?Simultaneous measurement? from the standpoint of quantum estimation theory

Yu Watanabe

Adnan Naimy, Abdallah Slaoui, Abderrahim Lakhfif +1 more

In this work, we introduce an experimentally viable scheme to enhance the simultaneous estimation precision of the couplings $G_{mc}$ and $G_{mb}$, with a particular focus on the performance of heterodyne detection. By comparing simultaneous and individual estimation strategies, we demonstrate that the simultaneous approach offers a notable advantage in our system. To support this, we compute the quantum Fisher information matrices (QFIMs) based on the symmetric logarithmic derivative (SLD) and the right logarithmic derivative (RLD). Our results show that the quantum Cramér Rao bound (QCRB) associated with the RLD is consistently lower than that of the SLD, indicating superior estimation precision. From a physical standpoint, this improvement reflects the system's enhanced capacity to encode, transfer, and extract quantum information while allowing optimal control of fundamental interactions. We show that increasing the Rabi frequency, cavity loss rate, and the average number of photons and phonons, combined with reduced mechanical damping and temperature, enhances the system's sensitivity to the coupling parameters. These mechanisms act on the available quantum resources, such as entanglement, squeezing, and state purity, leading to more precise estimations. Furthermore, our analysis reveals that under certain conditions, heterodyne detection can closely approach the ultimate precision set by the QFIM. This suggests that a measurement strategy based on heterodyne detection can offer an efficient and practical route for estimating the couplings $G_{mc}$ and $G_{mb}$, paving the way for high precision hybrid quantum sensors.

Shosuke Sasaki, T. Kebukawa

The eigenvalue problem in a one-dimensional many boson system with a repulsive delta-function potential has been solved exactly from the standpoint of field theory. All eigenstates are expressed in a simple and compact from by introducing appropriate quantum numbers for their specification. The energy eigenstate are determined by solutions of simultaneous equations. It is verified that the simultaneous equations have unique solutions.

Sanjoy K. Mitter, Stephen K. Young

Yaoling Yang, Víctor Montenegro, Abolfazl Bayat

The simultaneous estimation of multiple unknown parameters is the most general scenario in quantum sensing. Quantum multiparameter estimation theory provides fundamental bounds on the achievable precision of simultaneous estimation. However, these bounds can become singular (no finite bound exists) in multiparameter sensing due to parameter interdependencies, limited probe accessibility, and insufficient measurement outcomes. Here, we address the singularity issue in quantum sensing through a simple mechanism based on a sequential measurement strategy. This sensing scheme overcomes the singularity constraint and enables the simultaneous estimation of multiple parameters with a local and fixed measurement throughout the sensing protocol. This is because sequential measurements, involving consecutive steps of local measurements followed by probe evolution, inherently produce correlated measurement data that grows exponentially with the number of sequential measurements. Finally, through two different examples, namely a strongly correlated probe and a light-matter system, we demonstrate how such singularities are reflected when inferring the unknown parameters through Bayesian estimation.

Sanjoy K. Mitter, Stephen K. Young