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Optimizing quantum process tomography with unitary 2-designs. (English) Zbl 1141.81009
This paper characterises optimal measurements for unital quantum channels, assuming linear tomographic reconstruction. They are determined by weighted projective unitary 2-designs (loosely, countable sets of unitaries with enough spread and symmetry to approximate the Haar measure on the projective unitary group). Examples include complete sets of mutually unbiased unitary operator bases. The open problem of optimal measurements for non-unital quantum channels is discussed.

81P68 Quantum computation
81P15 Quantum measurement theory, state operations, state preparations
94A40 Channel models (including quantum) in information and communication theory
28C10 Set functions and measures on topological groups or semigroups, Haar measures, invariant measures
05B30 Other designs, configurations
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