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arXiv:2305.08774 · Quantum

Minimal orthonormal bases for pure quantum state estimation

Leonardo Zambrano, Luciano Pereira, A. Delgado

Published Feb 8, 2024• 2 citations
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Abstract

We present an analytical method to estimate pure quantum states using a minimum of three measurement bases in any finite-dimensional Hilbert space. This is optimal as two bases are insufficient to construct an informationally complete positive operator-valued measurement (IC-POVM) for pure states. We demonstrate our method using a binary tree structure, providing an algorithmic path for implementation. The performance of the method is evaluated through numerical simulations, showcasing its effectiveness for quantum state estimation.

DOI
10.22331/q-2024-02-08-1244

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Informationally complete measurements on a quantum system allow one to estimate the expectation value of any arbitrary operator by just averaging functions of the experimental outcomes. We show that such kinds of measurement can be achieved through positive-operator valued measures (POVMs) related to unitary irreducible representations of a group on the Hilbert space of the system. With the help of frame theory we provide a constructive way to evaluate the data-processing function for arbitrary operators.