WEBVTT
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we are going to look at the generalized control
gate for example here so any quantum gate
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u u means unitary can be converted into
a control gate how do you control that what
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do you need is a control qubit associated
in addition to the the other gate that you
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have then you can produce the hm generalized
control gate and that's the reason why c not
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is a very important gate because taking any
kind of control unit you can actually produce
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another gate so c not is the controlled x
gate which is a zor gate you also have
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we also have c c not ok which were we use
another control to sort of have condition
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on the c not gate and as you know this is
our starting gate so you can add on controls
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to any particular gate that you have so for
example i have the zor gate or the not gate
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the starting one i had a control i get a c
not i put in another control then it becomes
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a c c not gate ok all these are possible so
we can also generalized saying that hm whenever
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we take one control bit or in this case qubit
we will produce a generalized control gate
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so that's the idea
now this is actually useful because in quantum
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computing having or adding a control bit or
a control qubit on the existing gates can
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become very use it and that is the very important
parameter as we will see now the next very
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important thing is the measurement part hm
again before also we have discussed this that
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generally speaking we do not want to make
any measurement in quantum conditions because
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once you make the measurement typically that
is like the end of the line hm you cannot
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any more talk in terms of what else was possible
because that's a definitive answer so whenever
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you make the measurement you have essentially
decided to terminate or come to the result
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that you are interested but at some point
of time anyway you have make measurement and
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it is best to be able to make quantum measurements
so that you are able to get the solution that
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you are looking for
now in terms of the circuitry we have been
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drawing the measurement in a quantum circuit
is drawn in this fashion that i have the
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state that we are talking about this is our
measurement process and once you have done
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the measurement you end up producing the classical
bit representing the outcome of the measurement
03:19.250 --> 03:25.349
please note that now i have specifically mention
that that's the classical bit now that's the
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very important part of this entire exercise
making it clear that the movement you have
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come here you have decided to look at your
results and whenever you look at a result
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in a quantum system you are essentially coming
to the classical world looking is always in
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the classical world that's how you understand
so for example hm for any two states any two
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possibilities as long as you don't make the
measurement as we have seen even in this case
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for example rotation the the spinning top
can be anywhere until i measure right its
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schrodingers cat all the possibilities
everybody who has been talking about are all
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based on this principle that until i make
the measurement the outcome is not clear hm
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just reminded shordingers cat is that experiment
taught experiment which essentially talks
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about the case where if inside a box a cat
and poison is put together what is the possibility
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that once you open the box you will find the
cat alive or dead depends on the condition
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whether the cat eats the poison or does not
ok
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so that's always the possibility because a
cat might not be hungry might be sleeping
04:52.259 --> 04:58.099
would not interested in that food whatever
be the case it is you can find it alive but
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the other possibility is equally true that
it might be very hungry immediately gets the
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food eats it and dies and when you open you
see its dead but as long as you don't make
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the measurement which is opening the box and
seeing the condition of the cat you have no
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no similarly for all quantum systems as long
