Quantification of quantum correlation of ensembles of states

Physical Review A - Atomic, Molecular, and Optical Physics

Volumn 75, Issue 6, 2007, Pages

  Horodecki, Michał ^a   Sen, Aditi ^a,b,c   Sen, Ujjwal ^a,b,c  

^a UNIVERSITY OF GDA SK   (Poland)

^b ICFO INSTITUT DE CIENCIES FOTONIQUES   (Spain)

^c LEIBNIZ UNIVERSITY HANNOVER   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

BOUNDARY CONDITIONS; ELECTRONIC STATES; HILBERT SPACES;

HEISENBERG UNCERTAINTY RELATION; QUANTUM CORRELATION;

QUANTUM THEORY;

EID: 34547237916     PISSN: 10502947     EISSN: 10941622     Source Type: Journal    
DOI: 10.1103/PhysRevA.75.062329     Document Type: Article

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32. (x1,..., xd) is "majorized" by (y1,..., yd) (both arranged in decreasing order), if i=1 l xi ≤ i=1 l yi, where l=1,...d-1, and equality holds when l=d. See, e.g., R. Bhatia, Matrix Analysis (Springer, New York, 1997).
33. η ik {ηi AB} i=1 n has "nonzero overlap" with A, if η ik 0, for some A. The set of such η ik of {ηi AB} i=1 n is called "overlap of { ηi AB } i=1 n with A. "
34. To be precise, a set of N states {ηi} are LOCC distinguishable if the corresponding ensemble of those states, given with equal probabilities, has an accessible information under LOCC equal to log2 N. If the accessible information under LOCC is strictly less than log2 N, then the set of states are LOCC-indistinguishable.
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40. For orthogonal bases i=1 dim Hk of Hk (k=A,B,...), i,j, =1 dim HA, dim HB, is the corresponding multiorthogonal basis. Such a basis is trivially distinguishable by LOCC between A,B,..., and so has Q=0.