Related papers: Preferred Measurements: Optimality and Stability i…
Consider a joint quantum state of a system and its environment. A measurement on the environment induces a decomposition of the system state. Using algorithmic information theory, we define the preparation information of a pure or mixed…
We present a graduate course on ideal measurements, analyzed as dynamical processes of interaction between the tested system S and an apparatus A, described by quantum statistical mechanics. The apparatus A=M+B involves a macroscopic…
Von Neumann projections are the main operations by which information can be extracted from the quantum to the classical realm. They are however static processes that do not adapt to the states they measure. Advances in the field of adaptive…
A number of issues related to measurement show that self-consistency is lacking in quantum mechanics as this theory has been generally understood. Each issue is presented as a point in this paper. Each point can be resolved by incorporating…
Parameter estimation is of fundamental importance in areas from atomic spectroscopy and atomic clocks to gravitational wave detection. Entangled probes provide a significant precision gain over classical strategies in the absence of noise.…
Quantum sensors are now universally acknowledged as one of the most promising near-term quantum technologies. The traditional formulation of quantum sensing introduces a concrete bound on ultimate precision through the so-called local…
The purpose of this paper is to survey some topics on mathematical foundations of quantum information developed mainly by the present author and co-workers for the last three decades. The topics include an axiomatic construction of quantum…
Heisenberg's uncertainty principle has recently led to general measurement uncertainty relations for quantum systems: incompatible observables can be measured jointly or in sequence only with some unavoidable approximation, which can be…
We address the trade-off between information and disturbance in qubit thermometry from the perspective of quantum estimation theory. Given a quantum measurement, we quantify information via the Fisher information of the measurement and…
Precise parameter estimation plays a central role in science and technology. The statistical error in estimation can be decreased by repeating measurement, leading to that the resultant uncertainty of the estimated parameter is proportional…
A large literature has grown up around the proposed use of 'weak measurements' (i.e., unsharp measurements followed by post-selection) to allegedly provide information about hidden ontological features of quantum systems. This paper…
Quantization for probability distributions refers broadly to estimating a given probability measure by a discrete probability measure supported by a finite number of points. We consider general geometric approaches to quantization using…
In quantum metrology, entangled states of many-particle systems are investigated to enhance measurement precision of the most precise clocks and field sensors. While single-parameter quantum metrology is well established, many metrological…
We investigate the problem of representing information measures in terms of the moments of the underlying random variables. First, we derive polynomial approximations of the conditional expectation operator. We then apply these…
Quantum information is a rapidly advancing area of interdisciplinary research. It may lead to real-world applications for communication and computation unavailable without the exploitation of quantum properties such as nonorthogonality or…
We consider the impact that temporal correlations in the measurement statistics can have on the achievable precision in a sequential metrological protocol. In this setting, and for a single quantum probe, we establish that it is the…
Correlations disguised in various forms underlie a host of important phenomena in classical and quantum systems, such as information and energy exchanges. The quantum mutual information and the norm of the correlation matrix are both…
Quantum detectors provide information about quantum systems by establishing correlations between certain properties of those systems and a set of macroscopically distinct states of the corresponding measurement devices. A natural question…
We perform a quantum information analysis for multi-mode Gaussian approximate position measurements, underlying noisy homodyning in quantum optics. The "Gaussian maximizer" property is established for the entropy reduction of these…
Using the convex structure of positive operator value measurements and of several quantities used in quantum metrology, such as quantum Fisher information or the quantum Van Trees information, we present an efficient numerical method to…