On approximately symmetric informationally complete positive operator-valued measures and related systems of quantum states

DOI10.1063/1.1998831zbMath1110.81028arXivquant-ph/0503239OpenAlexW2003583756MaRDI QIDQ3438543

Arne Winterhof, Andreas Klappenecker, Martin Roetteler, Igor E. Shparlinski

Publication date: 16 May 2007

Published in: Journal of Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/quant-ph/0503239

Mathematics Subject Classification ID

Applications of operator theory in the physical sciences (47N50) Quantum measurement theory, state operations, state preparations (81P15)

Related Items (20)

Two constructions of approximately symmetric informationally complete positive operator-valued measures ⋮ Some connections between frames, mutually unbiased bases, and POVM's in quantum information theory ⋮ Two new constructions of approximately mutually unbiased bases ⋮ Resolvable block designs in construction of approximate real MUBs that are sparse ⋮ A new construction of approximately SIC-POVMs derived from Jacobi sums over finite fields ⋮ Complementarity in quantum walks ⋮ Two new constructions of approximately SIC-POVMs from multiplicative characters ⋮ Construction of \(\varepsilon_d\)-ASIC-POVMs via 2-to-1 PN functions and the Li bound ⋮ Weighted complex projective 2-designs from bases: Optimal state determination by orthogonal measurements ⋮ Approximately mutually unbiased bases by Frobenius rings ⋮ New constructions of approximately SIC-POVMs via difference sets ⋮ On mutually orthogonal extraordinary supersquares ⋮ MORE CONSTRUCTIONS OF APPROXIMATELY MUTUALLY UNBIASED BASES ⋮ Discrete Wigner function by symmetric informationally complete positive operator valued measure ⋮ On approximate real mutually unbiased bases in square dimension ⋮ Approximate quasi-orthogonality of operator algebras and relative quantum privacy ⋮ Two new constructions of approximately symmetric informationally complete positive operator-valued measures ⋮ Symmetric informationally complete positive-operator-valued measures: A new computer study ⋮ The Lie algebraic significance of symmetric informationally complete measurements ⋮ Constructions on approximately mutually unbiased bases by Galois rings

Cites Work

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• t-designs in projective spaces
• Information-theoretical aspects of quantum measurement
• 64 lines from a quaternionic polytope
• Finite normalized tight frames
• Equal-norm tight frames with erasures
• A new proof for the existence of mutually unbiased bases
• The Difference Between Consecutive Primes, II
• Spherical-code key-distribution protocols for qubits
• UNITARY OPERATOR BASES
• The Z/sub 4/-linearity of Kerdock, Preparata, Goethals, and related codes
• Unknown quantum states: The quantum de Finetti representation
• Symmetric informationally complete quantum measurements

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