Related papers: Notes on Joint Measurability of Quantum Observable…
We construct a single observable measurement of which mean value on four copies of an {\it unknown} two-qubit state is sufficient for unambiguous decision whether the state is separable or entangled. In other words, there exists a universal…
In this article, we revisit the century-old question of the minimal set of observables needed to identify a quantum state: here, we replace the natural coincidences in their spectra by effective ones, induced by an imperfect measurement. We…
Ernst Specker considered a particular feature of quantum theory to be especially fundamental, namely that pairwise joint measurability of sharp measurements implies their global joint measurability (https://vimeo.com/52923835). To date,…
Quantum theory famously entails the existence of incompatible measurements; pairs of observables which cannot be simultaneously measured to arbitrary precision. Incompatibility is widely regarded to be a uniquely quantum phenomenon, linked…
Following a review of quantum-classical hybrid dynamics, we discuss the ensuing proliferation of observables and relate it to measurements of (would-be) quantum mechanical degrees of freedom performed by (would-be) classical ones (if they…
We provide a compendium of inequalities between several quantum state distinguishability measures. For each measure these inequalities consist of the sharpest possible upper and lower bounds in terms of another measure. Some of these…
We first present a generalization of the Robertson-Heisenberg uncertainty principle. This generalization applies to mixed states and contains a covariance term. For faithful states, we characterize when the uncertainty inequality is an…
Two quantum events, represented by positive operators (effects), are coexistent if they can occur as possible outcomes in a single measurement scheme. Equivalently, the corresponding effects are coexistent if and only if they are contained…
In the operator formalism of quantum mechanics, the density operator describes the complete statistics of a quantum state in terms of d^2 independent elements, where d is the number of possible outcomes for a precise measurement of an…
It is pointed out that there exists an unambiguous definition of locality that enables one to distinguish local and nonlocal quantities. Observables of both types coexist in quantum optics but one must be very careful when attempting to…
Uncertainty and entanglement are both profound and key concepts in quantum theory. For three observables, the tightest uncertainty constants for both product and summation forms are revealed. In this work, we give an alternative proof for…
The existence of observables that are incompatible or not jointly measurable is a characteristic feature of quantum mechanics, which lies at the root of a number of nonclassical phenomena, such as uncertainty relations, wave--particle dual…
We show that bipartite concurrence for rank-2 mixed states of qubits is written by an observable which can be exactly and directly measurable in experiment by local projective measurements, provided that four copies of the composite quantum…
The paper reviews and discusses four ideas scattered in previous papers of the author. First, objective properties of quantum systems are not associated with observables but are defined by preparations. Second, measurable results of…
The impossibility of measuring noncommuting quantum mechanical observables is one of the most fascinating consequences of the quantum mechanical postulates. Hence, to date the investigation of quantum measurement and projection is a…
Consider a scenario where $N$ separated quantum systems are measured, each with one among two possible dichotomic observables. Assume that the $N$ events corresponding to the choice and performance of the measurement in each site are…
Irreversibility is often considered to characterize measurements in quantum mechanics. Fundamental problems with this characterization are addressed. First, whether a measurement is made in quantum mechanics is an arbitrary decision on the…
Four common optimality criteria for measurements are formulated using relations in the set of observables, and their connections are clarified. As case studies, 1-0 observables, localization observables, and photon counting observables are…
A limitation on simultaneous measurement of two arbitrary positive operator valued measures is discussed. In general, simultaneous measurement of two noncommutative observables is only approximately possible. Following Werner's formulation,…
It is known that non-commuting observables in quantum mechanics do not have joint probability. This statement refers to the precise (additive) probability model. I show that the joint distribution of any non-commuting pair of variables can…