The sticky elactic in the Bloch sphere

In summary, Aerts describes a model of a qubit on the Bloch sphere that is measured along a different direction than its initial position. The measurement is represented by an elastic band between two opposite points on the sphere. The qubit falls orthogonally on the band and is projected to either point A or B, according to the probability formula of quantum mechanics. This can be visualized through a circuit diagram, where the probability of a wire being measured as On closely follows its vertical position on the Bloch sphere representation.
  • #1
naima
Gold Member
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I found a funny model of the qubit written by Aerts in
Foundations of quantum physics: a general
realistic and operational realistic and operational approach.

At the beginning the qubit is at the point P on the Bloch sphere. It will be measured along another direction (two opposite points on the sphere). There is an elastic between these points. A and B. P falls orthogonally on AB at Q and then the elastic breaks somewhere between A and B. So Q is projected to up (A) or down (B) according to the probability formula of QM!
 
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  • #2
Yes; as far as the probabilities go, measurement is like a projection. This is true even for complicated measurements involving many qubits, though there's not a nice sphere-based visualization of those.

Here's a circuit diagram showing it happening. Notice how the probability of a wire being measured as On (+Z instead of -Z) closely tracks the vertical position on the Bloch sphere representation of the wire's state, and how the measured wire's state is pinned along the Z axis:

kINmB9c.gif
 
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Related to The sticky elactic in the Bloch sphere

1. What is the Bloch sphere and how does it relate to quantum physics?

The Bloch sphere is a geometric representation of the quantum state of a two-level system, such as an electron or a spin-1/2 particle. It is commonly used in quantum physics to visualize the state of a qubit, which is the basic unit of quantum information.

2. What is the significance of the sticky elastic in the Bloch sphere?

The sticky elastic in the Bloch sphere refers to the phenomenon of the qubit's state being able to "stick" to certain points on the surface of the sphere. This is due to the nature of quantum superposition, where the qubit can exist in multiple states at the same time.

3. How does the sticky elastic affect the measurement of the qubit's state?

The sticky elastic can affect the measurement of the qubit's state by causing it to collapse to a specific point on the Bloch sphere, depending on where it was "sticking" before the measurement. This is important in quantum computing, where measurements are used to read the output of a quantum circuit.

4. Can the sticky elastic ever be broken or removed from the Bloch sphere?

The sticky elastic on the Bloch sphere is a metaphor for the inherent unpredictability of quantum states. It cannot be physically broken or removed, as it represents the uncertain nature of quantum particles and their states.

5. How does the sticky elastic in the Bloch sphere relate to quantum entanglement?

Quantum entanglement is a phenomenon where two or more particles become connected in such a way that the state of one particle affects the state of the others, regardless of their physical distance. The sticky elastic in the Bloch sphere can represent this connection, as the state of one particle can affect the state of another particle even if they are separated.

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