates C HV ( • ) and C HV ′ ( ) as function of the path length difference ∆ [3] for
two different Bell states: (a)
+
Ψ and (b)
5. Conclusion
Entanglement breaks new record in June 2004, when physicists succeeded in
entangling five photons for the first time. This was a key step, which makes it possible to
check computations for errors and teleport quantum information within and between
computers. With the GHZ method of multiparticle entanglement, the doors are open to
entangle as many particles wanted, which announces the progress of quantum computers.
By taking advantage of quantum phenomena such as entanglement, teleportation (a
process where a certain quantum state of a single particle is transferred from Alice to
Bob, without actually delivering the particle itself) and superposition, a quantum
computer could, in principle, outperform a classical computer in certain computational
tasks (For example, a system of 500 qubits, which is impossible to simulate classically,
represents a quantum superposition of as many as 2 500 states. Each state would be
classically equivalent to a single list of 500 1's and 0's. Any quantum operation on that
system - a particular pulse of radio waves, for instance, whose action might be to execute
a controlled NOT operation on the 100th and 101st qubits - would simultaneously operate
on all 2 500 states. Hence with one fell swoop, one tick of the computer clock, a quantum
operation could compute not just on one machine state, as serial computers do, but on
2 500 machine states at once!) [4], [8].
New discoveries regarding quantum entanglement could revolutionize long
distance communication.
−
Ψ
16

6. References
[1] A. Zeilinger, G. Weihs, T. Jennewein, M. Aspelmeyer, "Happy centenary, photon",
Nature, Vol. 433, pp. 230-238, 2005
[2] H. Weinfurther, "The power of entanglement", Physics World, January 2005
[3] D. Boukwmeester, A. Ekert, A. Zeilinger, The Physics of Quantum Information,
Springer-Verlag Berlin Heidelberg, 2000
[4] http://physicsweb.org/articles/news/8/6/18/1
[5] Z. Zhao et al., "Experimental demonstration of five-photon entanglement and
open-destination teleportation", Nature, Vol. 430, pp. 54-58, 2004
[6] http://beige.ovpit.indiana.edu/B679/node70.html
[7] C. Kurtsiefer, M. Oberparleiter, H. Weinfurter," Generation of correlated photon
pairs in type-II parametric down-conversion", Journal of modern optics, February 7,
2001
[8] http://www.cs.caltech.edu/~westside/quantum-intro.html
[9] R.W. Boyd, Nonlinear optics, Academic press, 1992, pp. 85 -90
17