POVM construction: a simple recipe with applications to symmetric states
Abstract
We propose a simple method for constructing POVMs using any set of matrices which form an orthonormal basis for the space of complex matrices. Considering the orthonormal set of irreducible spherical tensors, we examine the properties of the construction on the -dimensional subspace of the -dimensional Hilbert space of qubits comprising the permutationally symmetric states. Similar in spirit to Neumark's result on realization of a POVM as a projective measurement, we present a method to physically realize the constructed POVMs for symmetric states using the Clebsch--Gordan decomposition of the tensor product of irreducible representations of the rotation group. We illustrate the proposed construction on a spin-1 system, and show that it is possible to generate entangled states from separable ones.
Keywords
Cite
@article{arxiv.1505.00123,
title = {POVM construction: a simple recipe with applications to symmetric states},
author = {Swarnamala Sirsi and Karthik Bharath and S. P. Shilpashree},
journal= {arXiv preprint arXiv:1505.00123},
year = {2015}
}