Heisenberg's uncertainty principle for simultaneous measurement of positive-operator-valued measures

Physical Review A - Atomic, Molecular, and Optical Physics

Volumn 78, Issue 5, 2008, Pages

  Miyadera, Takayuki ^a   Imai, Hideki ^a  

^a NATIONAL INSTITUTE OF ADVANCED INDUSTRIAL SCIENCE AND TECHNOLOGY AIST   (Japan)

Author keywords

[No Author keywords available]

Indexed keywords

TURBULENT FLOW;

HEISENBERG'S UNCERTAINTY PRINCIPLES; NONCOMMUTATIVE; NONCOMMUTATIVITY; SIMULTANEOUS MEASUREMENTS;

UNCERTAINTY ANALYSIS;

EID: 56849110147     PISSN: 10502947     EISSN: 10941622     Source Type: Journal    
DOI: 10.1103/PhysRevA.78.052119     Document Type: Article

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18. A map Γ from a von Neumann algebra A to a von Neumann algebra B is called a unital completely positive map if (i) it is linear, (ii) Γ (1) =1, and (iii) its extension Γid:AM (CN) →BM (CN) [M (CN) is a set of all the N×N matrices] for any positive integer N is positive. The condition (iii) is called complete positivity. If A is Abelian, the complete positivity of the map Γ automatically follows from its positivity.