Quantum Computing Postulate

28 May 2022

Postulate is a proposition assumed to be true without proof.

All physical systems correspond to a complex vector space (Hilbert space) with internality. These spaces are called state spaces of the system.
The unit vector of the state space represents the physical system of that state space, called the state vector.
State vectors contain all the information known to the system.
All observations of a physical system are expressed as Hermitian operators that act on the state space of that system.
Any measurement performed on a quantum system must involve interaction between the system and the observer.
Therefore, when an observation is measured and a specific result λ is obtained, the meter remains in the eigenvector state of the operator whose eigenvalue is λ.
The probability of measuring the observed quantity with the quantum state λ is as follows:
```
prob(λ) = |<α|λ>|²
```
where |α> is the eigenvector of the corresponding Hermit operator with a vaiue of λ.
Measurement results from a system with identical state vectors may not be the same.
Only the probabilities of various results can be known.
The expected value of measurable amount Q is defined as the average value obtained when measuring Q on a number of systems having the same status vector |u>.The expected values are assumed to be:
```
 <u|Q|u>
```
where <u|u> = 1
The state space of the composite physical system is the tensile power of the state space of the component system.
The variation of the quantum system over time is described as unitary transformation.