Related papers: Classical Fisher information for differentiable dy…
A comparison of structural features of quantum and classical physical theories, such as the information capacity of systems subject to these theories, requires a common formal framework for the presentation of corresponding concepts (such…
Starting from the Hamilton-Jacobi equation describing a classical ensemble, one may infer a quantum dynamics using the principle of maximum uncertainty. That procedure requires an appropriate measure of uncertainty: Such a measure is…
Expected Fisher information can be found a priori and as a result its inverse is the primary variance approximation used in the design of experiments. This is in contrast to the common claim that the inverse of observed Fisher information…
The dynamical status of isolated quantum systems, partly due to the linearity of the Schrodinger equation is unclear: Conventional measures fail to detect chaos in such systems. However, when quantum systems are subjected to observation --…
We address the fundamental limits of learning unknown parameters of any stochastic process from time-series data, and discover exact closed-form expressions for how optimal inference scales with observation length. Given a parametrized…
It is a widely accepted fact that the computational capability of recurrent neural networks is maximized on the so-called "edge of criticality". Once the network operates in this configuration, it performs efficiently on a specific…
Quantum dynamics can be regarded as a generalization of classical finite-state dynamics. This is a familiar viewpoint for workers in quantum computation, which encompasses classical computation as a special case. Here this viewpoint is…
Standard quantum metrology relies on ensemble-averaged quantities, such as the Quantum Fisher Information (QFI), which often mask the fluctuations inherent to single-shot realizations. In this work, we bridge the gap between quantum…
Despite the widespread use and success of machine-learning techniques for detecting phase transitions from data, their working principle and fundamental limits remain elusive. Here, we explain the inner workings and identify potential…
We consider an open quantum system undergoing Markovian dynamics, the latter being modelled by a discrete-time quantum Markov semigroup $(\Phi^n)_{n \in {\mathbb{N}}}$, resulting from the action of sequential uses of a quantum channel…
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…
We extend the speed limit of a distance between two states evolving by different generators for quantum systems [K. Suzuki and K. Takahashi, Phys. Rev. Res. 2, 032016(R) (2020)] to the classical stochastic processes described by the master…
The dynamics of quantum Fisher information (QFI) of the phase parameter in a driven two-state system is studied within the framework of non-Markovian dissipative process. The influences of memory effects, classical driving and detunings on…
In this paper, the dynamics of quantum Fisher information of a qubit interacting with a squeezed thermal environment are studied. The optimal initial state of the qubit, the temperature of the environment, and the interaction time, which…
It is shown that the vacuum state of weakly interacting quantum field theories can be described, in the Heisenberg picture, as a linear combination of randomly distributed incoherent paths that obey classical equations of motion with…
In statistical estimation theory, it has been shown previously that the Wigner-Yanase skew information is bounded by the quantum Fisher information associated with the phase parameter. Besides, the quantum Cram\'er-Rao inequality is…
While the quantum mutual information is a fundamental measure of quantum information, it is only defined for spacelike-separated quantum systems. Such a limitation is not present in the theory of classical information, where the mutual…
Alternative proofs for the superadditivity and the affinity (in the large system limit) of the usual and some fractional Fisher informations of a probability density of many variables are provided. They are consequences of the fact that…
In this work, we develop a quantum metrological framework for quantum chaos by showing that local subsystems of information scrambling systems naturally function as quantum stopwatches. The reduced quantum state of a subsystem encodes the…
Heisenberg's uncertainty principle is often cited as an example of a "purely quantum" relation with no analogue in the classical limit where $\hbar \to 0$. However, this formulation of the classical limit is problematic for many reasons,…