Exploring Quantum States: Bell vs. Total Spin

In summary, towards the end of the video, the professor defines the four possible states of two entangled electrons as singlet and triplet states. These states are represented by specific combinations of the spin states of the two electrons. However, this definition seems to contradict the four Bell states as defined on Wikipedia, as the first triplet state does not require superposition. It is unclear which of the four Bell states corresponds to the singlet state, and there is no precise mathematical definition of a Bell state for this particular case.
  • #1
nateHI
146
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Towards the end of http://www.youtube.com/watch?v=IAgV-LKTiMI&feature=channel" video at 54:55, the professor defines the four possible states of two entagled electrons as follows:

singlet
|0,0> = |u,d> - |d,u>
triplet
|1,1> = |u,u>
|1,0> = |u,d> + |d,u>
|1,-1> = |d,d>

where:
|u,u>, |u,d>, |d,u>, |d,d>
form the 4 dimensional basis in the space of the total spin of the two electrons.

This doesn't seem to jive with the four bell states as defiend on wikipedia http://en.wikipedia.org/wiki/Bell_state" .

For example, the first triplet state of the total spin as defined above |1,1> is an eigenstate of the |u,u> state and doen't need to be superposed. However, every Bell State as defined by wikipedia is a superposition of two states. What am I missing?

Also, which of the four Bell States is the singlet state?
 
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  • #2
Do you have a precise mathematical definition of a "Bell state" for this particular case? If so, what is it? If not, what do you think it can be?
 

Related to Exploring Quantum States: Bell vs. Total Spin

1. What is the difference between Bell states and total spin states in quantum mechanics?

Bell states are quantum states that are entangled, meaning that the state of one particle is dependent on the state of another particle, even if they are separated by a large distance. Total spin states, on the other hand, refer to the total angular momentum of a system of particles.

2. How are Bell states and total spin states used in quantum computing?

Bell states are used in quantum computing to perform operations on multiple qubits simultaneously, allowing for faster processing and more complex calculations. Total spin states are used to encode information and perform logical operations in quantum algorithms.

3. Are Bell states and total spin states related in any way?

While both Bell states and total spin states are important in quantum mechanics and quantum computing, they are not directly related. However, they do both involve the concept of entanglement, which is a fundamental feature of quantum mechanics.

4. How do Bell states and total spin states contribute to the study of quantum entanglement?

Bell states are a specific type of entangled state that has been extensively studied in the context of quantum entanglement. Total spin states, on the other hand, are used to describe the entanglement of particles with spin, such as electrons or photons.

5. Can Bell states and total spin states be used interchangeably in quantum experiments?

No, Bell states and total spin states are distinct concepts and cannot be used interchangeably in quantum experiments. They have different properties and are used for different purposes in quantum mechanics and quantum computing.

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