Editing Probability amplitude (section)

==Composite systems==
For two quantum systems with spaces {{math|''L''<sup>2</sup>(''X''<sub>1</sub>)}} and {{math|''L''<sup>2</sup>(''X''<sub>2</sub>)}} and given states {{math|{{ket|&Psi;<sub>1</sub>}}}} and {{math|{{ket|&Psi;<sub>2</sub>}}}} respectively, their combined state {{math|{{ket|&Psi;<sub>1</sub>}} [[outer product|⊗]] {{ket|&Psi;<sub>2</sub>}}}} can be expressed as {{math|''&psi;''<sub>1</sub>(''x''<sub>1</sub>) ''&psi;''<sub>2</sub>(''x''<sub>2</sub>)}} a function on {{math|''X''<sub>1</sub> [[direct product|×]] ''X''<sub>2</sub>}}, that gives the
[[product measure|product of respective probability measures]]. In other words, amplitudes of a non-[[quantum entanglement|entangled]] composite state are [[multiplication|products]] of original amplitudes, and [[#convenient|respective observables]] on the systems 1 and 2 behave on these states as [[independent random variables]]. This strengthens the probabilistic interpretation explicated [[#The laws of calculating probabilities of events|above]] .