ok so based on what we did in the last class
we will now get in to the concept of cryptography
and in terms of cryptography the definition
or the description is given from various ah
dictionaries for example merriam webster dictionary
cryptography means the coding and decoding
of secrete messages nobody else can read for
example cryptography you are write in a way
that you can't understand that sought of like
the dictionary definition and we can represent
it as a way in which we are not able to understand
what is being sent or discussed about unless
it is looked at in a proper way so cryptography
can be coded in such a way that nobody else
except the way other people can look at it
so the basic idea is to modify a message so
as to make it unintelligible to anyone but
the intended recipient that's the main idea
so for example you have a plaintext message
m which is are going to be encrypted in such
a way that unless it is decrypted you can't
understand what the message is so that is
the basic idea behind a cryptography
so in this process the idea is to have a way
to do this process so you need some keys and
once you have the keys which can be distributed
only those who have the keys will be able
to understand the message so the principle
is this k for example is the key the key is
known only to the sender and the receiver
and that's how it is a secrete ok
anyone who knows the key can decrypt the message
so the first problem in this field is therefore
the idea of key distribution because you want
to actually distribute the key in a way so
that is only for the intended receiver and
no one else that's the main idea behind this
so perfect secrecy and ah is roughly provided
when the key that you are going to use is
only going to be for once or in other words
it is called the one time pad so there this
is known as the perfect encryptosystem because
whatever you are using for example this is
the case which is a onetime pad only if anything
happens more than once it will not be same
the problem of distributing the keys in the
first place however will still remain because
no matter what you do this one time pad also
has to be provided appropriately to the right
person so the distribution of key remains
as one of the most important parameter in
this ok so we use quantum key distribution
as one of the best ways of doing key distribution
because the quantum key distribution process
is done in such a way that the distribution
of the keys will be in perfect secrecy so
the perfect cryptosystem essentially requires
therefore a quantum computing which can utilize
the quantum key distribution and one time
pad
once you have that then you have a perfect
success in terms of secrecy so that's the
reason why quantum key distribution and that
has become very powerful so what is the key
idea from the quantum world first is the measurement
part which you have ah read the idea observing
or measurement which you have done in a quantum
way will alter its states which means that
whenever we use a quantum way of doing our
measurement then it is only one time use
so that's our principle of getting our one
time pad in some sense so in this regard the
qubit when it is observed the state of the
qubit will collapse to either one of the two
states but unless it is measured it will be
either in one of the two combination states
so one example which is very popular in this
case is the case of photons why because photons
are quantum objects which can be transmitted
very easily across so these are the physical
qubits where any subatomic particle can be
use typically physical units can be any subatomic
particle which can be use to represent qubit
for quantum key distribution a photon is a
convenient choice
because it can be transmitted very easily
that's the basic idea the other kind of qubit
that we have been encountered subatomic particles
they are generally localized in someone in
the sense that whatever is happening in one
area that you are looking at the subatomic
particles interact and do things in a certain
way
but transmission which is a key part in this
quantum key distribution that would be preferred
if use a photon and that's why photon is a
convenient choice for quantum key distribution
photons can be represented as electromagnetic
waves where the quantum phenomena is the part
which will be utilized when we do our key
distribution
say photons has a property called polarization
which is the plane in which the electric field
is oscillating right so we can use photon
sub different polarization to represents quantum
sates so a photon with say having an angle
or an oscillation in a certain way which we
call as our zero degree we can rep labeled
at as states zero and something which is ninety
degrees to that state we can represent it
as one so for example if this is my zero then
ninety degree is to it is my state one ok
so that is the idea behind this definition
and we can use this principle that it can
oscillate in one way versus the other way
as one of the approaches to deciding our quantum
state so once we use polarization as our basis
of qubit or a quantum state we need a device
called a polarizer that will allow us to place
a photon in a particular polarization so and
there are things call pockels cells which
are going to allow only certain polarizations
to go through and it can be change to the
other kind based on applied field or voltages
that's the idea where pockels cell that's
a material a crystal which lets the light
of a certain polarization to pass through
