Vector Notation of Quantum States for 2 Qubit System

[MrMuscle]

TL;DR

How can I write the vector notation of quantum states when I have a 2 qubit system?

I am confused about the vector notation of quantum states when I have a 2 qubit system.

For 1 qubit, I just write l1> = (0 ;1 ) for representing 1,

and l0> = (1;0) for representing 0.

Dirac notation is straightforward
However when it comes to representing two qubits in linear algebra I am confused :(

What is the vector notations for the following ones? Can you suggest a method to calculate them I don't want to memorize.

l00> = ?
l11>= ?
l10>= ?
l01>= ?

Thanks in advance!

 

[Mentz114]

Summary: How can I write the vector notation of quantum states when I have a 2 qubit system?

I am confused about the vector notation of quantum states when I have a 2 qubit system.

For 1 qubit, I just write l1> = (0 ;1 ) for representing 1,

and l0> = (1;0) for representing 0.

Dirac notation is straightforward
However when it comes to representing two qubits in linear algebra I am confused :(

What is the vector notations for the following ones? Can you suggest a method to calculate them I don't want to memorize.

l00> = ?
l11>= ?
l10>= ?
l01>= ?

Thanks in advance!

What you are doing is making a tensor product of two vector spaces, each of dimension 2. Read the first part of this
https://en.wikipedia.org/wiki/Tensor_productor may be this is clearer
https://www.math3ma.com/blog/the-tensor-product-demystified

 

[atyy]

Here are some more links in addition to those above from @Mentz114.
https://www.cs.cmu.edu/~odonnell/quantum15/lecture02.pdfhttps://people.eecs.berkeley.edu/~vazirani/s09quantum/notes/lecture2.pdfhttps://www.cl.cam.ac.uk/teaching/0910/QuantComp/notes.pdf