1) The phenomenon of quantum entanglement, where two particles become correlated in such a way that the state of one particle is instantaneously influenced by the measurement of the other particle, might seem to violate the principles of special relativity, which state that no information can be transmitted faster than the speed of light. However, this is not the case, and quantum entanglement does not violate the no-signalling theorem.
The no-signalling theorem ensures that no information can be communicated between two distant entangled particles through their entanglement faster than the speed of light. While the measurement of one entangled particle can instantaneously determine the state of the other, this does not enable any form of communication or information transfer. The outcomes of the measurements on the entangled particles are inherently random and unpredictable before the measurements take place, so there is no way to use entangled particles to transmit information in a controlled manner.
2) If an observer measures the spin of Particle A along the z-axis and finds it to be "up," the state of Particle B will be instantaneously determined to be "down" in the z-axis direction. This is a consequence of their entanglement, which guarantees opposite spin outcomes.
If a second observer, unaware of the first measurement, measures the spin of Particle B along the x-axis, there are two possible outcomes:
- The probability of finding Particle B's spin to be "up" along the x-axis is 50%.
- The probability of finding Particle B's spin to be "down" along the x-axis is also 50%.
The previous measurement of Particle A along the z-axis does not affect the outcome probabilities of the x-axis measurement on Particle B, as the outcomes are statistically independent.
3) Quantum teleportation is a remarkable quantum communication protocol that allows the transfer of an unknown quantum state from one location (sender) to another distant location (receiver) using entanglement as a resource. Here's a step-by-step explanation of the process:
- Entanglement Preparation: Alice and Bob share an entangled pair of particles, typically photons, in a Bell state. Alice keeps one particle, and Bob keeps the other.
- Initial State Preparation: Alice possesses a quantum state |ψ⟩ that she wants to teleport to Bob.
- Bell Measurement: Alice performs a joint measurement of her unknown state |ψ⟩ and her part of the entangled pair.
- Communication of Classical Information: Alice obtains two classical bits of information as a result of the measurement and communicates these to Bob through classical channels.
- Conditional Operations: Based on the classical information, Bob performs specific quantum operations on his particle.
- Teleportation Complete: After Bob performs the operations, his particle now holds the exact quantum state |ψ⟩ that Alice wanted to teleport.
Quantum teleportation is a fundamental process in quantum information science and enables secure quantum communication and quantum computing.