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In quantum mechanics a state space is a separable complex Hilbert space.The dimension of this Hilbert space depends on the system we choose to describe. [1] [2] The different states that could come out of any particular measurement form an orthonormal basis, so any state vector in the state space can be written as a linear combination of these basis vectors.
While the state space of a single quantum harmonic oscillator contains all the discrete energy states of one oscillating particle, the state space of a quantum field contains the discrete energy levels of an arbitrary number of particles.
The general state in a Fock space is a linear combination of product states. A state that cannot be written as a convex sum of product states is called an entangled state. When we speak of one particle in state , we must bear in mind that in quantum mechanics identical particles are indistinguishable. In the same Fock space, all particles are ...
Quantum mechanics specifies the construction, evolution, and measurement of a quantum state. The result is a prediction for the system represented by the state. Knowledge of the quantum state, and the rules for the system's evolution in time, exhausts all that can be known about a quantum system.
A quantum state in the Fock space is called a Fock state if it is an element of the occupancy number basis. A Fock state satisfies an important criterion: for each i, the state is an eigenstate of the particle number operator ^ corresponding to the i-th elementary state k i. The corresponding eigenvalue gives the number of particles in the state.
As the field strength, i.e. the oscillation amplitude α of the coherent state is increased, the quantum noise or uncertainty is constant at 1/2, and so becomes less and less significant. In the limit of large field the state becomes a good approximation of a noiseless stable classical wave.
In quantum mechanics and computing, the Bloch sphere is a geometrical representation of the pure state space of a two-level quantum mechanical system , named after the physicist Felix Bloch. [ 1 ] Mathematically each quantum mechanical system is associated with a separable complex Hilbert space H {\displaystyle H} .
Quantum mechanics is a fundamental theory that describes the behavior of nature at and below the scale of atoms. [2]: 1.1 It is the foundation of all quantum physics, which includes quantum chemistry, quantum field theory, quantum technology, and quantum information science.