Related papers: Soundness and completeness of quantum root-mean-sq…
The Heisenberg limit is acknowledged as the ultimate precision limit in quantum metrology, traditionally implying that root mean square errors of parameter estimation decrease linearly with the time T of evolution and the number N of…
We formulate the error and disturbance in quantum measurement by invoking quantum estimation theory. The disturbance formulated here characterizes the non-unitary state change caused by the measurement. We prove that the product of the…
The convenience of coherent state representation is discussed from the viewpoint of what is in a broad sense called the measurement problem in quantum mechanics. Standard quantum theory in coherent state representation is intrinsically…
In prior work, we have shown how the basic concepts and terms of quantum mechanics relate to factorizations and marginals of complex-valued quantum mass functions, which are generalizations of joint probability mass functions. In this…
Quantifying coherence is an essential endeavour for both quantum foundations and quantum technologies. Here the robustness of coherence is defined and proven a full monotone in the context of the recently introduced resource theories of…
A central feature of quantum metrology is the possibility of Heisenberg scaling, a quadratic improvement over the limits of classical statistics. This scaling, however, is notoriously fragile to noise. While for some noise types it can be…
A standard approach to quantum computing is based on the idea of promoting a classically simulable and fault-tolerant set of operations to a universal set by the addition of `magic' quantum states. In this context, we develop a general…
We analyze the Schwarz inequality and its generalizations, as well as inequalities resulting from the Jensen inequality. They are used in quantum theory to derive the Heisenberg-Robertson (HR) and Schroedinger-Robertson (SR) uncertainty…
Relational Quantum Mechanics (RQM) is an interpretation of quantum theory based on the idea of abolishing the notion of absolute states of systems, in favor of states of systems relative to other systems. Such a move is claimed to solve the…
We consider quantum metrology in noisy environments, where the effect of noise and decoherence limits the achievable gain in precision by quantum entanglement. We show that by using tools from quantum error-correction this limitation can be…
Quantum measurement and quantum operation theory is developed here by taking the relational properties among quantum systems, instead of the independent properties of a quantum system, as the most fundamental elements. By studying how the…
We introduce the notion of fault-tolerant quantum metrology to overcome noise beyond our control -- associated with sensing the parameter, by reducing the noise in operations under our control -- associated with preparing and measuring…
Understanding and mitigating noise in quantum systems is a fundamental challenge in achieving scalable and fault-tolerant quantum computation. Error modeling for quantum systems can be formulated in many ways, some of which are very…
Understanding the invasive nature of quantum measurement and its implications in quantum foundations and information science demands a mathematically rigorous and physically well-grounded characterization of intrinsic back-action in general…
A central challenge in quantum metrology is identifying optimal measurements that saturate the quantum Cramer-Rao bound under realistic constraints, e.g., local measurements. We show that symmetries of the probe state provide a general…
This tutorial is devoted to review the modern tools of quantum mechanics, which are suitable to describe states, measurements, and operations of realistic, not isolated, systems in interaction with their environment, and with any kind of…
Heisenberg's uncertainty principle was originally formulated in 1927 as a quantitative relation between the "mean error" of a measurement of one observable and the disturbance thereby caused on another observable. Heisenberg derived this…
Multiparametric statistical model providing stable reconstruction of parameters by observations is considered. The only general method of this kind is the root model based on the representation of the probability density as a squared…
We present a new geometric formulation of uncertainty relation valid for any quantum measurements of statistical nature. Owing to its simplicity and tangibility, our relation is universally valid and experimentally viable. Although our…
We investigate a measure of quantum coherence and its extension to quantify quantum macroscopicity. The coherence measure can also quantify the asymmetry of a quantum state with respect to a given group transformation. We then show that a…