as you don't make the measurement which is
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finally the classical bit you are not getting
the result and until then you only talk about
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probability
so whenever you have two states and they can
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be represented either in times of alpha or
beta which are my corresponding amplitudes
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then the probability will be the square of
them which is associated with getting either
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one of the answers so that is the idea so
this is generally an important question
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to ask how much information is there in a
quantum state at hm because all these logic
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seems like if you don't measure the information
[qua/quatent] quantent of a quantum states
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can be infinite is that a correct statement
we should explore that so that's why this
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particular situation has to what do we mean
when we say how much information is there
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in a quantum state
so in order to make or extract information
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out of a quantum system you have to perform
a physical measurement so that's a whole important
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point then this is what we have been trying
to tell by making measurement of a quantum
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system you automatically change its state
that we have already said so once you make
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the measurement you have change its state
you can no longer get the original condition
06:46.300 --> 06:51.649
you obtain in general a random result which
may be different from the original state now
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that's also a very important point so just
making a measurement does not make sure that
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you are actually seeing what was there before
ok once again going back to the shordingers
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cat it might be that in spite of a having
the poison the can miracles had no effects
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that's also possibility right the poison was
meant for let say cockroach it was not big
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enough for potent enough for the cat nothing
happen to it right it was still fine
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so the original state cannot be talked about
it will be the other way round no matter what
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happens every time you open the hm box you
find the cat is dead may be it just died out
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of suffocation that are nothing to do with
the poison you don't give the poison even
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then it is dead that could also be the case
so the original case cannot be reflected by
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making this measurement so that's the reason
why it is important to notice the difference
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between the fact that the measurement has
not or may not always give raise to the original
07:56.379 --> 08:00.899
statement or the information about the original
statement so we have to actually known as
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a quantum measurement to make sure that we
can get repeatable answers and that's the
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more important thing because given all these
uncertainty if he is now want to claim that
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we have no knowledge about what is going to
do when we make a measurement then we cannot
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have a competition so in terms of competition
we have to define it in such a way that the
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quantum measurement is a specific kind of
measurement which will give rise to a repeatable
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answers that's what we are after
so when we try to make a measurement say
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away the given state which is super position
up to states let say you will never be able
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to so this is one of the very important reason
why this is true you will be never be able
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to make the independent measures of only the
alpha or the beta you will be making a measure
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of their squares right i mean since alpha
and beta can be complex numbers knowing theirs
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squares does not again necessarily give the
values of their original alphas and betas
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ok that's the other way of looking at the
so hm it is also important therefore to know
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the basic idea of the basis set that's why
when you make a measurement in the frame that
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you are sitting in typically or roughly known
as the laboratory frame the basis set is chosen
09:29.250 --> 09:34.180
by you in terms of the laboratory frame it
might have solve the entire problem in some
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other frame and so when you make a final measurement
and that is coming to you as a result of a
09:39.990 --> 09:44.310
particular basis that is due to the frames
of the measurement also so that's another
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very important point to may understand so