under certain condition if you change the
voltage across the pockels cell then the polarization
property of the light going through it can
be changed so that's a very nice way of changing
the polarization states that are going through
a medium so this is our manipulated in some
sense
it could be a static manipulator like a polarizer
which just sit there and does its job and
the other could be a dynamic one which is
like a pockels cell which depending on the
voltage applied will change the way the polarization
is going to be on the other side so the polarization
basis is the mapping we decide to use for
a particular state right
so the simplest one that we are use to are
the zero and ninety case which is our rectilinear
ah access geometric for example x and y and
the way we decide x y kind of thing that's
our rectilinear such that the angle across
is going to be ninety degrees the other option
is to have a rotated case which will be like
a diagonal such that the once again the ah
the angles are going to be ninety degrees
all right
but they are with respect to a given fame
can be rotated by forty five degree so it
could be their diagonal case or rectilinear
case so since the photons are going to follow
the laws of quantum mechanics the complex
numbers are added as oppose to their probabilities
that's one of the things which we have been
learning as a part of quantum mechanics right
so when the additions are happening in the
quantum world the complex numbers come in
to the picture but when we are observing it
it's that ah probability that we are observing
so there are so here is an example as a result
of this we start at say point zero and you
can go to different places under different
conditions but the design of the property
if you are going to use this particular approach
or propagation will be such that there will
be no photon at say point five right
so this is sort of known as annihilation operator
that we are use to in quantum mechanics that
the phases are oppositely set such that the
resultant can cancel each other right this
can only happen because we are looking at
their amplitudes and not their probability
so the probabilities will not cancel out ever
they will have no sig science associated with
it but these will have so that's the idea
so that was just an example now in a realistic
case what are you going to do in order to
measure photons ah and their polarizations
one of the most important physical object
is a calcite crystal ah this can be used to
recover the bits enclose in a stream of photons
so this is a ah non centrosymmetric crystal
this is not a very ah uniform optically it's
not a hundred percent uniform crystal it has
a non centrosymmetric geometry and as a result
of that when light passes through it it interacts
along the diagonal access and is able to ah
allow one verses the other kind of the polarization
coming through that is the main principle
out here and in some sense therefore it's
a polarizer right
so what will happen 
so we can therefore correlate how they going
to go across and be present as we go along
this calcite crystal so if all the ah four
possibilities of a diagonal polarization exists
then as they go through it they will switch
in to the cases that will considered into
so for example this diagonal axis of the of
the calcite crystal will routed forty five
degrees to the incident polarization that
we have
so therefore this particular one will come
out in a direction which we have defined as
one ok we define zero and one right one coming
out of the plane and one in the plane oscillating
that's have it was ah so this is a two dimension
representation of the actual thing so ah this
one forty five degrees will give rise to one
whereas the ah other one because it's going
to routed only in one direction ah and the
other one will end up producing at zero similarly
the other one which is again at ninety degrees
to it will end up producing one and visa versa
and so and so forth so you can get a series
of ah different zeros and once in the plane
that i am measuring because i am going to
always routed as a result of the calcite crystal
by forty five degrees to a given angle that's
the design
so you can actually set of the problem by
aliening the crystal with respect to they
applied polarization to start with so that
once you define one polarization as zero then
as soon as you routed the other one the correspondence
keeps on happening that's the idea now if
instead of the case that i just mention to
you where we are able to do the process the
way we have done it if we have wrong orientation
what will happen that's the question then
there is a fifty percent chance of getting
the right answer because fifty percent of
time you will get the right answer and fifty
percent of time you will not get the right
answer because there is always fifty fity
probability of getting one way versus the
other because there only two possibilities
in this kind of case right we are either zero
or one so if you get it wrong it will be fifty
percent wrong if you get it right it will
be fifty percent right ok
so in this design the way it was we discussed
it last time also when we are going to send
information across it's like having alice
and bob trying to send the information across
and there is a eavesdropper who is going to
come in to try to see if the information can
be stolen that's the basic idea so what is
the job of the quantum cryptographer he or
she has to prevent eve from evesdropping on
communication between alice and bob that's
