# Entanglement/correlations in time

• I
• WWCY
In summary, the concept of bi-partite entanglement involves writing the combined Hilbert space as a tensor-product of Hilbert spaces for two particles, with a non-separable state indicating entanglement. It is possible to extend this idea to a single particle at two different points in time, and there are published papers discussing this concept. For a free particle, the state at a later time is dependent on the state at an earlier time, indicating entanglement. However, it is possible to completely erase the information in the particle after the earlier time, resulting in no entanglement in the later state. In the case of two particles, it is possible to erase the entanglement and have two independent particles for a quantum experiment
WWCY
From what I know about (bi-partite) entanglement, we write the combined Hilbert space as a tensor-product of Hilbert spaces for a particle at ##A## and a particle at ##B##, ie ##\mathcal{H} = \mathcal{H} ^{A} \otimes \mathcal{H} ^{B}##. If the particles share a non-separable state, they are considered to be "entangled".

Is it possible to do this in terms of a single particle but at two instances in time? So: ##\mathcal{H} = \mathcal{H} ^{t_1} \otimes \mathcal{H} ^{t_2}## for ##t_1 < t_2##. If so, are there any published papers that expand on this idea?

Cheers.

If we have a free particle, then, obviously, its state at the time t_2 depends on the state at t_1. We may say that the states are entangled.

Can we completely erase the information in the particle after t_1? Then there would be no entanglement to the later state.

If we have two particles, they may be entangled before we prepare them to a quantum experiment. We assume that we can erase the entanglement, and we get two independent particles to the experiment.

The erasing is possible.

## 1. What is entanglement?

Entanglement is a phenomenon in quantum mechanics where two or more particles become connected in such a way that the state of one particle is dependent on the state of the other, even when they are separated by large distances.

## 2. How does entanglement relate to correlations in time?

Entanglement and correlations in time are closely related as entangled particles can exhibit correlations in their behavior over time, even when they are not in direct contact with each other.

## 3. Can entanglement be observed in everyday objects?

No, entanglement is a phenomenon that is only observed at the quantum level and cannot be observed in everyday objects. It requires extremely precise measurements and controlled conditions to be observed.

## 4. What are some potential applications of entanglement and correlations in time?

Entanglement and correlations in time have potential applications in quantum computing, quantum communication, and quantum cryptography. They can also be used to study and understand complex quantum systems.

## 5. Can entanglement be used for faster-than-light communication?

No, even though entanglement allows for instantaneous correlation between particles, it cannot be used for faster-than-light communication. This is because the information obtained from measuring an entangled particle is random and cannot be controlled or manipulated to transmit a specific message.

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