2015/05/01 by Swarnamala Sirsi, Sirsi, Swarnamala, Karthik Bharath +3
Computer Science · Mathematics · #Algebraic structures and combinatorial models #FOS: Physical sciences #Mathematical Physics (math-ph) #Matrix Theory and Algorithms #Quantum Information and Cryptography #Quantum Physics (quant-ph)
paper · pdf · doi:10.48550/arxiv.1505.00123
openalex publication_date 2015/05/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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 N+1-dimensional subspace of the 2N-dimensional Hilbert space of N 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.