in this context when you have many many systems
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together then we talk about an easy another
approach which is known as the density operator
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ok
so how do we define density operator the density
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operator is essentially a projection of one
frame into the other so if there is a state
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says v cat state and i have the w cat state
is the other one ok they are at some angles
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with respect to each other the projection
of v cat on to the w cat is sort of like the
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density given for the particular condition
that we are looking at so this particular
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projection the length of the projection is
a scalar product using the fact that all the
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probabilities all the w is are kind of
normalized ok so this is the case where we
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are taking advantage of the fact that we are
in a frame of reference where that frame of
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reference is only composed of normalized states
so anything else which is happening in any
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other frame of reference when we look at them
we only see their projections hm those of
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you who have been dealing with hm engineering
drawings and many other forms of doing things
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whenever you take a solid picture and you
draw its two d projection on a piece of
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paper you are doing the exact same thing ok
hm you are representing a three d picture
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on a two d plain so here also we are not really
able to get the actual state in its form
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the particular frame that we are using we
are projecting it on that frame and its looking
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at so that's why you need an operation which
will do the job for you and this is typically
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known as the density operator which gives
you the length of the projection in terms
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of the scalar product ok clear
so actually an operator right so this is all
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we are doing in terms of measurement because
at the end of it when wherever we are whatever
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we are we have to get the measurement so if
we measure with the respect to lets say zero
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one basis and psi by wave function is essentially
just zero vector then the answer will be zero
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with the probability of hundred percent similarly
if it is going to be only state one then the
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answer will be with probability hundred percent
the value of state one anytime i measure
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wave function i either get one because its
only one or i will get zero because its only
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zero ok but in all other cases the result
will be probabilistic it can be exactly in
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the middle which means that i have a equal
mixture
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so in the large number game the typical
case is always that either one of them is
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equally likely so like the coin toss problem
ok without for a bias coin unbiased coin
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the probability of getting a head or a tail
is almost always equal so we give the probability
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as half right so no matter what you do you
will always get the probability of half and
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this is exactly like saying that that it will
get a alpha square and beta square will always
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be equal to point five so that's the simple
thing
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the point however to note here which is interesting
which you do not really think about when do
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classical measurement even say coin toss thinkings
in terms of measurement after the point of
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making the measurement the value permanently
changes to the result obtained ok its like
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saying that hm if psi at some point of time
change from zero to one but at the point of
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time that you make the measurement it was
found to be one then after measurement this
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state will always remain in one because it
has been made into a classical state now right
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the measurement essentially takes it there
so once you have made the measurement original
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it could be have been an zero or one with
some probability but but just by chance that
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you measured it at a time when you just converted
into the zero case if that's the way it is
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then the measurement will always show forever
its going to be one ok that's the point which
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is very important to note that its not exactly
like the classical case there is a certain
