Projectivities of Informationally Complete Measurements

摘要

The physical problem behind informationally complete (IC) measurements is determining an unknown state statistically by measurement outcomes, known as state tomography. It is of central importance in quantum information processing such as channel estimating, device testing, quantum key distribution, etc. However, constructing such measurements with good properties is a long-standing problem. In this work, projective realizations of IC measurements are investigated. Conditions of informational completeness are presented with proofs first. Then the projective realizations of IC measurements, including proposing the first general construction of minimal projective IC measurements (MPICM) in no prime power dimensional systems, as well as determining an unknown state in Cn$C<^>{n}$ via a single projective measurement with some kinds of optimalities in a larger system, are investigated. Finally, The results can be extended to local state tomography. Some discussions on employing several kinds of optimalities are also provided. @@@ The paper investigates projective realizations of informationally complete measurements. The definition of minimal projective informationally complete measurement (MPICM), which extends mutually unbiased bases (MUB), is proposed with a general construction provided, and the realizations of informational completeness via a single projective measurement with certain optimalities are studied. It indicates that projective ones are always better than others on certain criteria.image

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