Two systems (microscopic particles or even macroscopic bodies [12]) are said to be quantum entangled if they are described by a joint wave function that cannot be written as a product of wave functions of each of the subsystems (or, for mixed states, if a density matrix cannot be written as a weighted sum of product density matrices). The subsystems can be said not to have a state of their own, even though they may be arbitrarily far apart.
Dirak
- Wants to talk about
- superposition of states, so first talks about
- states
One can describe the state (or states) of a component (such as a particle, something that has properties such as mass, moment of inertia, etc.) in an atomic system that interact according to specific laws.
Each motion of a particle or body in this atomic system is a state of the system.
Quantum limitations mean that a state of an atomic system cannot be given in the degree of specificity that classical physics would suggest is possible. A quantum state of an atomic system will have fewer data or more indefinite data than that.
"A state of a system may be defined as an undisturbed motion that is restricted by as many conditions or data as are theoretically possible without mutual interference or contradiction." p. 11
"The general principle of superposition of quantum mechanics applies to the states, with either of the above meanings, of any one dynamical system. It requires us to assume that between these states there exist peculiar relationships such that whenever the system is definitely in one state we can consider it as being partly in each of two or more other states. The original state must be regarded as the result of a kind of superposition of the two or more new states, in a way that cannot be conceived on classical ideas. Any state may be considered as the result of a superposition of two or more other states, and indeed in an infinite number of ways.