On approximately symmetric informationally complete positive operator-valued measures and related systems of quantum states
- Department of Computer Science, Texas A and M University, College Station, Texas 77843-3112 (United States)
We address the problem of constructing positive operator-valued measures (POVMs) in finite dimension n consisting of n{sup 2} operators of rank one which have an inner product close to uniform. This is motivated by the related question of constructing symmetric informationally complete POVMs (SIC-POVMs) for which the inner products are perfectly uniform. However, SIC-POVMs are notoriously hard to construct and, despite some success of constructing them numerically, there is no analytic construction known. We present two constructions of approximate versions of SIC-POVMs, where a small deviation from uniformity of the inner products is allowed. The first construction is based on selecting vectors from a maximal collection of mutually unbiased bases and works whenever the dimension of the system is a prime power. The second construction is based on perturbing the matrix elements of a subset of mutually unbiased bases. Moreover, we construct vector systems in C{sup n} which are almost orthogonal and which might turn out to be useful for quantum computation. Our constructions are based on results of analytic number theory.
- OSTI ID:
- 20699335
- Journal Information:
- Journal of Mathematical Physics, Vol. 46, Issue 8; Other Information: DOI: 10.1063/1.1998831; (c) 2005 American Institute of Physics; Country of input: International Atomic Energy Agency (IAEA); ISSN 0022-2488
- Country of Publication:
- United States
- Language:
- English
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