Related papers: Measuring measurement--disturbance relationships w…
Heisenberg's uncertainty principle forms a fundamental element of quantum mechanics. Uncertainty relations in terms of entropies were initially proposed to deal with conceptual shortcomings in the original formulation of the uncertainty…
We develop a new approach to formulate and prove the weak uncertainty inequality which was recently introduced by Okoudjou and Strichartz. We assume either an appropriate measure growth condition with respect to the effective resistance…
Following Deligne and Ribet (`Values of abelian $L$-functions at negative integers over totally real fields.' Invent. Math. 59 (1980), 227-286) we prove that the `torsion congruences' (as introduced in our paper `Non-abelian pseudomeasures…
The inherent connection between noise and disturbance is one of the most fundamental features of quantum measurements. In the two well-known extreme cases a measurement either makes no disturbance but then has to be totally noisy or is as…
We examine weak measurements of arbitrary observables where the object is prepared in a mixed state and on which measurements with imperfect detectors are made. The weak value of an observable can be expressed as a conditional expectation…
Quantum uncertainty relations have deep-rooted significance on the formalism of quantum mechanics. Heisenberg's uncertainty relations attracted a renewed interest for its applications in quantum information science. Robertson derived a…
Aharonov's weak value amplification realized via weak measurement provides a versatile means to measure physical parameters with high accuracy, similar to quantum resonance epitomized by the Rabi and Ramsey resonances. The similarity…
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…
The formalism of weak measurement in quantum mechanics has revealed profound connections between measurement theory, quantum foundations, and signal processing. In this paper, we develop a pointer-free derivation of superoscillations,…
We study the outcomes in a general measurement with postselection, and derive upper bounds for the pointer readings in weak measurement. Using the idea of weak measurement, we study Hardy's gedanken experiment and show how the "negative…
A recent Letter in Physical Review Letters, "Contextual Values of Observables in Quantum Measurements", by J. Dressel, S. Agarwal, and A. N. Jordan (abbreviated DAJ below), introduces the concept of "contextual values" and claims that they…
One unique feature of quantum mechanics is the Heisenberg uncertainty principle, which states that the outcomes of two incompatible measurements cannot simultaneously achieve arbitrary precision. In an information-theoretic context of…
According to the uncertainty principle, every quantum measurement accompanies disturbance. In particular, accurate sequential measurements need the accurate control of disturbance. However, the correct role of disturbance in the uncertainty…
In a previous work (arXiv:1609.05654v2), an experimental setup aiming at the measurement of deviations from the Newtonian $1/r^2$ distance dependence of gravitational interactions was proposed. The theoretical idea behind this setup was to…
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…
This work demonstrates that repeated weak measurements together with post-selection can produce sharp dynamical discontinuities in meter observables, even in minimal quantum systems. The discontinuous behavior is governed by the polar angle…
Quantum weak measurement has attracted much interest recently [J. Dressel et al., Rev. Mod. Phys. 86, 307 (2014)] because it could amplify some weak signals and provide a technique to observe nonclassical phenomena. Here, we apply this…
Measurements in classical and quantum physics are described in fundamentally different ways. Nevertheless, one can formally define similar measurement procedures with respect to the disturbance they cause. Obviously, strong measurements,…
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…
We quantify the disturbance of a quantum state undergoing a sequence of observations, and particularly focus on a weak measurement followed by post-selection and compare these results to the projective counterpart. Taking into account the…