Related papers: Sum uncertainty relations based on Wigner-Yanase s…
A fundamental concept of quantum physics, the Wigner Yanase information, is here used as a measure of quantum coherence in spin-dependent radical-pair reactions pertaining to biological magnetic sensing. This measure is connected to the…
The uncertainty relation, as one of the fundamental principles of quantum physics, captures the incompatibility of noncommuting observables in the preparation of quantum states. In this work, we derive two strong and universal uncertainty…
We present new generalizations of Cauchy-Schwarz (CS) inequalities to multiple vectors and use them to derive multi-operator quantum uncertainty relations and propose multi-operator squeezing.
Quantum mechanical uncertainty relations for position and momentum are expressed in the form of inequalities involving the Renyi entropies. The proof of these inequalities requires the use of the exact expression for the (p,q)-norm of the…
We investigate quantum average correlations and complementarity relations based on metric-adjusted skew information. Several natural averaging procedures are considered, including complete families of mutually unbiased bases, all…
Measurement outcomes of a quantum state can be genuinely random (unpredictable) according to the basic laws of quantum mechanics. The Heisenberg-Robertson uncertainty relation puts constrains on the accuracy of two noncommuting observables.…
The current study aims to examine uncertainty relations for measurements from generalized equiangular tight frames. Informationally overcomplete measurements are a valuable tool in quantum information processing, including tomography and…
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…
The uncertainty relation is a distinguishing feature of quantum theory, characterizing the incompatibility of noncommuting observables in the preparation of quantum states. Recently, many uncertainty relations were proposed with improved…
In this paper, we aim to replace in the definitions of covariance and correlation the usual trace {\rm Tr} by a tracial positive map between unital $C^*$-algebras and to replace the functions $x^{\alpha}$ and $x^{1-\alpha}$ by functions $f$…
A generalized skew information is defined and a generalized uncertainty relation is established with the help of a trace inequality which was recently proven by J.I.Fujii. In addition, we prove the trace inequality conjectured by S.Luo and…
We extend the concept of Wigner-Yanase-Dyson skew information to something we call ``metric adjusted skew information'' (of a state with respect to a conserved observable). This ``skew information'' is intended to be a non-negative quantity…
We prove uncertainty relations that quantitatively express the impossibility of jointly sharp preparation of pre- and post-selected quantum states for measuring incompatible observables during the weak measurement. By defining a suitable…
We study the uncertainty relation in the product form of variances and obtain some new uncertainty relations with weight, which are shown to be tighter than those derived from the Cauchy Schwarz inequality.
A quantitative extension of the Wigner-Araki-Yanase theorem is obtained on the limitation on precise, non-disturbing measurements of observables which do not commute with additive conserved quantities, and applied to obtaining a limitation…
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 of three quantities in quantum mechanics is estimated in terms of commutators. The Pauli matrices are used to find a contribution of third-order commutators. The resulting inequality refines the Heisenberg…
Unsolved controversies about uncertainty relations and quantum measurements still persists nowadays. They originate around the shortcomings regarding the conventional interpretation of uncertainty relations. Here we show that the respective…
We explore the uncertainty relation for unitary operators in a new way and find two uncertainty equalities for unitary operators, which are minimized by any pure states. Additionally, we derive two sets of uncertainty inequalities that…
Historically, the element of uncertainty in quantum mechanics has been expressed through mathematical identities called uncertainty relations, a great many of which continue to be discovered. These relations use diverse measures to quantify…