相关论文: Fisher information in quantum statistics

A framework for a quantum information theory is introduced that is based on the measure of quantum information associated with probability distribution predicted by quantum measuring of state. The entanglement between states of measured…

A closed-form expression for Wigner-Yanase skew information in mixed-state quantum systems is derived. It is shown that limit values of the mixing coefficients exist such that Wigner-Yanase information is equal to Helstrom information. The…

We derive a general upper bound to mutual information in terms of the Fisher information. The bound may be further used to derive a lower bound for the Bayesian quadratic cost. These two provide alternatives to other inequalities in the…

The minimum error of unbiased parameter estimation is quantified by the quantum Fisher information in accordance to the Cram\'{e}r-Rao bound. We indicate that only superposed NOON states by simultaneous measurements can achieve the maximum…

The quantum information and the Bures metric are equivalent to each other, except at points where the rank of the density matrix changes. Here we show that by slightly modifying the definition of the Bures metric, the quantum information…

The optimal phase estimation strategy is derived when partial a priori knowledge on the estimated phase is available. The structure of the optimal measurements, estimators and the optimal probe states is analyzed. The results fill the gap…

The importance of Fisher information is increasing in nonequilibrium thermodynamics, as it has played a fundamental role in trade-off relations such as thermodynamic uncertainty relations and speed limits. In this work, we investigate…

We introduce a positive Hermitian operator, the Fisher operator, and use it to examine a measurement process incorporating unitary dynamics and complete measurements. We develop the idea of information complement, the minimization of which…

We introduce a semidefinite programming algorithm to find the minimal quantum Fisher information compatible with an arbitrary dataset of mean values. This certification task allows one to quantify the resource content of a quantum system…

We study optimal quantum sensing of multiple physical parameters using repeated measurements. In this scenario, the Fisher information framework sets the fundamental limits on sensing performance, yet the optimal states and corresponding…

Information theory is a powerful framework to capture aspects of dynamical systems with multiple degrees of freedom. Mathematically, the dynamics can be represented as a continuous curve $\mathcal{C}$ on a suitable hyperplane in flat space…

We derive a new variational principle for the quantum Fisher information leading to a simple iterative alternating algorithm, the convergence of which is proved. The case of a fixed measurement, i.e. the classical Fisher information, is…

Resolving frequencies in a time-dependent field is classically limited by the measurement bandwidth. Using tools from quantum metrology and quantum control may overcome this limit, yet the full advantage afforded by entanglement so far…

We consider the general problem of estimating an unknown control parameter of an open quantum system. We establish a direct relation between the evolution of both system and environment and the precision with which the parameter can be…

Many statistical models require an estimation of unknown (co)-variance parameter(s) in a model. The estimation usually obtained by maximizing a log-likelihood which involves log determinant terms. In principle, one requires the…

The quantum Fisher information represents the continuous family of metrics on the space of quantum states and places the fundamental limit on the accuracy of quantum state estimation. We show that the entire family of the quantum Fisher…

Quantum Fisher information (QFI) sets the ultimate precision of optical phase measurements and reveals multiphoton entanglement, but it is not accessible with conventional photodetection. We theoretically predict that a photodetector…

We explore the task of learning about the dynamics of a Markovian open quantum system by monitoring the information it radiates into its environment. For an open system with Hilbert space dimension $D$, the quantum state of the emitted…

Quantum metrology has been studied for a wide range of systems with time-independent Hamiltonians. For systems with time-dependent Hamiltonians, however, due to the complexity of dynamics, little has been known about quantum metrology. Here…

Quantum metrology is a science about quantum measurements and it plays a key role in precision of quantum parameter estimation. Meanwhile, quantum coherence is an important quantum feature and quantum Fisher information (QFI) is an…