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difference there ok
if you measure with respect to a different
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basis things can become very complicated so
hm for example here is the case when you are
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measuring this is something which which i
think we have there are practice which has
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been done on a one of the practice problems
will do in class it will become clear also
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this is something which we will doing here
hm same measurement of a function psi which
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is having the hm mixtures of alpha times zero
and beta times one now we are going to measure
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it with respect to the plus minus basis which
is some other basis the this will give you
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one of the results plus and the other one
minus with some other particular probabilities
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ok
now this is different from our earlier measurement
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because there we were measuring with respect
to zero and one now we are suddenly decided
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to measure with the respective alpha sorry
plus and minus and so the measurements found
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from the this result will not be the same
that we are gotten for the other basis so
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if you make a basis transform and you get
answers for a quantum system they need not
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be necessarily the same ok if by chance they
are same then you can be lucky but there is
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no guaranty that they will be the same most
likely they will not so and this is always
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true whenever you make a measurement it changes
anyways this is all way have been telling
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formally all the time that any time you make
a measurement you will get their probability
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and the movement you change the basis of measurement
the results will be one of the basis sets
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with different probabilities
now when you have many qubits as of now we
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had been talking about this one or the other
state so they were essentially single qubits
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one state or the other when you go for many
qubits then you are now talking about different
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probabilities of their each combinations right
so hm alpha zero so the since they their amplitudes
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are difference now they becomes different
states right hm and when when you are looking
17:39.549 --> 17:46.420
at the wave function they are basically as
we have discussed before they are hm tensor
17:46.420 --> 17:54.980
products the probabilities are the final function
is a larger basis set and if you look out
17:54.980 --> 18:02.289
for what they look like then you will find
that they are composites of say the zero zero
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state zero one state one zero state and one
one state they are all different ok
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so we started off with zero and on one all
right ok but we ended up with having all these
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different combinations because they are tensor
products so the probabilities will then have
18:26.100 --> 18:33.330
given rise to different products so the probability
of the first measurements will reduce psi
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to one of these smaller states are given by
these probabilities right you can actually
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do these very simply and you can prove it
yourself that this is how it works once you
18:45.360 --> 18:51.240
have made the measurements once if you make
the second measurement then you will reduce
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this to one of the four states which is these
four states right
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now once you do that measurement then you
get another set of probabilities which will
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be of this kind because every time you are
making one set of measurement we are basically
19:09.500 --> 19:16.809
converting it to go to that particular basis
that you are measure right so each of them
19:16.809 --> 19:27.470
will have different probabilities as has been
shown here you can go ahead and do these maths
19:27.470 --> 19:34.230
so by multiplying the branches of the overall
tree the way they are breaking up every time
19:34.230 --> 19:40.490
you make the measurement we can obtain the
probability of each result so for a state
19:40.490 --> 19:47.749
which is given by this combination which means
that it started off with just two qubits coming
19:47.749 --> 19:55.740
together with all these different probabilities
two consecutive measurements will give rise
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to a result which is zero zero with a probabilities
of this result which is zero one with the
20:02.690 --> 20:09.570
probabilities of this result which is one
zero with a probability of this and the result
20:09.570 --> 20:17.269
of one one with the probability of beta delta
square mode of beta delta square
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so now there is a specific thing that i wanted
to mention here that in this particular case
20:22.730 --> 20:29.080
when we talked about we were able to measure
each of them individually that was important
20:29.080 --> 20:37.200