idea so this is the famous problem which is
first proposed and described well in quantum
information theory by bennett charles bennett
and later on he is associate ah brassard will
have the names again later on added to the
levels of cryptography that can be done and
so the there are codes which co by their names
so there are these two names so these are
basically b b ok and i they used certain number
of parameters to do their things so there
is this famous code called called b b eighty
six coding so is bennett and brassards thing
it is nineteen ninety six when they deal it
and that's how b b eighty six but we go ahead
and see how it is going
so what are these steps it requires as we
mention quantum key distribution which exploits
their effects discussed in order to thwart
the eavesdropper if an eavesdropper uses the
wrong polarization basis to measure the channel
the result of the measurement will be random
fifty fifty means random right the protocols
are important parameters here a protocol is
a set of rules governing the exchange of messages
over a channel unless you set it up you will
have difficulty in getting to know how information
chance we will happen so a security protocol
is a special protocol designed to ensures
security properties are met during the communications
there are three main ok it was not eighty
four eighty six it is a b b eighty four there
are three main security protocols for q k
d b b eighty four b b in b ninety two and
entanglement based q k d so we will only discuss
b b eighty four here so that's the reason
i introduced you earlier i am sorry this was
eighty four so i just correct it here ok ok
so b b eighty four was the first security
protocol implementing quantum key distribution
this uses the idea so as i mention this charges
h bennett and g brassard this it uses the
idea of photon polarization ok the key consists
of bits that will be transmitted as photons
ok each bit is encoded with the random polarization
basis now that's the main important thing
the random polarization basis will come to
it in so when there is no is eavesdropping
how is it going to work so the sender alice
is going to send bob the key she begins with
a random sequence of bits bits are encoded
with a random basis and then sent to bob so
the basis can be something like plus cross
cross plus cross so cross is zero plus is
one lets say now accordingly you will get
your coding done in a certain way for the
photons and you get this kind of a resultant
ok 
now when bob receive the photons and must
decode them using a random basis
some of his measurements are only going to
be correct why because there is a possibility
of getting them correctly and he uses a basis
in which lets say one of his basis doesn't
match up which what was used by alice and
so instead of getting the right numbers there
was a place where the right number didn't
come through so some are corrects some are
not so then what happens alice and bob talk
on the telephone because there are no eavesdropper
so you don't need to worry about this alice
chooses a set a subset of the bits the test
bits and reveals which basis she used to encode
them to bob right
so this is basically hand shaking this is
the beginning part you are testing it out
so bob tells alice which basis he used to
decode the same bits where the same bits basis
was used alice tells bob what bits he ought
to have got right so this is like they are
they are checking their results on whatever
they have done and trying to find out what
went true what was going on so when they do
the comparing of the measurements they find
that two of the basis of all the set that
was used where correct where matching so they
call that as test bits right so once this
test bits is established then alice and bob
can actually exchange information in where
the test bits are included to be able to test
if the channel is secure because if somebody
tamper with this message the parts which are
not in the test bit it doesn't matter because
that's not going to actually effect anything
but once you keep on sending the information
somewhere along the line the test bits also
be having an effect right so if that happens
then they know that the channel is corrupted
otherwise it is secure
so so where is trick as long as no errors
and no eavesdropping have occurred the test
bits should agree every time alice and bob
have now made sure that the channel is secure
the test bits are removed alice tells bob
the basis she used for the other bits and
they are both have a common set of bits the
final key ok
now you can actually imagine this iterative
process going on for a very long time such
that you can actually send across a two fifty
six bit key imagine what will happen how long
will it take you to other place but that's
one possibilities there you can do it step
by step to see what happens so for example
here the with this particular set how do you
get the final key what you have to do is you
have gotten this region where the test bits
where there you discard them and what you
find then is that there were these two which
still matched in spite of the fact that ah
they were not using them as our test as their
test bits still they match
so they considered that as a final key so
even if somebody is actually sitting they
are trying to figure out what is the security
channel they will end up getting this which
is the discussion bits the test bits as the
security channel is that's what they are been
discussing so in other words you know the
