Quantum trajectories Consider that we have a pair of qubits that are initialized in the state: 14 (0)) = 100). We want to evolve those qubits such as the sideband interaction such that the timestep dt is set at 0.1 and that at each timestep we can apply the following: 14 (t + dt)) = eil0:01+0707 )dt|4 (t)) *Sideband coupling-interaction, in the Z basis, return zero when multiplied or acting on 101) and 11). It will swaps to 100) and 11). Host = (0707 0'0') = 0,*0,1 +070 (a) Use a coding software (preferably python-show screenshot of the code) to plot the expectation values as a function of time, for t running from 0 to 10. We want to identify the points where the state is maximally entangled and the points when there is no entanglement at all. The sideband interaction is define such that (b) The state is most entangled when its overlap with a Bell state (100) i|11/72) is 1 (maximize), and unentangled when it is a product state like 100) and 11). Identify then the points where the state is maximally entangled and the points where entanglement does not exit. (d) Let's imagine that every time t is an integer such t= 1,2,3...), we measure the state of the second qubit along Z. Meaning, if found in 10), nothing is done and if found in (1) an X, to flip it back to 10). Rest operation and we want to continue evolving the system in time. Plot (21) as a function of time for a sequence of measurements. (e) Construct a few hundred such traces, average them, and plot the result. (Quantum trajectory average), and is a way of predicting what you would. Quantum trajectories Consider that we have a pair of qubits that are initialized in the state: 14 (0)) = 100). We want to evolve those qubits such as the sideband interaction such that the timestep dt is set at 0.1 and that at each timestep we can apply the following: 14 (t + dt)) = eil0:01+0707 )dt|4 (t)) *Sideband coupling-interaction, in the Z basis, return zero when multiplied or acting on 101) and 11). It will swaps to 100) and 11). Host = (0707 0'0') = 0,*0,1 +070 (a) Use a coding software (preferably python-show screenshot of the code) to plot the expectation values as a function of time, for t running from 0 to 10. We want to identify the points where the state is maximally entangled and the points when there is no entanglement at all. The sideband interaction is define such that (b) The state is most entangled when its overlap with a Bell state (100) i|11/72) is 1 (maximize), and unentangled when it is a product state like 100) and 11). Identify then the points where the state is maximally entangled and the points where entanglement does not exit. (d) Let's imagine that every time t is an integer such t= 1,2,3...), we measure the state of the second qubit along Z. Meaning, if found in 10), nothing is done and if found in (1) an X, to flip it back to 10). Rest operation and we want to continue evolving the system in time. Plot (21) as a function of time for a sequence of measurements. (e) Construct a few hundred such traces, average them, and plot the result. (Quantum trajectory average), and is a way of predicting what you would