Why are interacting states necessarily entangled?

In summary, the conversation discusses the concept of entanglement in composite systems of interacting particles. It is questioned why these particles are always in entangled states instead of product states. The conversation concludes that there are no special physical conditions for particles to be in an entangled state upon interaction, and that entanglement can exist between particles and their environment rather than just between the particles themselves.
  • #1
metroplex021
151
0
It just occurred to me that I don't know why composites of interacting particles are always in entangled -- as opposed to mere product -- states. Obviously if they are not interacting we will just represent them as being in a product state; but why is it that being in a product state entails not interacting?

Any comments appreciated! Thanks!
 
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  • #2
You have to clarify what you mean I think. I don't see any problem with particles being interacting and in a product state at the same time. A straightforward example is 2 ions trapped in the same ion trap. They would have to be considered as interacting because they affect each other with mutual coulomb forces, but they can surely be in a product state.

Where you think of some special situations or interactions?
 
  • #3
Huh! I was wrong about that then. Thanks for putting me straight. Can I then ask: does anyone know what physical conditions have to be fulfilled for a pair of particles to go into an entangled state upon interaction? Thanks to anyone who can help!
 
  • #4
metroplex021 said:
does anyone know what physical conditions have to be fulfilled for a pair of particles to go into an entangled state upon interaction?
There are no special physical conditions. Most states in the composite Hilbert space of two single systems are entangled states. If the particles interact and we initially prepare a product state, it is simply much more likely that at an arbitrary later time, the product state has evolved into an entangled state instead of another product state.

In the example of the ion trap, we have to consider an additional third system: the trap. If the particles are in a product state at all times, this means that the interaction with the trap is such that it destroys the entanglement of the particles on a short time scale (decoherence). Entanglement then exists between the particles and the trap and not between the particles themselves.
 
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  • #5
Perfect, thank you. Much appreciated!
 

1. Why are interacting states necessarily entangled?

Interacting states are necessarily entangled because when two particles interact with each other, their quantum states become correlated. This means that the state of one particle cannot be described independently of the other particle's state. This correlation is known as entanglement.

2. What is the significance of entanglement in quantum mechanics?

Entanglement is a fundamental property of quantum mechanics that allows particles to be connected in a non-local way. This means that the state of one particle can affect the state of another particle, even if they are separated by large distances. Entanglement plays a crucial role in many quantum technologies, such as quantum computing and quantum cryptography.

3. Can entanglement be created artificially?

Yes, entanglement can be created artificially through a process called quantum entanglement. This involves manipulating the quantum states of particles to make them correlated with each other. This can be achieved through various methods, such as using quantum gates in a quantum computer or using entangling measurements in a quantum system.

4. How does entanglement affect the measurement of quantum states?

Entanglement can have a significant impact on the measurement of quantum states. When two entangled particles are measured, the outcome of the measurement for one particle is instantly determined by the measurement of the other particle, regardless of the distance between them. This phenomenon, known as quantum non-locality, is one of the most mysterious and fascinating aspects of entanglement.

5. Is entanglement a fragile phenomenon?

Entanglement is considered to be a fragile phenomenon because it can be easily disrupted by interactions with the environment. This is known as decoherence, and it can destroy the entanglement between particles, making them behave like classical, non-entangled objects. Therefore, careful control and isolation of entangled particles are essential for maintaining their entangled state and harnessing its potential in quantum technologies.

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