phone conversation is classical for example
so somebody manages to hear the phone conversation
so they will focus on getting this as the
answer right because that's the discussion
point they had the test bits but they really
don't use the test bits they discarded and
then look for the once where the thing worked
and that they considered as their final key
ok
now this is without having any eavesdropper
with assumption that you know when everything
happened ideally there was nobody who was
listening so they went through the exercise
as if there was going to be something happening
but nothing was there and so they were able
to get their answer very easily in had it
been that there was eavesdropping what would
have happened so if see eve is there is an
eavesdropper and he is trying to tap the channel
this will automatically show up on bobs measurement
in those cases where alice and bob have used
the same basis bob is likely to obtain an
incorrect measurement eves measurements are
bound to affect the states of the photons
and that's the beauty of quantum part here
had it been classical this was not going to
be reflected
because in a classical system you can always
take a little bit out and nothing happens
right ah but in a quantum system that's what
you have learnt all this time any kind of
a partabition or a change or as you call it
measurement which is interaction is going
to affect whatever is left and that's the
reason the places where they were having the
correct match is now going to have an incorrectness
and that's how the immediately know that there
was an so the advantage therefore is the quantum
gates allow us to manipulate quantum states
without measuring them as the first thing
which is very important because that's the
basic principle behind quantum gates so this
is this is actually i don't know if i mentioned
it before but this is something which will
have to be always ah focusing on that the
reason for having quantum gates is that we
will be able to manipulate the quantum states
without measuring them ok
so the definition of a quantum gate is right
there and that's why they are sometimes very
difficult to come up with quantum sates cannot
be cloned now that again one of the things
which you know as a this is a property of
quantum mechanics teleportation allows a quantum
states to be recreated by its exchanging only
two bits of a classical information now this
is the part which is very important so at
the end of the day what happen was they only
exchange two bits which was their test bits
to be able to know what was going on with
the entire information transfer process
there did not use anything else ok quantum
coin flipping is more fun than the classical
coin ah there are many other aspects of quantum
information processing ah and one of them
is also quantum coin flipping because that
has much more probability than doing a classical
coin flipping and that's how the ah it can
be more fun than the classical coin flipping
but i don't know whether i will be doing that
next turn out let me see a we are doing that
next ok
so ah before i go there let me actually just
do a quick review on what will ah what was
the main process here in terms of quantum
information processing so this part of the
presentation or the classes you have done
has focus more on the quantum information
processing right ah you have to understand
one very important part of quantum computing
per say that this quantum computing heavily
realize if realize heavy on quantum information
so you cannot have quantum computing or anything
to do close to it unless you have quantum
information process in term in the right way
and so ah information processing or quantum
information processing is some very important
place where photons or light plays a very
important role because they are the once which
can be transmitted across much more easily
than anything else any other quantum or qubit
that you can think of photons have the best
in terms of transferring and therefore quantum
information will almost always in focus ah
quantum information will almost always have
photons as a part of its study
so this is one thing which we have done so
basically studied this now ah to make things
a little bit more friendly lets say we will
be looking at the quantum coin flipping ah
kind of a situation ah there is this entire
area which is known as quantum games and its
defiantly ah lot more interesting to the to
do a quantum game verses the regularly because
it's a matter of chance right and you know
that matter of chance is much much better
off with the quantum system then with the
classical systems right so that's why its
the more much more interesting case so what
do we mean by ah quantum coin flipping so
the quantum coin flipping principles is based
on the following game so this again this ah
alice and bob kind of an idea alice places
a coin head upwards in a box alice and bob
then take turns to optionally turn the coin
over without looking at it ah that the key
pad
if you look at it then it has becomes classical
information you can't do that at the end of
the game the box is opened and bob wins if
the coin is head upwards otherwise alice wins
in the quantum version of the game the coin
is a quantum state so when we say heads or
tails these are classical but if i say h state
and t state then it's a quantum system now
ah for those of you might be thinking that
why is this is so exciting because this is
ah this is related to your security in terms
of ah tailor machines banking ok so will come
