Probability of an entanglement state

[phyky]

given two system is entangled, |A>=(|0_{A}>+|1_{A}>)/√2, |B>=(|0_B{}>+|1_B{}>)/√2. entangle state |AB>what is the probability to find |0_A{}0_B{}> and |1_A{}1_B{}>. are there still 1/2 just like normal inner product formulation?

 

[bhobba]

|AB>=(|0a>+|1b>)/√2, what is the probability to find |0a> and |1b>. are there still 1/2?

You need to rephrase that - states with two particles have terms of the form |a>|b>.

Thanks
Bill

 

[bhobba]

Well your rephrased question would be |U> = (|0a>|0b> + |1a>|1b>)/root 2. If you have an observation |0a>|0b> or |1a>|1b> then one or the other will be detected with probability 1/2. This is directly from the Born rule trace formula eg trace (|U><U| |1a>|1b>) = 1/2.

Thanks
Bill