Related papers: Number operator-annihilation operator uncertainty …

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…

We develop a unified, information theoretic interpretation of the number-phase complementarity that is applicable both to finite-dimensional (atomic) and infinite-dimensional (oscillator) systems. The relevant uncertainty principle is…

Coherent states are usually defined as eigenstates of an unbounded operator, the so-called annihilation operator. We propose here possible constructions of {\em quasi-coherent states}, which turn out to be {\em quasi} eigenstate of a…

The problem of entanglement produced by an arbitrary operator is formulated and a related measure of entanglement production is introduced. This measure of entanglement production satisfies all properties natural for such a characteristic.…

We develop a unified, information theoretic interpretation of the number-phase complementarity that is applicable both to finite-dimensional (atomic) and infinite-dimensional (oscillator) systems, with number treated as a discrete Hermitian…

We reformulate the notion of uncertainty of pairs of unitary operators within the context of guessing games and derive an entropic uncertainty relation for a pair of such operators. We show how distinguishable operators are compatible while…

The uncertainty principle is fundamentally rooted in the algebraic asymmetry between observables. We introduce a new class of uncertainty relations grounded in the resource theory of asymmetry, where incompatibility is quantified by an…

This is a pedagogical paper where we present a physically motivated approach to introduce the coherent states of a harmonic oscillator from which it is simple to rigorously derive their mathematical definition. We do this in two different…

We provide a unified and strengthened framework for the product form and the sum form variance-based uncertainty relations by constructing a unified uncertainty relation. In the unified framework, we deduce that the uncertainties of the…

We define the standard quantum limit (SQL) for phase and number fluctuations, and describe two-mode squeezing for number and phase variables. When phase is treated as a unitary quantum-mechanical operator, number and phase operators satisfy…

Integrability in quantum theory has been defined in more than one ways. Recently, Braak suggested a new definition that a quantum system is integrable if the number of parameters required to specify the eigenstates and the number degrees of…

We present an approach to estimate the operational distinguishability between an entangled state and any separable state directly from measuring an entanglement witness. We show that this estimation also implies bounds on a variety of other…

In this letter, the number-phase entropic uncertainty relation and the number-phase Wigner function of generalized coherent states associated to a few solvable quantum systems with nondegenerate spectra are studied. We also investigate time…

The known approaches of number-phase problem (for a quantum oscillator) are mutually contradictory. All of them are subsequent in respect with the Robertson-Schr\"{o}dinger uncertainty relation (RSUR). In oposition here it is proposed a new…

An operator connection is a binary operation assigned to each pair of positive operators satisfying monotonicity, continuity from above and the transformer inequality. In this paper, we introduce and characterize the concepts of…

Operator quantum error-correction is a technique for robustly storing quantum information in the presence of noise. It generalizes the standard theory of quantum error-correction, and provides a unified framework for topics such as quantum…

Quantum measurements can be described by operators that assign conditional probabilities to different outcomes while also describing unavoidable physical changes to the system. Here, we point out that operators describing information gain…

We derive several uncertainty relations for two arbitrary unitary operators acting on physical states of a Hilbert space. We show that our bounds are tighter in various cases than the ones existing in the current literature. Using 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…

We construct a quantum-control-assisted multi-observable variance-based uncertainty relation, and the uncertainty relation obtained indicates that we can prepare a quantum state, in which the measurement results of any observables can be…