to that ah
so quantum coin flipping so in this case let
us formalize it in a slightly ah more regress
fraction let us say that alice can only perform
a flipping operation that is a gate which
is sigma x we know that the sigma x just does
a flip so what does sigma x do it takes the
super positions and puts them in the opposite
order so the alpha becomes associated with
one and the beta becomes associated with zero
right there is a strategy that allows bob
to win always he must perform hadamard operation
so now that that's the very important principles
so this means that if you do it in this fashion
there is a strategy which can be used by bob
which will make him always win if it does
that
so thus bob places the strategy of the coins
in a superposition of heads and tails ok because
in order to get to the hadamard operations
you need to have a superposition of the two
states so i think we have gone through cases
where we have discussed before that there
were some gates some processes some discussions
of quantum ah principles which allowed us
to make superpositions states they are actually
very very important ah there are some resent
ah work that we have also done in terms of
research where we have actually shown that
creating superposition states are possible
say in optical qubit and something and they
are very very important because that's one
of the principles of hadamard gates
and hadamard gates or hadamard operations
not just appearing in only these cases they
appearing in almost every where will also
find that they appearing robust algorithm
and there often there in even in parts of
doing this ah sorry the shors algorithm so
let us see what do we do here so here in this
coin flip experiments ah what you have to
do is you have the bob who is going to do
his hadamard operation on the orginal states
alice is going to do a flip and once again
bob does a hadamard to find out what the original
state was
so if he keeps on so that's what alice just
say that if bob keeps on doing hadamard he
finally always wins because the flip character
will be always seen correctly by bob every
time he does a flip right so that's one part
the next very important thing which i mentioned
which is again a difficult one is the cloning
right because these are the things which ah
we have to be looking at over and over again
because these are the places which are otherwise
very difficult to do in a quantum system so
the idea of a quantum or a qubit cloning circuit
is very important so why are we doing all
this we are doing it because these are essential
steps towards providing a full quantum teleportation
circuit
so will find it out later that all these different
steps that we are doing see for example the
quantum coin flipping that we just did is
one of the steps that is always necessary
when we are finally going to do our quantum
teleportation process so this is one phase
the other important thing we need to do in
this connection is to actually have a cloning
so how do you cloning we have perhaps visited
it once before but let's do it once more in
this context because we would need it
so a qubit cloning circuit is something which
we need which we know that it's very difficult
to get otherwise because in quantum mechanics
you can't clone anything but we know for example
in classical case you can always do that for
instance by using a reversible xor gate it
is possible to copy a classical bit by using
the same analogy because it is a reversible
case in case of classical we should be able
to do the same in the classical so here we
are looking at it can we build a quantum circuit
that performs with this kind of a situation
with qubits is it possible
so what is the idea a qubit cloning circuit
would therefore be that will have to do something
which will be utilizing one principle or the
other so if you take pure states then it is
possible to do such things right however if
you have states which is super position states
then it's not that simple what you will have
is you will end up producing and entangled
states right so in order to actually clone
all the time is not possible to just say that
ok i will just use the same principles that
have been used in a reversible classical system
is not true so ah the reason i wanted to make
this a point clear here is that many a times
you may think that if i take a perfect reversible
classical computer i should be able to do
this same now take it and just map it in to
my quantum computer ah map it in to the quantum
world and i get a quantum computer is not
going to happen it's not that way
so a direct mapping is not the idea between
classical and quantum something more is necessary
the idea is correct it somewhere there but
it's not exact so we have to do something
more what is it so in this case for example
ah first statement is it is impossible to
clone in qubit that we know there is nothing
new about it ah but there is a way to do this
in a slightly different way but we should
note that when we take any two states which
has superposition states we will be getting
terms which we just discussed which where
entangle that's because in quantum systems
alpha beta is not equal to beta alpha that's
typically the case
right you cannot just because most of them
most of the time they are also complex numbers
and so complex numbers are not going to be
often looking like this so in that case you
have to do something more than that and hadamard
gates again become very important so in this
connection lets actually look at the bell
