First, you are saying this backwards: operators act on states, not states on operators.deepalakshmi said:I know that |α⟩ don't act on (a^†) because |α⟩ is a eigenstate of lowering operator.
A "Cat state" is a type of quantum state that exhibits properties of both classical and quantum systems. It is a superposition of two distinct states, such as a dead and alive state, that can exist simultaneously until measured or observed.
A Cat state acts on a given Hamiltonian by evolving according to the Schrödinger equation, which describes the time evolution of quantum systems. The Hamiltonian is an operator that represents the total energy of the system, and the Cat state will evolve based on the specific interactions and energies present in the Hamiltonian.
Cat states have been proposed for use in quantum computing, quantum communication, and quantum cryptography. They have also been studied in the context of quantum metrology and precision measurements.
Yes, a Cat state can be observed or measured, but the act of measurement will collapse the state into one of its two distinct states. This is known as the "collapse of the wavefunction" in quantum mechanics.
A Cat state is different from other types of quantum states because it is a superposition of two distinct states, rather than just one state. This allows for the potential for different outcomes or behaviors, depending on the specific interaction with the given Hamiltonian.