QM: Purity, two-outcome measurements

In summary, the conversation was about using additional equations, Tr(B) and purity, for two questions. The person asking for help expressed confusion with calculating trace and purity, and asked for guidance on how to proceed with the second question. The expert suggested going step by step and provided a clarification for the first question.
  • #1
alc95
7
0

Homework Statement


upload_2017-11-13_23-44-34.png


Homework Equations


in addition to those provided in the questions, I used the following:

Tr(B) = sigma<x_j|B|x_j>
purity = Tr(rho^2)

The Attempt at a Solution


upload_2017-11-13_23-49-1.png


upload_2017-11-13_23-49-37.png

[/B]
I find calculating trace and purity very confusing. Am I on the right track with question 1? With question 2, I am really unsure about how to proceed further. Any help would be greatly appreciated.

Thanks in advance. :smile:
 

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  • #2
In Q1, you didn't specify what ##|x_k \rangle## is.

For Q2, just go step by step, either by replacing the density operator for its bracket representation then taking the trace, or the other way around.
 

1. What is QM purity?

QM purity refers to the measure of the degree of "purity" or coherence of a quantum state. It is a measure of how much a quantum state is in a single, specific state, as opposed to a mixture of multiple states.

2. How is QM purity calculated?

QM purity is calculated using the density matrix of a quantum state. It is equal to the trace of the density matrix squared, and ranges from 0 to 1, with 1 representing a pure state and 0 representing a completely mixed state.

3. What is a two-outcome measurement in QM?

A two-outcome measurement in QM is a type of measurement that results in only two possible outcomes. This type of measurement is commonly used in quantum information processing and can provide information about the state of a quantum system.

4. How does QM purity relate to two-outcome measurements?

In QM, the purity of a state can be affected by measurements. In the case of two-outcome measurements, the purity of a state can decrease if the measurement is not perfectly accurate. This is because the measurement introduces uncertainty into the state, making it less pure.

5. What are some real-world applications of QM purity and two-outcome measurements?

QM purity and two-outcome measurements have various applications in fields such as quantum computing, quantum cryptography, and quantum sensing. These concepts are also important in understanding and manipulating quantum systems for technologies like quantum teleportation and quantum communication.

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