TY - JOUR

T1 - Clean positive operator valued measures

AU - Buscemi, Francesco

AU - Keyl, Michael

AU - D'Ariano, Giacomo Mauro

AU - Perinotti, Paolo

AU - Werner, Reinhard F.

N1 - Funding information: The authors are grateful to Madalin Guta for interesting discussions. This work has been cofounded by EC and Ministero Italiano dell’Università e della Ricerca (MIUR) through the cosponsored ATESIT Project No. IST-2000-29681 and Cofinanziamento 2003. One of the authors (P.P.) acknowledges support from the Istituto Nazionale di Fisica della Materia under Project No. PRA-2002-CLON. One of the authors (R.W.) acknowledges hospitality of the QUIT group and partial support from European Science Foundation. Another author (G.M.D.) also acknowledges partial support from the Multiple Universities Research Initiative (MURI) program administered by the U.S. Army Research Office under Grant No. DAAD1900-1-0177.

PY - 2005

Y1 - 2005

N2 - In quantum mechanics the statistics of the outcomes of a measuring apparatus is described by a positive operator valued measure (POVM). A quantum channel transforms POVMs into POVMs, generally irreversibly, thus losing some of the information retrieved from the measurement. This poses the problem of which POVMs are undisturbed, i.e., they are not irreversibly connected to another POVM. We will call such POVMs clean. In a sense, the clean POVMs would be perfect, since they would not have any additional extrinsical noise. Quite unexpectedly, it turns out that such a cleanness property is largely unrelated to the convex structure of POVMs, and there are clean POVMs that are not extremal and vice versa. In this article we solve the cleannes classification problem for number n of outcomes n d dimension of the Hilbert space), and we provide a set of either necessary or sufficient conditions for n along with an iff condition for the case of informationally complete POVMs for n=d.

AB - In quantum mechanics the statistics of the outcomes of a measuring apparatus is described by a positive operator valued measure (POVM). A quantum channel transforms POVMs into POVMs, generally irreversibly, thus losing some of the information retrieved from the measurement. This poses the problem of which POVMs are undisturbed, i.e., they are not irreversibly connected to another POVM. We will call such POVMs clean. In a sense, the clean POVMs would be perfect, since they would not have any additional extrinsical noise. Quite unexpectedly, it turns out that such a cleanness property is largely unrelated to the convex structure of POVMs, and there are clean POVMs that are not extremal and vice versa. In this article we solve the cleannes classification problem for number n of outcomes n d dimension of the Hilbert space), and we provide a set of either necessary or sufficient conditions for n along with an iff condition for the case of informationally complete POVMs for n=d.

U2 - 10.1063/1.2008996

DO - 10.1063/1.2008996

M3 - Article

VL - 46

SP - 082109

JO - J. Math. Phys.

JF - J. Math. Phys.

SN - 1089-7658

IS - 8

ER -