When a probabilistic bit is in (10)(10) , we apply the operator (1/21/201)(1/201/21)  three times. What is the probability of being in state  ⌈1⌋⌈1⌋   at the end?

We apply a controlled-NOT operator on two probabilistic bits where the second one is the controlled bit and the first one is the target bit.Which of the following matrix represent this operator?Group of answer choices⎛⎝⎜⎜⎜⎜1000010000100001⎞⎠⎟⎟⎟⎟(1000010000100001) ⎛⎝⎜⎜⎜⎜1000010000010010⎞⎠⎟⎟⎟⎟(1000010000010010) ⎛⎝⎜⎜⎜⎜0001001001001000⎞⎠⎟⎟⎟⎟(0001001001001000) ⎛⎝⎜⎜⎜⎜1000000100100100⎞⎠⎟⎟⎟⎟(1000000100100100) ⎛⎝⎜⎜⎜⎜1000001001000001⎞⎠⎟⎟⎟⎟(1000001001000001)  PreviousNext

hich of the following valid probabilities represents an event that is impossible? −1 0 0.0001 1

We apply a controlled-NOT operator on two probabilistic bits where the second one is the controlled bit and the first one is the target bit.Which of the following matrix represent this operator?Group of answer choices⎛⎝⎜⎜⎜⎜1000010000010010⎞⎠⎟⎟⎟⎟(1000010000010010) ⎛⎝⎜⎜⎜⎜0001001001001000⎞⎠⎟⎟⎟⎟(0001001001001000) ⎛⎝⎜⎜⎜⎜1000001001000001⎞⎠⎟⎟⎟⎟(1000001001000001) ⎛⎝⎜⎜⎜⎜1000000100100100⎞⎠⎟⎟⎟⎟(1000000100100100) ⎛⎝⎜⎜⎜⎜1000010000100001⎞⎠⎟⎟⎟⎟(1000010000100001)

Assume we had a particle which initially was at position 𝑅𝑖⃗R i​ ​ . Now, after time 𝑡t has passed, what is the probability of finding that particle in a position 𝑅𝑓⃗R f​ ​ ?⟨𝑅𝑖⃗∣𝑈(𝑡)∣𝑅𝑖⃗⟩⟨ R i​ ​ ∣U(t)∣ R i​ ​ ⟩⟨𝑅𝑓⃗∣𝑅𝑖⃗⟩⟨𝑅𝑖⃗∣𝑅𝑓⃗⟩⟨ R f​ ​ ∣ R i​ ​ ⟩⟨ R i​ ​ ∣ R f​ ​ ⟩⟨𝑅𝑓⃗∣𝑈(𝑡)∣𝑅𝑖⃗⟩⟨ R f​ ​ ∣U(t)∣ R i​ ​ ⟩⟨𝑅𝑓⃗∣𝑈(𝑡)∣𝑅𝑖⃗⟩⟨𝑅𝑖⃗∣𝑈(𝑡)∣𝑅𝑓⃗⟩⟨ R f​ ​ ∣U(t)∣ R i​ ​ ⟩⟨ R i​ ​ ∣U(t)∣ R f​ ​ ⟩⟨𝑅𝑓⃗∣𝑅𝑖⃗⟩⟨ R f​ ​ ∣ R i​ ​ ⟩

A binary source transmits either a symbol "1" or "0" at discrete time intervals. The source could transmit independently either symbol with equal probability. What is the probability of transmitting exactly two "1"s in the first five transmitted symbols?