Direct characterization of arbitrary qubit systems without auxiliary states

Abstract

Characterization of unknown quantum measurements and quantum states are important tasks in quantum information processing. However, traditional quantum tomography cannot measure arbitrary matrix elements of measurement operators and state density matrices because it requires a global reconstruction algorithm. The direct characterization scheme obtains specific matrix elements without using a global reconstruction algorithm; hence, the scheme has received attention from various researchers. Previous studies have described that direct measurement schemes are based on weak measurements and require the introduction of additional auxiliary states and weak-coupling approximation, which increases the complexity of the practical experimentation and reduces the measurement precision. In this study, we propose a circuit scheme for the direct characterization of positive-operator-valued measure without auxiliary states. In addition, the scheme is suitable for direct measurements of general quantum states. Next, when considering that qubit resources are insufficient, we introduce a coherent superposition state that improves the measurement efficiency in such a case. Finally, we also propose a quantum non-demolition measurement scheme for general quantum states based on the circuit scheme.