right we measured zero zero one zero zero
one one one with certain probabilities although
20:37.200 --> 20:47.159
we started off with states which were zero
and one ok ok just remember that
20:47.159 --> 20:57.220
now that was possible which mean that we were
going and looking at how their probabilities
20:57.220 --> 21:04.049
where when we looked at them individually
in different basis now they can be also states
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in the mid in this many qubit situations which
cannot be broken down into a tensor product
21:11.590 --> 21:18.100
of a kind where i can associate individual
probability to each of these kinds of states
21:18.100 --> 21:24.909
that you that we kind of discuss
so let us consider for example is a condition
21:24.909 --> 21:36.820
were it looks like this now when this happens
see what i am trying to say is that these
21:36.820 --> 21:47.580
zero zero and one one are the states where
you were able to break them into these individual
21:47.580 --> 21:53.940
cases on these tensor cases but in some cases
it is such that you cannot break them and
21:53.940 --> 21:58.610
then they are known as the entangled states
i cannot really go back to my original states
21:58.610 --> 22:03.890
no matter what they are that is because of
the rule of the tensor product every time
22:03.890 --> 22:08.970
you multiply you matrix ends up multiplying
every element of the other matrix that's the
22:08.970 --> 22:13.009
basic idea behind the tensor product and a
vector product right
22:13.009 --> 22:19.259
so the point what i am trying to do is that
it is when you do simple matrix multiplications
22:19.259 --> 22:23.799
you can always breaks them up easily but when
you are doing matrix multiplications when
22:23.799 --> 22:29.639
they are involving tensors what we are doing
is every element of the matrix is getting
22:29.639 --> 22:37.809
multiplied by the other all the elements of
the matrix right and so that is different
22:37.809 --> 22:47.100
as compare to so these cases where we are
not able to get back to the original states
22:47.100 --> 22:52.929
where they came from they are known as entangled
states now this is a mathematical issue which
22:52.929 --> 22:58.940
makes quantum systems behave very different
from classical system because this doesnt
22:58.940 --> 23:06.980
happen in classical systems ok right
so in this period the most important condition
23:06.980 --> 23:18.909
arises which was given by bell john bell hm
is the one who looked at the e p r problem
23:18.909 --> 23:26.900
which basically hm asked the question about
actually we will do this in detail right now
23:26.900 --> 23:33.269
let me just do the mathematical part of way
hm for a two qubit system the four possible
23:33.269 --> 23:43.330
entangled states are named as bell states
because these states are the once which are
23:43.330 --> 23:50.519
possible to be transmitted and measured in
a very specific manner ok and then this is
23:50.519 --> 24:04.580
very important because this one helps in quantum
teleportation
24:04.580 --> 24:10.399
what is quantum teleportation quantum teleportation
is the case where you are transmitting qubits
24:10.399 --> 24:22.129
across a quantum path way and unless and
until you know how to look back at it or you
24:22.129 --> 24:30.519
have the exact code to understand the particular
set that has been transported you will not
24:30.519 --> 24:36.850
be able to know what has come to you
so that's why it is extremely important in
24:36.850 --> 24:43.549
quantum teleportation and cryptography where
it is a absolutely important to able to transfer
24:43.549 --> 24:51.960
qubits securely so this is the place where
quantum teleportation case where bell states
24:51.960 --> 25:03.789
are very important
ok if you go with more than two states
25:03.789 --> 25:12.529
so this was with two quibit situation if you
go with say three quibit situation or generalized
25:12.529 --> 25:17.880
m qubit situation then the similar states
which are the entangled states were given
25:17.880 --> 25:27.899
by zeilinger and greenberger so these are
the three so here we had bell states which
25:27.899 --> 25:34.090
were associated with e p r conditions and
here we have many many states which were eventually
25:34.090 --> 25:42.080
generalized by greenberger horne and zeilinger
where they had used m states to create the
25:42.080 --> 25:48.980
same kind of entanglement conditions which
can be transmitted across securely so entangled
25:48.980 --> 25:53.970
quantum states which involve at least three
subsytems so these has to be at least three
25:53.970 --> 26:02.289
or more ok anything up to two is the bells
condition satisfies the bells states three
26:02.289 --> 26:10.480
or more are the once which i given by g h
z g h z or the greenberger horneberg zeiliger
26:10.480 --> 26:18.730
conditions many measures define g h z to be
maximally entangled
26:18.730 --> 26:23.159
now this term maximally entangled is something
once again we will come back to it this is
26:23.159 --> 26:28.980
theoretical principle but the idea of maximally
entangled means no matter what happens you
26:28.980 --> 26:34.629
will not be able to get to a scenario where
they can be separated out so let me actually
26:34.629 --> 26:42.580
tell you this the right a way here that entanglement
has its own degree also there has some cases
26:42.580 --> 26:51.909
where under certain basis set under certain
conditions you might be able to hm separate
26:51.909 --> 26:58.470
the states to some level then they not really
maximally entangled but they are sort of entangle
26:58.470 --> 27:05.230
to level as long as you are not doing the
states transforms to a certain levels
27:05.230 --> 27:10.630
in a given condition you can get them to be
entangle but when they are maximally entangle
27:10.630 --> 27:14.879
no matter what happens they are always going
to remain entangled in the entangles state
27:14.879 --> 27:23.240
you cannot actually treat them as individual
units for two dimensional subsytems g h z
27:23.240 --> 27:35.470
can be as simple as zero raise to the power
