Vector Notation of Quantum States for 2 Qubit System

In summary, the conversation is about finding the vector notation for representing quantum states in a 2 qubit system. The speaker is confused about how to do this and is asking for a method to calculate the vector notations without having to memorize them. They also mention the concept of tensor product and provide links for further reading.
  • #1
MrMuscle
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TL;DR 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!
 
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  • #2
MrMuscle said:
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
 
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1. What is vector notation in quantum mechanics?

Vector notation in quantum mechanics is a way of representing quantum states using mathematical vectors. This notation is based on the concept of superposition, where a quantum state can exist in multiple states simultaneously. The vectors used in this notation are called ket vectors, and they represent the possible states of a quantum system.

2. What is a 2 qubit system in quantum mechanics?

A 2 qubit system in quantum mechanics refers to a system that has two quantum bits, or qubits. A qubit is the basic unit of quantum information and can exist in multiple states at once, unlike classical bits which can only be in one state at a time. 2 qubit systems are often used in quantum computing and quantum communication.

3. How is vector notation used in 2 qubit systems?

Vector notation is used to represent the quantum states of a 2 qubit system. The ket vectors in this notation represent the possible states of the two qubits, and the coefficients in front of the ket vectors represent the probability amplitudes of each state. By manipulating these vectors, we can perform operations and measurements on the 2 qubit system.

4. Can vector notation be used for larger quantum systems?

Yes, vector notation can be used for any quantum system, regardless of its size. However, as the number of qubits in a system increases, the number of possible states and the complexity of the calculations also increase. This is why vector notation is often used for smaller quantum systems, while other notations may be used for larger ones.

5. What are the advantages of using vector notation in quantum mechanics?

Vector notation is a powerful tool in quantum mechanics because it allows us to easily represent and manipulate quantum states. This notation also allows for the use of linear algebra techniques, making calculations and operations on quantum systems more efficient. Additionally, vector notation helps us visualize and understand the complex concept of superposition in quantum mechanics.

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