Entangled quantum states as direction indicators

Physical Review Letters

Volumn 86, Issue 18, 2001, Pages 4160-4162

  Peres, Asher ^a   Scudo, Petra F ^a  

^a TECHNION ISRAEL INSTITUTE OF TECHNOLOGY   (Israel)

Author keywords

[No Author keywords available]

Indexed keywords

BESSEL FUNCTIONS; EIGENVALUES AND EIGENFUNCTIONS; ELECTRON ENERGY LEVELS; ERRORS; INTEGRAL EQUATIONS; MATRIX ALGEBRA; POLYNOMIALS; PROBABILITY; VECTORS;

ENTANGLED QUANTUM STATES; MEAN SQUARE ERROR; POSITIVE OPERATOR VALUED MEASURE;

QUANTUM THEORY;

EID: 17144447031     PISSN: 00319007     EISSN: None     Source Type: Journal    
DOI: 10.1103/PhysRevLett.86.4160     Document Type: Article

References (15)

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6. Y. Aharonov and S. Popescu (private communication).
7. If N ≤ 4, an optimal POVM can have a finite number of components, corresponding to the vertices of regular polyhedra. In general, a POVM with a nonuniform distribution of directions on the unit sphere can be converted into a uniform one by rotational symmetrization. This does not affect the fidelity of transmission if the input is uniform. We can therefore assume that the POVM distribution is uniform without loss of generality.
8. k.
9. This is the reason each value of j can occur only once in the POVM, as otherwise there would be off-diagonal elements in the sum. Such off-diagonal elements can still be avoided by introducing new "internal" quantum numbers but, as explained above, any additional information would refer to these new numbers, not to the direction indicated by Alice.
10. A. R. Edmonds, Angular Momentum in Quantum Mechanics (Princeton University Press, Princeton, 1957).
11. 2 = 1 for each j. Likewise, Alice's signal state (12) may include all j and all m. In that case, it can be proved that fidelity is optimal if a single value of m is used.
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