the tensor product to m and its a super
27:35.470 --> 27:42.489
position with the other state over phi two
and the simplest three qubit state is exactly
27:42.489 --> 27:48.159
like this actually the reason why it is at
least three more subsystems is because if
27:48.159 --> 27:56.549
you go to the two qubit state it essentially
reduces down to bells state because its essentially
27:56.549 --> 28:02.239
the same all the signs and everything put
together the fact that this as to this tensor
28:02.239 --> 28:08.299
of the matrix on top also correct for the
science that you want at a in a middle so
28:08.299 --> 28:16.769
that's how it works out so if you compare
them similar terms exist this is always
28:16.769 --> 28:21.999
with two states where as in this case you
have at least three or more but they have
28:21.999 --> 28:26.350
the same characters
so and they cannot be sort of never taken
28:26.350 --> 28:32.289
out together so maximally entangled all of
them all the bell states as well as the or
28:32.289 --> 28:40.970
maximal entangle if you are hm doing multiple
sub states or sub systems you can have other
28:40.970 --> 28:46.090
kind of situation where they are not maximally
entangle conditions there we do not talk about
28:46.090 --> 28:54.559
g h z but if you want to get bell kind of
situations taken on to larger number of qubits
28:54.559 --> 28:58.940
then this is the only kind of conditions that
will be able to use and they have to be maximally
28:58.940 --> 29:11.379
entangled now what is the amazing thing about
hm entangles states what is it which makes
29:11.379 --> 29:19.869
entangles states so important in quantum mechanics
and quantum computing is a term associated
29:19.869 --> 29:34.020
with this spooky or in common language ok
hm [laughter] if we up to super position which
29:34.020 --> 29:42.049
has a classical analogue waves you can always
justify whatever you are seeing with some
29:42.049 --> 29:48.820
sort of a physical analogue when you come
to entanglement since you cannot ever fall
29:48.820 --> 29:54.600
back to the individual states there is almost
know particular condition where you can say
29:54.600 --> 30:00.809
that i have a classical analogue is just really
not there right
30:00.809 --> 30:07.119
and therefore everything in this area looks
very spooky but for the movement if you don't
30:07.119 --> 30:11.429
worry about the spooky pair there are some
amazing fun associated with entangled states
30:11.429 --> 30:15.840
so the first thing is after measuring an entangled
pair for the first time the outcome of the
30:15.840 --> 30:20.149
second measurement is known hundred percent
its like this and that's why this question
30:20.149 --> 30:28.330
arises that lie that information can move
faster than speed of light because according
30:28.330 --> 30:34.289
to this theory what did i just say i said
that i have an entangled pair which i have
30:34.289 --> 30:41.460
just created right and now i let the other
so i have two of them lets say the simplest
30:41.460 --> 30:48.880
case two quantum systems i have made in a
entangled pair so i get two one i keep with
30:48.880 --> 30:56.850
myself and the other one i put it on say anything
i mean lets say the the rocket which is
30:56.850 --> 31:04.239
going to moon i put it on there it goes
away to moon its there
31:04.239 --> 31:11.259
now i measure the one that i have it with
me the theory says the movement you measure
31:11.259 --> 31:15.239
you that you have the information of other
one because that's how it is mathematically
31:15.239 --> 31:20.749
done mathematics says that if that's the way
it is then you have just violate it what do
31:20.749 --> 31:30.399
otherwise things is speed of light you got
information faster than the speed of light
31:30.399 --> 31:36.759
because the movement you measure the hm one
of the pairs here you have the information
31:36.759 --> 31:43.200
of other one which is now sit residing in
say moon and you can do thought experiments
31:43.200 --> 31:49.879
where you can say that the it has been
send to the other galaxy lets say right and
31:49.879 --> 31:54.749
yet the movement you measure it here you have
the fully information of the other ok
31:54.749 --> 31:59.970
now this is one of the fallacy which bell
was able to prove there is something known
31:59.970 --> 32:06.989
as bells in quality which proves that the
e p r paradox is is not leading to this
32:06.989 --> 32:13.309
kind of a situation which says that you can
have faster than light transformer information
32:13.309 --> 32:19.950
that's not possible the reason being the concept
of this entire information quantum that we
32:19.950 --> 32:28.080
just talked about is decided a priory at the
time of the creation of this information whatever
32:28.080 --> 32:35.210
you do after that has no many so its a little
difficult to come to it that's why it came
32:35.210 --> 32:41.139
all these names spooky and everything associated
with it but the basic act of the idea which
32:41.139 --> 32:46.399
is kind of fun to at least think about it
is the fact that if you have state and it
32:46.399 --> 32:51.979
is a bells state for example like this one
then the movement you make any measurement
32:51.979 --> 32:59.100
of this then you have the other measurement
perfectly known to you ok so that's the that's
32:59.100 --> 33:04.570
the idea then the outcome of the second measurement
is known with hundred percent precision and
33:04.570 --> 33:08.399
this one definitely is hundred percent there
is no probability associated with this at
33:08.399 --> 33:13.769
all this is deterministic right that's the
basic idea
33:13.769 --> 33:18.570
so we are going to review what we have
done until know because there is kind of heavy
33:18.570 --> 33:24.129
staff that we did though it might not look
heavy because i avoided much of the math here
33:24.129 --> 33:30.029
hm and hence whatever i tried to write somewhere
it didnt come out properly but i think will
33:30.029 --> 33:37.070
some of the math little bit more hm but what
we try to do as we we showed you in these
33:37.070 --> 33:43.940
last two lectures that today at the last one
