Minimum tomography of two entangled qutrits using local measurements of one-qutrit symmetric informationally complete positive operator-valued measure

Experimental Realization of Quantum Tomography of Photonic Qudits via Symmetric Informationally Complete Positive Operator-Valued Measures

N. Bent, H. Qassim, A. A. Tahir, D. Sych, G. Leuchs, L. L. Sánchez-Soto, E. Karimi, and R.W. Boyd Department of Physics, University of Ottawa, 150 Louis Pasteur, Ottawa, Ontario, K1N 6N5 Canada Max-Planck-Institut für die Physik des Lichts, Günther-Scharowsky-Straße 1, Bau 24, 91058 Erlangen, Germany Departamento de Óptica, Facultad de Física, Universidad Complutense, 28040 Madrid, Spain Instit...

On Approximately Symmetric Informationally Complete Positive Operator-Valued Measures and Related Systems of Quantum States

We address the problem of constructing positive operator-valued measures (POVMs) in finite dimension n consisting of n2 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 con...

Symmetric Informationally Complete Quantum Measurements

We consider the existence in arbitrary finite dimensions d of a POVM comprised of d rank-one operators all of whose operator inner products are equal. Such a set is called a “symmetric, informationally complete” POVM (SIC-POVM) and is equivalent to a set of d equiangular lines in C . SIC-POVMs are relevant for quantum state tomography, quantum cryptography, and foundational issues in quantum me...

Symmetric Informationally Complete Measurements of Arbitrary Rank

There has been much interest in so-called SIC-POVMs: rank 1 symmetric in-formationally complete positive operator valued measures. In this paper we discuss the larger class of POVMs which are symmetric and informationally complete but not necessarily rank 1. This class of POVMs is of some independent interest. In particular it includes a POVM which is closely related to the discrete Wigner func...

Positive Operator - Valued Measurements