Related papers: Soundness and completeness of quantum root-mean-sq…
It is shown that all the known uncertainty relations are the secondary consequences of Robertson's relation. The basic idea is to use the Heisenberg picture so that the time development of quantum mechanical operators incorporate the…
A usual assumption in quantum estimation is that the unknown parameter labels the possible states of the system, while it influences neither the sample space of outcomes nor the measurement aimed at extracting information on the parameter…
This article deals with the problem of the uncertainty in rule-based systems (RBS), but from the perspective of quantum computing (QC). In this work we first remember the characteristics of Quantum Rule-Based Systems (QRBS), a concept…
Quantum state tomography is the task of inferring the state of a quantum system by appropriate measurements. Since the frequency distributions of the outcomes of any finite number of measurements will generally deviate from their asymptotic…
We give a bound to the precision in the estimation of a parameter in terms of the expectation value of an observable. It is an extension of the Cramer-Rao inequality and of the Heisenberg uncertainty relation, where the estimation precision…
The uncertainty principle being a cornerstone of quantum mechanics, it is surprising that in nearly 90 years there have been no direct tests of measurement uncertainty relations. This lacuna was due to the absence of two essential…
The notions of error and disturbance appearing in quantum uncertainty relations are often quantified by the discrepancy of a physical quantity from its ideal value. However, these real and ideal values are not the outcomes of simultaneous…
A new, realist interpretation of the quantum measurement processes is given. In this scenario a quantum measurement is a non-equilibrium phase transition in a ``resonant cavity'' formed by the entire physical universe including all its…
Quantum measurement is a fundamental concept in the field of quantum mechanics. The action of quantum measurement, leading the superposition state of the measured quantum system into a definite output state, not only reconciles…
Distinguishing assigned quantum states with assigned probabilities via quantum measurements is a crucial problem for the transmission of classical information through quantum channels. Measurement operators maximizing the probability of…
Ultimately, any explanation of quantum measurement must be extendable to relativistic quantum mechanics (RQM), since many precisely confirmed experimental results follow from quantum field theory (QFT), which is based on RQM. Certainly, the…
The paper gives a systematic review of the basic ideas of (non-relativistic) quantum mechanics including all changes that result from previous work of the authors. This shows that the new theory is self-consistent and (in certain sense)…
Noise is the greatest obstacle in quantum metrology that limits it achievable precision and sensitivity. There are many techniques to mitigate the effect of noise, but this can never be done completely. One commonly proposed technique is to…
In quantum metrology, one of the major applications of quantum technologies, the ultimate precision of estimating an unknown parameter is often stated in terms of the Cram\'er-Rao bound. Yet, the latter is no longer guaranteed to carry an…
Heisenberg's uncertainty principle, exemplified by the gamma ray thought experiment, suggests that any finite precision measurement disturbs any observables noncommuting with the measured observable. Here, it is shown that this statement…
Quantum-enhanced metrology surpasses classical metrology by improving estimation precision scaling with a resource $N$ (e.g., particle number or energy) from $1/\sqrt{N}$ to $1/N$. Through the use of nonlinear effects, Roy and…
The uncertainty relation, which displays an elementary property of quantum theory, was originally described by Heisenberg as the relation between error and disturbance. Ozawa presented a more rigorous expression of the uncertainty relation,…
The history based formalism known as Quantum Measure Theory (QMT) generalizes the concept of probability-measure so as to incorporate quantum interference. The resulting \textit{quantum measure} $\mu$ is defined for arbitrary events (sets…
Heisenberg's uncertainty principle is one of the main tenets of quantum theory. Nevertheless, and despite its fundamental importance for our understanding of quantum foundations, there has been some confusion in its interpretation: although…
An analysis of quantum measurement is presented that relies on an information-theoretic description of quantum entanglement. In a consistent quantum information theory of entanglement, entropies (uncertainties) conditional on measurement…