These 2 keywords seems almost meaning same. So I wondered how we should distinguish to use these words to use them appropriately.
Response from ChatGPT
Observables: Observables refer to operators used to measure the physical properties or states of a quantum system. Specifically, they represent physical quantities such as energy, spin, or position. Observables are represented as either Unitary operators or Hermitian operators. Unitary operators are used to transform the state of quantum bits and play a significant role in executing algorithms in quantum computation. On the other hand, Hermitian operators represent physical quantities, and during measurement, they project the state of the quantum bit onto a basis state (e.g., |0> or |1>) to obtain physical information.
Projection Measurements: Projection measurements are a measurement technique used to project the state of a quantum bit onto a specific basis state. When a quantum bit is in a superposition state, a projection measurement can determine the probability of it being projected onto a particular basis state. For example, if a quantum bit is in a superposition state (α|0> + β|1>), a projection measurement in the Z basis (basis of |0> and |1>) will reveal that |0> is measured with a probability of |α|^2 and |1> is measured with a probability of |β|^2. Projection measurements are also essential for determining physical quantities, and measurements using Observables (Hermitian operators) are effectively performed through projection measurements.
In simple terms, Observables are operators representing physical quantities, and projection measurements are a technique to measure a quantum bit’s state by projecting it onto a specific basis state. Observables and projection measurements are crucial concepts in quantum computing for obtaining physical information and are indispensable for understanding quantum algorithms and executing calculations.
Conclusion
Observables is a term used for physical quantum measurements, while Projection Measurements is a term used for measuring quantum states in quantum computing. Although both terms have similar meanings, Observables can be considered a broader concept.
