Quantum tomography via unambiguous state discrimination

Abstract

We study the determination of an unknown mixed state of a d-dimensional quantum system by means of unambiguous state discrimination. We show that optimal and nonoptimal unambiguous state discrimination can be used to reconstruct unknown states of a qubit. This result is extended to the case of a qudit by a sequence of reconstructions in two-dimensional subspaces. The total number of projections scales approximately as 2d 2 for d large; this is twice as much as in the case of tomography based on mutually unbiased bases or symmetric informationally complete positive-operator-valued measures, and less than the d 3 projections required by standard tomography.

Determining ann-qubit state by a single apparatus through a pairwise interaction

“…The optimal Hamiltonian is the Heisenberg XZ model while the natural Hamiltonian of the sample is the Ising model of Eq. (16). In general, if the different terms of Hamiltonian do not commute with each other, we cannot realize the terms sequentially.…”

“…Usually the process of reconstructing an unknown quantum state by measurement is called quantum state tomography (QST) [1]. In the last several decades, different QST schemes have been presented including standard QST [2,3], QST by means of a single apparatus [4][5][6][7], QST on symmetric informationally complete positive-operator valued measure [8][9][10][11][12], QST on mutually unbiased bases [13][14][15], QST via unambiguous state discrimination [16], direct QST via weak measurement [17,18], QST via compressed sensing [19,20], and self-calibrating tomography [21][22][23][24][25].…”

Optimal unbiased state characterization

“…Finally, we would like to mention a recent paper [35] where a tomographic reconstruction of a single qubit by applying methods of quantum state discrimination was proposed.…”

Estimation of pure states using three measurement bases

“…The existence of SIC-POVMs and MUBs has been proven in restricted sets of dimensions. For this reason alternative schemes have been proposed [29][30][31][32], which require in the order of d 2 measurement outcomes. In the case of a multipartite system formed by n d-dimensional systems, the total number of measurement outcomes becomes d 2n .…”