How Do Bell States Compare to Total Spin States in Quantum Mechanics?

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SUMMARY

The discussion centers on the comparison between Bell states and total spin states in quantum mechanics, specifically regarding two entangled electrons. The four total spin states are defined as singlet |0,0> = |u,d> - |d,u> and triplet states |1,1> = |u,u>, |1,0> = |u,d> + |d,u>, |1,-1> = |d,d>. The confusion arises from the distinction that while triplet states can exist as eigenstates, Bell states are defined as superpositions of two states. The singlet state corresponds to one of the Bell states, specifically the state that represents maximal entanglement.

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  • Understanding of quantum mechanics concepts, particularly entanglement
  • Familiarity with quantum state notation, including Dirac notation
  • Knowledge of Bell states and their mathematical definitions
  • Basic grasp of spin states in quantum systems
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  • Study the mathematical definitions of Bell states in quantum mechanics
  • Explore the implications of entanglement in quantum computing
  • Learn about the differences between eigenstates and superposition states
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Quantum physicists, students of quantum mechanics, and researchers in quantum information science will benefit from this discussion.

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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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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?
 

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