Difference between interaction and interference of QM systems

In summary, the postulate of quantum mechanics states that identical quantum mechanical systems isolated from each other are described by rays in the tensor product space. If there is no interference between the states, they will be a product state. However, interference between wavefunctions can lead to entangled states that cannot be factored and can affect the outcomes of measurements on the systems. Interaction between systems can also lead to entanglement, but it is not the only factor. Coherence (interference) is an exceptional case that requires a common past, while decoherence is a more general case.
  • #1
jdstokes
523
1
Suppose I have n identical quantum mechanical systems [itex]\mathcal{H}[/itex] isolated from each other. It is a postulate of quantum mechanics that the states of this composite system are described by rays in the tensor product space [itex]\mathcal{H}^{\otimes n}[/itex].

If the states are not allowed to interfere with each other then the state will be a product state of the form [itex]\otimes_{i=1}^n|\alpha_i \rangle[/itex].

Interference between the wavefunctions opens the possibility of entangled states which cannot be factorized into the form above. In this case, the outcomes of measurements on each of the systems can affect the probabilities of the outcomes of measurements on the remaining systems. An example would be the [itex]2^2[/itex] dimensional Hilbert space associated with an electron/positron pair created in the decay of a neutral pion.

Is it correct to say that entanglement is a consequence of wavefunction intereference rather than interaction? In reality the electron/positron pair in the last exam interact via pairwise Coulomb interaction.

Can interactions other than wavefunction interference affect the entanglement between quantum mechanical systems?
 
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  • #2
If I am not wrong in all cases we know, entanglement(interference) is the result of a common (interacting) past as it is in your case.

So I would put the question this way: If two different pions decay at distant locations. Is it possible that the electron from the first decay can be entangled with the positron from the second decay?

I guess it is not principally impossible but it is extremely unlikely because coherence(interference) is an exceptional case (and can therefore occur only if there is a common past) where decoherence is the more general case.

Am I right?
 
  • #3


Yes, it is correct to say that entanglement is a consequence of wavefunction interference rather than interaction. In quantum mechanics, the wavefunction describes the state of a system, and interference occurs when the wavefunctions of different systems overlap and interact with each other. This can lead to entanglement, where the state of one system is dependent on the state of another system, even if they are physically separated.

In the scenario described, the entanglement between the electron and positron is a result of their wavefunctions overlapping and interfering with each other. However, interactions between the two particles, such as the Coulomb interaction, can also affect the entanglement. This is because interactions can change the wavefunctions of the particles, leading to different types of interference and potentially altering the entanglement between the systems.

Additionally, there are other types of interactions that can affect entanglement between quantum mechanical systems. For example, external forces or fields can impact the wavefunctions of the systems and therefore influence their entanglement. Ultimately, any type of interaction between quantum systems can have an impact on their entanglement, as it is a fundamental property of the wavefunction and its behavior.
 

FAQ: Difference between interaction and interference of QM systems

What is the main difference between interaction and interference of quantum mechanical systems?

The main difference between interaction and interference of quantum mechanical systems is the nature of their effects on the systems. Interaction refers to the direct influence of one quantum system on another, while interference refers to the indirect effects resulting from the superposition of quantum states.

How do interactions and interference affect the behavior of quantum systems?

Interactions and interference can both cause changes in the state of a quantum system, but in different ways. Interactions result in the collapse of the system's wave function, while interference leads to the emergence of new probabilities for the system's behavior.

Can interactions and interference occur simultaneously in a quantum system?

Yes, interactions and interference can occur simultaneously in a quantum system. In fact, they often coexist and can even amplify or cancel each other out, leading to complex and unpredictable behaviors.

How does the concept of entanglement relate to interactions and interference?

Entanglement is a phenomenon that arises from the interactions between quantum systems, where the state of one system becomes inseparably linked to the state of another. This entanglement can then lead to interference effects between the two systems.

What are some real-world applications of understanding the difference between interaction and interference of quantum mechanical systems?

Understanding the difference between interaction and interference of quantum mechanical systems is crucial for various technological applications, such as quantum computing, quantum cryptography, and quantum sensing. It also helps us better understand the fundamental principles of quantum mechanics and the behavior of matter at a microscopic level.

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