Optimal compression for mixed signal states

Physical Review A - Atomic, Molecular, and Optical Physics

Volumn 61, Issue 5, 2000, Pages 523091-523094

  Horodecki, Michal ^a  

^a UNIVERSITY OF GDA SK   (Poland)

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EID: 0347741639     PISSN: 10502947     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article

References (29)

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5. This result was generalized to cover the case of unknown parameters of the source; see M. Horodecki, R. Horodecki, and P. Horodecki, Acta Phys. Slov. 48, 133 (1998); R. Jozsa, M. Horodecki, P. Horodecki, and R. Horodecki, Phys. Rev. Lett. 81, 1714 (1998). See also C. Krattenthaler and P. Slater, e-print quant-ph/9612043; M. Nielsen Ph.D. thesis, University of New Mexico, 1998.
6. This result was generalized to cover the case of unknown parameters of the source; see M. Horodecki, R. Horodecki, and P. Horodecki, Acta Phys. Slov. 48, 133 (1998); R. Jozsa, M. Horodecki, P. Horodecki, and R. Horodecki, Phys. Rev. Lett. 81, 1714 (1998). See also C. Krattenthaler and P. Slater, e-print quant-ph/9612043; M. Nielsen Ph.D. thesis, University of New Mexico, 1998.
7. This result was generalized to cover the case of unknown parameters of the source; see M. Horodecki, R. Horodecki, and P. Horodecki, Acta Phys. Slov. 48, 133 (1998); R. Jozsa, M. Horodecki, P. Horodecki, and R. Horodecki, Phys. Rev. Lett. 81, 1714 (1998). See also C. Krattenthaler and P. Slater, e-print quant-ph/9612043; M. Nielsen Ph.D. thesis, University of New Mexico, 1998.
8. This result was generalized to cover the case of unknown parameters of the source; see M. Horodecki, R. Horodecki, and P. Horodecki, Acta Phys. Slov. 48, 133 (1998); R. Jozsa, M. Horodecki, P. Horodecki, and R. Horodecki, Phys. Rev. Lett. 81, 1714 (1998). See also C. Krattenthaler and P. Slater, e-print quant-ph/9612043; M. Nielsen Ph.D. thesis, University of New Mexico, 1998.
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14. H. Barnum, C. Caves, C. A. Fuchs, R. Jozsa, and B. Schumacher (unpublished); C. A. Fuchs and J. van de Graaf, IEEE Trans. Inf. Theory 45, 1216 (1999).
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19. Recall that the purification of a state ρ acting on H is a pure state P acting on H⊗H′. such that ρ is its partial trace over the space H′. [15] By "signal state" we mean the state of sequence of the systems emitted by the source.
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23. The presented reasoning is also true within the blind scheme. Then formula (9) holds for passive information too (although the involved extensions may be different).
24. In fact, one has F(σ,σ′)≤F(Λ(σ),Λ(σ′)) for any trace-preserving completely positive map A [see H. Barnum, C. M. Caves, C. A. Fuchs, R. Jozsa, and B. Schumacher, Phys. Rev. Lett. 76, 2818 (1996)].
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28. M. Fannes, Commun. Math. Phys. 31, 291 (1973); see also M. Ohya and D. Petz, Quantum Entropy and Its Use (Springer-Verlag, Berlin, 1993), p. 22.
29. M. Horodecki (unpublished).