state circuit now we have encountered bell
state before had where we have taken states
and put them together and we found out that
these bell states cannot be separated back
down to the individual states that was the
basic ideas so we have just seen in similar
condition here we ended up produce in entangle
states
so ah if you take ah this kind of a circuit
what you will end of producing depending on
how you have your ah the inputs states the
output will essentially form the entire ah
bell state situation so just a simple hadamard
along with the c not gate will end up producing
the bell states that you need so this is the
bell states circuit so here is an example
how it goes 
so you have the original you start with the
same state one of them goes to an hadamard
so it becomes reposition states is going to
the c not producing the bell state here so
this is my bell state then
in order to get to your quantum teleportation
circuit all of this that we discussed as of
now and necessary why ok by the way i should
mention that this symbol represents measurement
whenever we have a symbol we sort of shows
a meter of some short it means we are looking
at a measurement point ok so what is it that
we have doing now we are actually having one
state say for example the particular way function
is been put through a control not with control
bits which are of certain kind which is going
to go through ah this system where one of
the cases can be a measurement case but the
other case we are not measuring if you measure
in the other case then we in trouble we are
only measuring one part of it so these are
my measurements m one and m two and if you
remembered we always saying that will be using
two qubits on the classical channel which
is the case where we allow the measurement
to happen but the other which was my quantum
case remained as it is it just got some kind
of a mixture or it it it got ah sort of ah
impacted by these other states to finally
give rise to state that is how use so we look
at it in a slightly ah more difference way
so at each point how does it looks so here
as we entered so this is another way of so
whenever we write down circuits at every point
when we look at it we kind of put a circle
and then we represent what we are seeing right
there
so my psi naught is a resultant of the interaction
which is happening at this point of my circuit
right so this is how i have look at it this
is how it looks ah ok now what happens when
i go this point so this is how the second
point would look like one of them go through
the c not the other one is already is as we
had seen before so this part now is going
to go through a c not on the one part so this
point is going to go through a c not this
part we have already computed so when we apply
that we get this so this is how it looks like
here now at next one will be having a hadamard
on one of them and so when i apply the hadamard
after this point then the this is my resultant
and then you will be measuring
and you will be measuring these which are
basically the bell states right between two
qubits actually this are basically the two
qubits different possibilities of the two
qubits been measured now that measurement
is essentially what alices has done attorente
right so that measurement is essentially what
alice is done attorente because she preferred
condition there this is how she prepared this
the states she measured before sending it
out and see she got these conditions and as
a result of that when its going to be looked
at by bob then bobs qubit states will be one
of the kinds and when bob applies any of these
states then he will be getting this
ah particular state generated which is the
psi states refine and re function so what
have we achieved as a result of all this the
teleportation process makes it possible to
reproduce a qubit in a different location
ok let's look back so the qubit started off
here which was my psi function which was this
original state right then see that that was
my psi psi was superposition of zero and one
with alpha and beta then i went through this
circuit and i looked at every possibility
right there and when the final measurement
was done by alice correspondingly what bob
got as a result of applying these gates is
the same state which alice had
so what is the result the teleportation process
makes it possible to reproduce so we started
off by saying you cannot clone the quantum
state right that was the basic idea but we
ended up managing to do that by using this
teleportation process and that's why it is
teleportation is not cloning but teleportation
this is not at the same location right and
the original qubits are destroyed because
once alice has done this the measurements
are done those qubits are no longer there
so that's the reason why we have to make this
statement with the original quibits are destroyed
the next topic is on quantum parallelism and
deutschs quantum algorithm which will do it
in the next class but before going there i
thing it what we did today is extremely important
so i am going to do once more revise this
once more because now we have seen the whole
thing so we should be able to understand it
will be little bit better when we were when
we are doing it by step so let me actually
go back on this a little bit to make sure
that we understand because we did the steps
without originally understanding why we wanted
to do those steps
now that you have seen how this is all happen
we are going to do this once more in a little
bit ah fast manner but just see so essentially