how qubits are represented how many qubits
33:43.940 --> 33:49.349
can be combined together which essentially
means that can be any but for practical purposes
33:49.349 --> 33:54.019
there is some limits that also we should know
what happens when you measure one or the more
33:54.019 --> 33:59.909
one or more qubits where entangled pair come
from what happens when you measure them now
33:59.909 --> 34:05.249
these are also very important right so this
is the review until now
34:05.249 --> 34:11.700
now based on these that we just did we should
be able to take one example which i have already
34:11.700 --> 34:20.010
alluded to which is teleportation now teleportation
you must have known science fiction then everything
34:20.010 --> 34:29.060
else cartoons chambers movies
student: sir if quantum are like if entangled
34:29.060 --> 34:35.290
principle how can we prepare
oh actually we are not really preparing them
34:35.290 --> 34:41.419
what happens is whenever you have so the question
is how do you prepare entangled state so the
34:41.419 --> 34:48.920
idea is whenever you can interact states together
ok in in a certain manner then you will be
34:48.920 --> 34:55.040
always creating the entangled state or super
position state now it depends on how you are
34:55.040 --> 34:59.320
making the interaction so that's the reason
why i through the gate before that because
34:59.320 --> 35:05.570
we wanted to make you appreciate that how
these operations are actually giving rise
35:05.570 --> 35:12.490
to the different results that we are getting
so one part is measurement but point of measurement
35:12.490 --> 35:16.240
is the once you are making the measurement
is the final answer which is like a classical
35:16.240 --> 35:23.660
answer but going before that are all the different
steps which were gates so first was definition
35:23.660 --> 35:27.730
of a qubit next was the operations which were
our gates
35:27.730 --> 35:33.710
now these operations sort of had different
results as a result of interactions some of
35:33.710 --> 35:39.910
them can end up producing only super position
or only amplitude enhancement or something
35:39.910 --> 35:45.570
like that nothing very amazing and they can
be completely ratified as for all our knowledge
35:45.570 --> 35:51.550
in terms of classical measurements or classical
understanding but there are some cases where
35:51.550 --> 35:56.070
the movement you do that you are not able
to get back to the individual behaviors or
35:56.070 --> 36:03.580
characteristics that's where we defined entanglement
we said that although we had two super positions
36:03.580 --> 36:08.950
of states so generally it starts off like
this when you have one qubit which is basically
36:08.950 --> 36:18.030
two states that's the simplest case once i
take one qubit mix with another qubit i get
36:18.030 --> 36:25.700
the next level of problem which can be as
simple a super position right its only hm
36:25.700 --> 36:31.170
some of the two conditions all possible sums
now when i take one super position state and
36:31.170 --> 36:37.690
i have another super position state come together
their interaction is going to be defining
36:37.690 --> 36:44.180
as to how they will interact do they choose
to remain to be like super position like in
36:44.180 --> 36:49.750
the sense that each of them will behave as
independent qubits and they will again only
36:49.750 --> 36:54.790
produce up to super position but that's the
rare in quantum system that doesnt happen
36:54.790 --> 37:01.420
they lose their individual identity at that
very point they all become something else
37:01.420 --> 37:08.050
when they come together so those four qubits
now which i initially started off has now
37:08.050 --> 37:13.670
actually no it was just two plus two right
so i had two one which had two conditions
37:13.670 --> 37:17.970
had another one which had two conditions we
put them together they already started in
37:17.970 --> 37:23.840
interacting in a different way right that's
the bell condition where i can produce entanglement
37:23.840 --> 37:29.110
when i can put another one that's getting
even harder and that's where the starting
37:29.110 --> 37:35.400
point of this other conditions starts and
then as you when you make it grow is the same
37:35.400 --> 37:43.080
idea mathematically it is to be represented
by tensors and before that whatever you do
37:43.080 --> 37:48.560
they are going to be represented as vectors
that's the idea
37:48.560 --> 37:54.400
and the biggest advantage we have as a result
of all of this one example is quantum teleportation
37:54.400 --> 37:58.570
is a reality by the way this is one thing
which i should first say that this part of
37:58.570 --> 38:05.650
quantum computing or quantum information processing
is essentially a reality and there are hundred
38:05.650 --> 38:15.530
percent proves that this one axis and it is
being used so this is the basic idea that
38:15.530 --> 38:24.830
there are two individual hm communicators
let say alice or bob that the common nomenclature
38:24.830 --> 38:30.490
in this area and if they have a single particles
so here we start the first one a single particle
38:30.490 --> 38:39.360
from an entangled pair ok then it is possible
for alice to teleport a qubit to bob using
38:39.360 --> 38:46.710
only a classical channel the state of the
original qubit will be destroyed right because
38:46.710 --> 38:53.030
the movement measurement is made state is
destroyed so the point is only using a classical
38:53.030 --> 39:00.110
channel this can be done and therefore its
kind of interesting to note that you can do
39:00.110 --> 39:07.300
this when you have an entangle pair and this
is this the question of this is the using
39:07.300 --> 39:12.760
the properties of entangled particles this
can be done so what is the idea behind this
39:12.760 --> 39:21.110
particular idea where teleportation the first
thing to remember in this cases is this is
39:21.110 --> 39:25.210
something which we have to done before in
quantum mechanics we cannot create something
39:25.210 --> 39:30.790
we cannot something nothing can be created
nothing to that's known which means that it
