Related papers: Extension of the Watanabe-Sagawa-Ueda uncertainty …
A universal formulation of uncertainty relations for quantum measurements is presented with additional focus on the representability of quantum observables by classical observables over a given state. Owing to the simplicity and operational…
By invoking quantum estimation theory we formulate bounds of errors in quantum measurement for arbitrary quantum states and observables in a finite-dimensional Hilbert space. We prove that the measurement errors of two observables satisfy…
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…
A universal formulation of the quantum uncertainty regarding quantum indeterminacy, quantum measurement, and its inevitable observer effect is presented with additional focus on the representability of quantum observables over a given…
The quantification of the "measurement uncertainty" aspect of Heisenberg's Uncertainty Principle---that is, the study of trade-offs between accuracy and disturbance, or between accuracies in an approximate joint measurement on two…
Uncertainty relations are one of the fundamental principles in physics. It began as a fundamental limitation in quantum mechanics, and today the word {\it uncertainty relation} is a generic term for various trade-off relations in nature. In…
Measurement uncertainty relations are lower bounds on the errors of any approximate joint measurement of two or more quantum observables. The aim of this paper is to provide methods to compute optimal bounds of this type. The basic method…
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…
We study universally valid uncertainty relations in general quantum systems described by general $\sigma$-finite von Neumann algebras to foster developing quantitative analysis in quantum systems with infinite degrees of freedom such as…
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…
We present a universal formulation of uncertainty relation valid for any conceivable quantum measurement and the resultant observation (observer) effect of statistical nature. Owing to its simplicity and operational tangibility, our general…
Defining an error of measurement has long been a foundational problem in science: even in classical experiments, data are statistical and admit no single universally optimal definition of error. In quantum mechanics, the challenge deepens:…
The evaluation of uncertainties in quantum measurements is problematic since the correct value of an observable between state preparation and measurement is experimentally inaccessible. In Ozawa's formulation of uncertainty relations for…
As a foundation of modern physics, uncertainty relations describe an ultimate limit for the measurement uncertainty of incompatible observables. Traditionally, uncertain relations are formulated by mathematical bounds for a specific state.…
In quantum physics, measurement error and disturbance were first naively thought to be simply constrained by the Heisenberg uncertainty relation. Later, more rigorous analysis showed that the error and disturbance satisfy more subtle…
Quantum multiparameter estimation focuses on the simultaneous inference of multiple parameters in quantum systems through measurement and data processing. Its complexity stems from two key factors: measurement incompatibility and parameter…
We present uncertainty relations based on Wigner--Yanase--Dyson skew information with quantum memory. Uncertainty inequalities both in product and summation forms are derived. \mbox{It is} shown that the lower bounds contain two terms: one…
Quantum states can be subjected to classical measurements, whose incompatibility, or uncertainty, can be quantified by a comparison of certain entropies. There is a long history of such entropy inequalities between position and momentum.…
Uncertainty relations are a fundamental feature of quantum mechanics. How can these relations be found systematically? Here we develop a semidefinite programming hierarchy for additive uncertainty relations in the variances of non-commuting…
Ozawa's measurement-disturbance relation is generalized to a phase-space noncommutative extension of quantum mechanics. It is shown that the measurement-disturbance relations have additional terms for backaction evading quadrature…