Distinguishability of complete and unextendible product bases

Physical Review A - Atomic, Molecular, and Optical Physics

Volumn 70, Issue 2, 2004, Pages

  De Rinaldis, S ^a,b  

^a UNIVERSITY OF TORONTO   (Canada)

^b IBM T J WATSON RESEARCH CENTER   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

ENTROPY; FUNCTIONS; MATHEMATICAL OPERATORS; MEASUREMENT THEORY; PROBABILITY; SET THEORY; THEOREM PROVING; VECTORS;

CLASSICAL COMMUNICATIONS; ENTROPY FUNCTION; LOCAL OPERATIONS AND CLASSICAL COMMUNICATIONS (LOCC); UNEXTENDIBLE PRODUCT STAGES (UPB);

QUANTUM THEORY;

EID: 19544369292     PISSN: 10502947     EISSN: None     Source Type: Journal    
DOI: 10.1103/PhysRevA.70.022309     Document Type: Article

References (17)

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12. This is only a necessary condition for writing a LOCC opera tor. Actually in the proof we never use neither that in every round the POVM element must sum to the identity nor classical communication. In fact the Part II of the proof is valid for separable operators, but only for the ones "near" the identity, since a complete product basis is always distinguishable by separable superoperators.
13. The fact, proved in part (i), that there are not POVM elements (except multiples of the identity, that keep the states orthogonal, is essential. If not we could have ∈>0 and δ=0 after stage I.
14. In the particular case of the nine dominolike state of Ref. [4], in Refs. [3,15] a similar argument is applied showing that a POVM different from the unitary operator leads to nonorthogonality of states. However it requires to write the equations for the specific case and to prove that they have no solutions.
15. B. Groisman and L. Vaidman, e-print quant-ph/0103084.
16. J. C. Lagarias, and P. Shor, Bull. Am. Math. Soc. 27, 279 (1992); Discrete Comput. Geom. 11, 359 (1994).
17. J. C. Lagarias, and P. Shor, Bull. Am. Math. Soc. 27, 279 (1992); Discrete Comput. Geom. 11, 359 (1994).