Related papers: Comment on "Uncertainty Relations for Positive Ope…
We study the problem of separating the data produced by a given quantum measurement (on states from a memoryless source which is unknown except for its average state), described by a positive operator valued measure (POVM), into a…
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…
Information entropies give a genuine way to characterize quantitatively an incompatibility in quantum measurements. Together with the Shannon entropy, few families of parametrized entropies have found use in various questions. It is also…
Entropic uncertainty relations play a fundamental role in quantum information theory. However, determining optimal (tight) entropic uncertainty relations for general observables remains a formidable challenge and has so far been achieved…
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…
The uncertainty principle restricts potential information one gains about physical properties of the measured particle. However, if the particle is prepared in entanglement with a quantum memory, the corresponding entropic uncertainty…
Indirect measurement can be used to read out the outcome of a quantum system without resorting to a straightforward approach, and it is the foundation of the measurement uncertainty relations that explain the incompatibility of conjugate…
We analyze entropic uncertainty relations in a finite dimensional Hilbert space and derive several strong bounds for the sum of two entropies obtained in projective measurements with respect to any two orthogonal bases. We improve the…
We employ quantum relative entropy to establish the relation between the measurement uncertainty and its disturbance on a state in the presence (and absence) of quantum memory. For two incompatible observables, we present the…
Entropic uncertainty relations play an important role in both fundamentals and applications of quantum theory. Although they have been well-investigated in quantum theory, little is known about entropic uncertainty in generalized…
Quantum coherence is a fundamental feature of quantum mechanics and an underlying requirement for most quantum information tasks. In the resource theory of coherence, incoherent states are diagonal with respect to a fixed orthonormal basis,…
Traditional uncertainty relations dictate a minimal amount of noise in incompatible projective quantum measurements. However, not all measurements are projective. Weak measurements are minimally invasive methods for obtaining partial state…
In quantum mechanics the statistics of the outcomes of a measuring apparatus is described by a positive operator valued measure (POVM). A quantum channel transforms POVM's into POVM's, generally irreversibly, thus loosing some of the…
We generalize recent work of Massar and Popescu dealing with the amount of classical data that is produced by a quantum measurement on a quantum state ensemble. In the previous work it was shown how spurious randomness generally contained…
We improve the entropic uncertainty relations for position and momentum coarse-grained measurements. We derive the continuous, coarse-grained counterparts of the discrete uncertainty relations based on the concept of majorization. The…
We characterize the asymptotic performance of a class of positive operator valued measurements (POVMs) where the only task is to make measurements on independent and identically distributed quantum states on finite-dimensional systems. The…
We derive a measurement-independent asymptotic continuity bound on the observational entropy for general POVM measurements, making essential use of its property of bounded concavity. The same insight is used to obtain continuity bounds for…
The concept of quantum coherence and its possible use as a resource are currently the subject of active researches. Uncertainty and complementarity relations for quantum coherence allow one to study its changes with respect to other…
In this work we investigate how to quantify the coherence of quantum measurements. First, we establish a resource theoretical framework to address the coherence of measurement and show that any statistical distance can be adopted to define…
In this work we study various notions of uncertainty for angular momentum in the spin-s representation of SU(2). We characterize the "uncertainty regions'' given by all vectors, whose components are specified by the variances of the three…