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The quantum component in uncertainty relation can be naturally characterized by the quantum coherence of a quantum state, which is of paramount importance in quantum information science. Here, we experimentally investigate quantum…
We show that any Petz $f$-divergence (where $f$ is operator convex) between quantum states admits a universal $\chi^2$-mixture representation: the distinguishability of $\rho$ from $\sigma$ is obtained as a positive superposition of…
Employing the lattice theory on majorization, we investigate the universal quantum uncertainty relation for any number observables and general measurement. We find: 1. The least bounds of the universal uncertainty relations can only be…
We study the trade-off relations given by the l_1-norm coherence of general multipartite states. Explicit trade-off inequalities are derived with lower bounds given by the coherence of either bipartite or multipartite reduced density…
In this Letter, we show that the fulfillment of uncertainty relations is a sufficient criterion for a quantum-mechanically permissible state. We specifically construct two pseudo-spin observables for an arbitrary non-positive Hermitian…
We study the quantum-mechanical uncertainty relation originating from the successive measurement of two observables $\hat{A}$ and $\hat{B}$, with eigenvalues $a_n$ and $b_m$, respectively, performed on the same system. We use an extension…
The aim of the work is to give the explicit proofs of the Renyi-entropy uncertainty relations presented in the previous work [A. Rastegin, arXiv:0805.1777]. The relations with both the state-dependent and state-independent entropic bounds…
We describe a setup for obtaining uncertainty relations for arbitrary pairs of observables related by Fourier transform. The physical examples discussed here are standard position and momentum, number and angle, finite qudit systems, and…
The uncertainty principle is one of the fundamental features of quantum mechanics and plays an essential role in quantum information theory. We study uncertainty relations based on variance for arbitrary finite $N$ quantum observables. We…
We derive universal entanglement entropy and Schmidt eigenvalue behaviors for the eigenstates of two quantum chaotic systems coupled with a weak interaction. The progression from a lack of entanglement in the noninteracting limit to the…
We derive the lower bound of uncertainty relations of two unitary operators for a class of states based on the geometric-arithmetic inequality and Cauchy-Schwarz inequality. Furthermore, we propose a set of uncertainty relations for three…
Given two or more non-commuting observables, it is generally not possible to simultaneously assign precise values to each. This quantum mechanical uncertainty principle is widely understood to be encapsulated by some form of uncertainty…
A tight information-theoretic measurement uncertainty relation is experimentally tested with neutron spin-1/2 qubits. The noise associated to the measurement of an observable is defined via conditional Shannon entropies and a tradeoff…
We derive two quantum uncertainty relations for position and momentum coarse-grained measurements. Building on previous results, we first improve the lower bound for uncertainty relations using the Renyi entropy, particularly in the case of…
Uncertainty relations for a pair of arbitrary measurements and for a single measurement are posed in the form of inequalities using the Renyi entropies. The formulation deals with discrete observables. Both the relations with…
Uncertainty relations and quantum entanglement are pivotal concepts in quantum theory. Beyond their fundamental significance in shaping our understanding of the quantum world, they also underpin crucial applications in quantum information…
The uncertainty relation is a distinctive characteristic of quantum theory. The uncertainty is essentially rooted in quantum states. In this work we regard the uncertainty as an intrinsic property of quantum state and characterize it…
The uncertainty principle lies at the heart of quantum physics, and is widely thought of as a fundamental limit on the measurement precisions of incompatible observables. Here we show that the traditional uncertainty relation in fact…
The uncertainty principle can be understood as constraining the probability of winning a game in which Alice measures one of two conjugate observables, such as position or momentum, on a system provided by Bob, and he is to guess the…
In practical measurements, it is widely recognized that reducing the measurement time leads to decreased accuracy. However, whether an inherent speed-accuracy trade-off exists as a fundamental physical constraint for quantum measurements is…