Related papers: Stronger Error Disturbance Relations for Incompati…
We propose a measure of macroscopic coherence based on the degree of disturbance caused by a coarse-grained measurement. Based on our measure, we point out that recently proposed criteria of macroscopic coherence may lead to inconsistent…
A major recent evelopment in observational cosmology has been an accurate measurement of the luminosity distance-redshift relation out to redshifts z=0.8 from Type Ia supernova standard candles. The results have been argued as evidence for…
We derive a fine-grained uncertainty relation for the measurement of two incompatible observables on a single quantum system of continuous variables, and show that continuous variable systems are more uncertain than discrete variable…
Many statistical applications require the quantification of joint dependence among more than two random vectors. In this work, we generalize the notion of distance covariance to quantify joint dependence among d >= 2 random vectors. We…
I consider the tradeoff between the information gained about an initially unknown quantum state, and the disturbance caused to that state by the measurement process. I show that for any distribution of initial states, the…
We discuss the disturbance by measurements which unambiguously discriminate between given candidate states. We prove that such an optimal measurement necessarily changes distinguishable states indistinguishable when the inconclusive outcome…
We propose an extension of the classical R\'enyi divergences to quantum states through an optimization over probability distributions induced by restricted sets of measurements. In particular, we define the notion of locally-measured…
The conflict between Quantum Mechanics (QM) and the intuitive concepts of Locality and Realism (LR) is manifest in the correlation between measurements performed in remote regions of a spatially spread entangled state. In this paper, it is…
Universally valid uncertainty relations are proven in a model independent formulation for inherent and unavoidable extra noises in arbitrary joint measurements on single systems, from which Heisenber's original uncertainty relation is…
The uncertainty relation is one of the key ingredients of quantum theory. Despite the great efforts devoted to this subject, most of the variance-based uncertainty relations are state-dependent and suffering from the triviality problem 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…
We formulate and prove a new, universally valid uncertainty relation for the necessary errors bar widths in any approximate joint measurement of position and momentum.
Distance correlation is a new measure of dependence between random vectors. Distance covariance and distance correlation are analogous to product-moment covariance and correlation, but unlike the classical definition of correlation,…
The proof of the Heisenberg uncertainty relation is modified to produce two improvements: (a) the resulting inequality is stronger because it includes the covariance between the two observables, and (b) the proof lifts certain restrictions…
We establish a quantitative relation between Hardy's paradox and the breaking of uncertainty principle in the sense of measurement-disturbance relations in the conditional measurement of non-commuting operators. The analysis of the…
We propose an EPR inequality based on an entropic uncertainty relation for complementary continuous variable observables. This inequality is more sensitive than the previously established EPR inequality based on inferred variances, and…
The concept of experimental accuracy is investigated in the context of the unbiased joint measurement processes defined by Arthurs and Kelly. A distinction is made between the errors of retrodiction and prediction. Four error-disturbance…
We consider the problem of bounding large deviations for non-i.i.d. random variables that are allowed to have arbitrary dependencies. Previous works typically assumed a specific dependence structure, namely the existence of independent…
Heisenberg-Robertson's uncertainty relation expresses a limitation in the possible preparations of the system by giving a lower bound to the product of the variances of two observables in terms of their commutator. Notably, it does not…
We show that for fermion states, measurements of any two finite outcome particle quantum numbers (e.g.\ spin) are not constrained by a minimum total uncertainty. We begin by defining uncertainties in terms of the outputs of a measurement…