Decoherence Pure States Into Mixed States

In summary, decoherence refers to the transformation of a pure state into an improper mixed state after interaction with the environment. This mixed state is equivalent to the apparent collapse and follows the Born rule probabilities. However, the specific mixed state that the pure state transforms into depends on the type of interaction between the system and the environment, and the observable being measured. This means that there are multiple possible mixed states that the pure state could transform into, depending on the basis or observable being measured. This is not always reflected in examples found online, which typically show only one possible mixed state.
  • #1
Electric to be
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According to decoherance.

Say there is a pure state initially in state:

|ψ⟩=α|0⟩+β|1⟩

After decoherance (interaction with environment), the system will transform into the improper mixed state of:

ρ=|α|2|0⟩⟨0|+|β|2|1⟩⟨1|

This is the "apparent" collapse that decoherance refers to. With the probabilities of the mixed state being equal to the Born rule probabilities. However, why is this the mixed state that the pure state transforms into? For example, doesn't this assumes that the "measurement" interaction of the environment is for the observable/basis that the pure state was initially expressed in?

Is the mixed state shown above just one of many possible mixed states that the pure state could have transformed into? Depending on the type of interaction of the system and the environment. Or in other words, which observable was being measured?

For example, using a standard measurement collapse postulate, I could have collapsed an original wavefunction into many different final states with different probabilities depending on which operator/observable I am measuring. Shouldn't this be reflected in the pure state being decohered into a mixed state? All examples I've seen online have shown exactly what I wrote above.

Thanks.
 
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  • #2
Electric to be said:
doesn't this assumes that the "measurement" interaction of the environment is for the observable/basis that the pure state was initially expressed in?
Yes. It depends on the system's interaction with the environment.
 
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  • #3
Yes consider |0><a| for a different basis.
 

FAQ: Decoherence Pure States Into Mixed States

What is decoherence?

Decoherence is a process in which a quantum system interacts with its surrounding environment, causing the system to lose its quantum properties and behave more like a classical system. This results in the pure states of the system becoming mixed states.

Why does decoherence occur?

Decoherence occurs due to the presence of external factors, such as interactions with other particles or the effects of temperature and radiation, which disrupt the quantum coherence of a system and lead to the loss of information about its exact state.

How does decoherence affect quantum computing?

In quantum computing, decoherence can negatively impact the performance of quantum algorithms by introducing errors and reducing the accuracy of results. This is why researchers work to minimize decoherence effects in quantum systems.

Can decoherence be reversed?

It is difficult to reverse decoherence once it has occurred, as the information about the original pure state of a system is lost. However, techniques such as error correction can be used to mitigate the effects of decoherence and improve the reliability of quantum computations.

What are the applications of studying decoherence?

Studying decoherence is important for understanding the behavior of quantum systems and how they interact with their environments. It has practical applications in quantum information processing, quantum simulations, and quantum metrology, among others.

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