Second Element is not 1 but It is coming as 1

Hello,

I have this matrix:

I saved this matrix in a list like : projectors_of_sigma_x_minus_sigma_z = [[(sqrt(2)-1);1],[(-sqrt(2)-1);1]];

and this is my code :

function B = CHSHmeasurement
    B=zeros(2,2,2,2);
   
    projectors_of_sigma_x_minus_sigma_z = [[(sqrt(2)-1);1],[(-sqrt(2)-1);1]];
    B(:,:,2,1) = projectors_of_sigma_x_minus_sigma_z(1);
    B(:,:,2,2) = projectors_of_sigma_x_minus_sigma_z(2);
end

But I have this result:

However I have not 1 as the second element of projectors_of_sigma_x_minus_sigma_z. I have [(-sqrt(2)-1);1] for the second element of projectors_of_sigma_x_minus_sigma_z(2); Where am I wrong ?

Answer 1

[madhan ravi]

>> B=zeros(2,2,2,2);
   projectors_of_sigma_x_minus_sigma_z = [[(sqrt(2)-1);1],[(-sqrt(2)-1);1]]
   B(:,:,2,1) = projectors_of_sigma_x_minus_sigma_z(1)
   B(:,:,2,2) = projectors_of_sigma_x_minus_sigma_z(2)

projectors_of_sigma_x_minus_sigma_z =

    0.4142   -2.4142
    1.0000    1.0000


B(:,:,1,1) =

     0     0
     0     0


B(:,:,2,1) =

    0.4142    0.4142
    0.4142    0.4142


B(:,:,1,2) =

     0     0
     0     0


B(:,:,2,2) =

     0     0
     0     0


B(:,:,1,1) =

     0     0
     0     0


B(:,:,2,1) =

    0.4142    0.4142
    0.4142    0.4142


B(:,:,1,2) =

     0     0
     0     0


B(:,:,2,2) =

     1     1
     1     1

>> 

You're copying a scalar to that entire page.

[Gözde Üstün]

I am sorry but I didnt understand. B(:,:,2,2) should be equal to (-sqrt(2)-1;1) then my logic is completely wrong how can I do that

[madhan ravi]

% a simple example
>> A = zeros(2)

A =

     0     0
     0     0

>> A(:,:) = 1

A =

     1     1
     1     1

>> A = zeros(2)

A =

     0     0
     0     0

>> A(:,:) = 2

A =

     2     2
     2     2

>> 

You're trying to assign 2 rows and 2 columns with 2 rows and 1 column.

 B(:,:,2,2)  = repmat([-sqrt(2)-1; 1],1,2) % this is what can be achieved 

[Gözde Üstün]

Then should I say

B(:,:,2,1)  = repmat([sqrt(2)-1; 1],1,2) 

for having B(:,:,2,1) = [(sqrt(2)-1);1] ? What does it mean this 1and 2 in the your script line?

[madhan ravi]

Yes.

 doc repmat

[Gözde Üstün]

doc repmat ? probably ypu wanted to give the link of document of repmat ? By the way Thanks !

Last question is that can I use it like that:

B(:,:,2,1) = repmat(projectors_of_sigma_x_minus_sigma_z(1),1,2);

Because I have too many value for elements of B and I dont want to wirte them by one by

[madhan ravi]

 projectors_of_sigma_x_minus_sigma_z(:, 1) % this was actually answered in your other question ;)

[Gözde Üstün]

I am actually trying that:

function [A,B] = CHSHmeasurement(d)
    A=zeros(d,d,2,d);
    B=A;
    projectors_of_sigma_x = [1/sqrt(2)*[1;1],1/sqrt(2)*[1;-1]];
    projectors_of_sigma_x_minus_sigma_z = [[(sqrt(2)-1);1],[(-sqrt(2)-1);1]];

    for k = 1:d
        for l =1:length(projectors_of_sigma_x)
           % A(k,k,1,k)=projectors_of_sigma_x(l);
            A(:,:,1,k)=repmat(projectors_of_sigma_x(l),2,2);
        end
        for o = 1: length(projectors_of_sigma_x_minus_sigma_z)
            %B(k,k,2,k)=projectors_of_sigma_x_minus_sigma_z(o);
            B(:,:,2,k)=repmat(projectors_of_sigma_x_minus_sigma_z(o),2,2);
        end 
    end
end

But I have a wrong result

[Gözde Üstün]

And Sorry I missed your previous answer

projectors_of_sigma_x_minus_sigma_z(:, 1) 

This is for what ?

[Gözde Üstün]

Sorry I just saw your answer now Thank you very much :)