Unified Framework for Direct and Complete Characterization of an Unknown Kraus Operator and Density Matrix Using a Single Input State
Sahil, Swarup Kumar Giri, Sohail
TL;DR
The paper presents a unified framework for direct and complete characterization of an unknown Kraus operator, its associated POVM element, and the system density matrix, as well as unknown unitary operators and observables, all from a single mixed input state. The approach uses a probe-system-environment setup with a controlled unitary $U_{PSE}$ and a minimal set of measurements on a single observable, enabling extraction of matrix elements via tripartite correlators that scale favorably compared to prior DCQM and DCDM methods. It provides explicit schemes to obtain each matrix element of $A_k$, $E_k$, a unitary, an observable, and $\rho_S$, including a full reconstruction with $d_S+1$ unitaries and without relying on weak coupling. The results offer a resource-efficient pathway for quantum measurement tomography in noisy, high-dimensional settings and hold practical significance for accurate POVM and state characterization in quantum information processing.
Abstract
Characterization of quantum measurements and dynamical processes is typically performed using pure state preparations. However, in realistic experimental settings, the preparation of pure states is often infeasible due to noise and system constraints. In this work, we present a unified framework that enables the direct and complete characterization of an unknown Kraus operator using only a single input state. The same framework also supports the characterization of unknown observable, unitary operator, and density matrix. Remarkably, all these tasks are accomplished using a single input state, a set of projector-based unitary evolution operators, and the measurement of a single observable. Importantly, our approach imposes no constraints on the strength of the coupling between the system and a probe.