Two particle system, products and entanglement

In summary: Particle A's most general state is the superposition |A>=a1|0>+a2|1>Particle B's most general state is |B>=b1|0>+b2|1>The reason I used the same basis vectors for both particles is that then the tensor product space is the same as the space of either particle (for 2 particles, the tensor product is the 4D space of all possible states of 2 particles). Writing the states in the form |A>=a1|0>+a2|1> means that the 1st coefficient is the amplitude for finding the particle in state |0> and the 2nd coefficient is the amplitude for finding the particle in state |1
  • #36
fog37 said:
So, when the total wavefunction is separable (i.e. it can be factored), it describes two systems that are two things:
a) Indistinguishable
b) Independent from each other

b), yes. a), no. There is no requirement that the two systems described by a total wave function that is separable be indistinguishable.

fog37 said:
I guess it is possible to have, after the measurement on an entangled system formed by one-two electrons system, two subsystems (the electrons) that are independent and now also distinguishable

They're distinguishable because we measured them, which really means that the "distinguishable" systems are not just the electrons by themselves, but the electrons plus the measuring devices that recorded the results.

Also, as I said before, you can always take the electrons you just measured and have them interact again (which could be as simple as just bringing them back into the same small region of space), which will make them indistinguishable again, so now you have to treat them as a two-particle system with a wave function that has to be antisymmetric under exchange. In other words, the "distinguishability" only lasts as long as you don't change the state of the electrons from the one you measured.
 
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<h2> What is a two particle system?</h2><p>A two particle system refers to a system of two particles that interact with each other. These particles can be atoms, molecules, or subatomic particles such as electrons or protons.</p><h2> What are the products of a two particle system?</h2><p>The products of a two particle system depend on the nature of the particles and their interactions. For example, in a chemical reaction between two molecules, the products may be new molecules or compounds. In a nuclear reaction between two subatomic particles, the products may be different types of particles or energy.</p><h2> What is entanglement in a two particle system?</h2><p>Entanglement in a two particle system refers to the phenomenon where the properties of the two particles become correlated and cannot be described independently. This means that the state of one particle is dependent on the state of the other particle, even if they are separated by a large distance.</p><h2> How is entanglement used in quantum computing?</h2><p>Entanglement is a key concept in quantum computing, where it is used to perform operations on multiple qubits simultaneously. This allows for faster processing and more complex calculations compared to classical computing.</p><h2> Can entanglement be observed in everyday objects?</h2><p>No, entanglement is a quantum phenomenon and is only observed in the microscopic world. It is not possible for everyday objects to exhibit entanglement.</p>

FAQ: Two particle system, products and entanglement

What is a two particle system?

A two particle system refers to a system of two particles that interact with each other. These particles can be atoms, molecules, or subatomic particles such as electrons or protons.

What are the products of a two particle system?

The products of a two particle system depend on the nature of the particles and their interactions. For example, in a chemical reaction between two molecules, the products may be new molecules or compounds. In a nuclear reaction between two subatomic particles, the products may be different types of particles or energy.

What is entanglement in a two particle system?

Entanglement in a two particle system refers to the phenomenon where the properties of the two particles become correlated and cannot be described independently. This means that the state of one particle is dependent on the state of the other particle, even if they are separated by a large distance.

How is entanglement used in quantum computing?

Entanglement is a key concept in quantum computing, where it is used to perform operations on multiple qubits simultaneously. This allows for faster processing and more complex calculations compared to classical computing.

Can entanglement be observed in everyday objects?

No, entanglement is a quantum phenomenon and is only observed in the microscopic world. It is not possible for everyday objects to exhibit entanglement.

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