there was a lot of background which we have
already done to just show that the they have
analogs in other information processing so
the quantum coin flipping was for example
an analog so you can use this in terms of
some games and other things but this was a
step in the process of quantum teleportation
please remember that so it was not like we
were trying to play games and anything here
it is true that there is a huge area quantum
game theory it's there now it is is very interesting
and you can even ah think in term of quantum
casinos and discuss about those things
we can have a discussion on all of that but
the basic original problem was that you have
stopper a and you wanting to have a secured
channel between two individuals were going
to transmit information and if it is a quantum
information what we claimed was that it will
be hundred percent secure how is that going
to happen so in this regard we went through
all the steps which showed how this is possible
so and we used photons in this case preferentially
because photons are much better in terms of
transmission of information in quantum sense
so use quantum ah photons and photons are
very convenient two states polarization of
one kind process the other kind we use that
and we made a parallel with the classical
to two bit system and we use that as an information
bit to exchange
and in this we also explored the possibilities
of something like a quantum coin flip and
we found out that we could use that principle
to understand how alice can make the measurement
or can set up the problem which can be always
recovered by bob with hundred percent outcome
which is very important had it been not that
way then this entire exercise would have stop
right there we don't want to do it that way
we want to do it that way
so we found out how the coin flip in principles
are once we understood that we put it through
in a circuit fashion and we ask the question
as to whether it's possible to clone which
definitely is not possible because we know
that in a classical system which possible
but in quantum system is not but in some sense
we realize that this teleportation business
might have something to do with this in that
connection and we started asking the question
where we landed up in the idea that in very
simple cases it is possible that you can use
simple control not gats to get to the principle
that you are able to perhaps get back the
same system but that is true only if you use
pure states or single states to start with
but if they are starting with a combination
state zero and one they combine in some percentage
order which is how a typical quantum state
is then you always end up getting and entangle
states we not be able to get the individual
states in the right order as we have started
and so the principle of cloning that it cannot
be done in reality survive which is required
for a quantum system and that's the security
by the way right so then what we ah so we
basically proof the fact of the principle
and it was important because that makes it
secure so that is our secure its very important
right so then once we when there then we started
to ask or re explode the idea that we have
already talked about before is the idea of
the bell state which we know we have discussed
in terms of entanglements earlier the two
states system always bell entangled that what
you get their highly entangle system
and since we are using polarization is always
going to be two states so we did that and
we found out that this always works out because
you all you need to do is for the two states
he just add an hadamard you always produce
bell states once you have gotten to that point
then you got one part of the circuit taken
care and once you did this then you are able
to get your final answer ah such that you
can always produce a pair connected properly
in this way this is the bell pair again that
you are generating so then we are ready for
our full quantum teleportation circuit where
in the criticality is we have a measurement
part associated because alice actually makes
the measurement and based on this measurements
they are able to compare and understand what's
going on right so you go through in a circuit
like this so you also learn this is very important
whenever we write down a quantum circuit like
this there are points and e at each point
we can write out how they are going to go
by in this process and then at every point
when we do that so for example we looked at
the first point then we went to the next point
then we went to the next point so at every
point of applying a gate we looked at what
we were left with or what we were generating
and we were able to go through these and finally
get to the point where the measurement was
made by alice and correspondingly whatever
board a boad applied on his side as a gate
that's what we applied and once we did that
we were able to get back the state that alice
said started with right whatever alice measured
is not the state which alice started with
please remember that that's very important
she ended up making something which was possible
to be applied a certain way of gates to get
the original state that was done by bob
so finally as a result of this entire process
we were able to do a teleportation where we
reproduce the qubit at the different location
and we maintain quantum mechanical principles
in the right way because the original state
was destroyed ok with this lets end here will
take up the next topic in the next class
thank you