39:30.790 --> 39:37.701
is impossible to clone or duplicate an unknown
quantum state when you know a quantum state
39:37.701 --> 39:45.180
then it is classical anyway right so that
part is gone however it is possible to recreate
39:45.180 --> 39:49.920
a quantum state in a different physical location
through the process of quantum teleportation
39:49.920 --> 39:58.220
now this is kind of very interesting which
means that although so these are the things
39:58.220 --> 40:06.610
why quantum computing in some sense can become
a prove reality because once i went if we
40:06.610 --> 40:12.780
go back we saw the cases where we decline
this cannot be done that cannot be in let
40:12.780 --> 40:22.970
me quickly go back so let see we started
off here ok now although it looked very pale
40:22.970 --> 40:31.150
hm it was very important to realize that in
a actual computer in a actual computation
40:31.150 --> 40:37.410
it would be necessary to have these situations
to arise also now the very fact in quantum
40:37.410 --> 40:44.010
systems which is supposed which has to be
reversible these are not going to happen which
40:44.010 --> 40:48.320
means that i will not be actually able to
create a quantum computer in this sense of
40:48.320 --> 40:56.700
how we know about a computer if this is strictly
all how it is going to happen but the very
40:56.700 --> 41:09.910
fact now i am telling you when i come here
is that it is true that i cannot do this ok
41:09.910 --> 41:14.350
so this is the no cloning i cannot really
do that that i already just told that that
41:14.350 --> 41:21.040
was my no cloning but it is also true that
since i have teleportation i can actually
41:21.040 --> 41:31.100
do this in a different way at a different
location see so i have found a way out of
41:31.100 --> 41:37.760
some of the necessary gates which i could
not otherwise i have implemented if i only
41:37.760 --> 41:43.900
go by the logics and laws of quantum mechanics
ok this is perfectly allowed through quantum
41:43.900 --> 41:49.260
mechanical system that i can actually do at
teleportation quantum teleportation ok
41:49.260 --> 41:54.800
so that's the reason why quantum teleportation
is important so the so although opened it
41:54.800 --> 41:59.800
by saying how we are going to do this here
is the mathematical point of how we are going
41:59.800 --> 42:06.070
to actually achieve the idea of quantum teleportation
so alice wants to teleport the particle one
42:06.070 --> 42:15.860
as i mentioned to bob so in order to do that
what is necessarily required is we need two
42:15.860 --> 42:23.150
other particles two and three that are prepared
in an entangled state so this is basically
42:23.150 --> 42:33.430
the bell pair as we have done so this is state
zero and zero having of of two and three which
42:33.430 --> 42:42.110
is we superpose super imposed with the
two and three three or one and one of root
42:42.110 --> 42:46.760
two so this is this is the bells state ok
that is created
42:46.760 --> 43:02.140
now particle two is given to alice particle
three is given to bob once you upgraded this
43:02.140 --> 43:09.140
in order to teleport particle one alice now
entangles it with her particle using the c
43:09.140 --> 43:17.430
not and hadamard gates now you have to
look back into your nots in the gates that
43:17.430 --> 43:24.110
you did before so c not you are going to apply
on one and two states and hadamard we are
43:24.110 --> 43:32.900
going to apply on the one states so now the
particle one is disassembled and combined
43:32.900 --> 43:38.810
with the entangled pair ok
so this was the process that i was telling
43:38.810 --> 43:44.910
you about earlier now you have to understand
one thing very important in this particular
43:44.910 --> 43:51.410
course is that in a implementation quantum
course this is the part which is the extremely
43:51.410 --> 43:58.980
important how is the process happening ok
knowing the mathematics as we have been doing
43:58.980 --> 44:05.080
in terms of saying that this is the math this
is the way it is fine but we have to somehow
44:05.080 --> 44:11.790
get to a point where we are discussing the
scenario as to how these are happening
44:11.790 --> 44:19.170
so once you have done this part where you
have manage to put your particle one with
44:19.170 --> 44:26.830
the entangled particle where sorry where you
have managed to entangle your particle one
44:26.830 --> 44:35.260
with the particle which is now with alice
then you are in a disassembled dis assembled
44:35.260 --> 44:43.510
these assembled state this assembled state
of particle one with entangle pair which alice
44:43.510 --> 44:50.250
has now alice measures particle particles
one and two producing a classical outcome
44:50.250 --> 45:00.620
which is all these possibilities now depending
on the outcome of alices measurement bob applies
45:00.620 --> 45:13.440
a pauli operator to particle three reincarnating
the the original qubit now if the outcome
45:13.440 --> 45:21.560
is zero zero bob uses operator i if the outcome
is zero one bob uses operator sigma x now
45:21.560 --> 45:28.780
this is the pauli set as you know if it is
one one then he uses sigma y if it is one
45:28.780 --> 45:34.640
zero he uses sigma z
so based on this measurements bob is able
45:34.640 --> 45:43.110
to produce the original state of particle
one so the basic idea behind this is that
45:43.110 --> 45:49.990
alice and bob can perform a sequence of measurements
on their qubits to move the quantum state
45:49.990 --> 45:56.790
of the particle from one location to the to
the other the actual operations are more involved
45:56.790 --> 46:02.500
than what we have presented here and the actual
of operations are something which will actually
46:02.500 --> 46:08.570
be doing in detail here this is just summary
so this is just to set you up as to how will
46:08.570 --> 46:17.970
be doing it i think i will be stopping here
because will hm we almost come into the point
46:17.970 --> 46:28.130
of here yeah will be stopping here and
will be exploring more details on this areas
46:28.130 --> 46:31.220
from the next class ok
thank you