Related papers: L\"{u}ders Theorem for Unsharp Quantum Measurement…

A method is proposed that allows one to infer the sum of the values of an observable taken during contacts with a pointer state. Hereby the state of the pointer is updated while contacted with the system and remains unchanged between…

Malley discussed {[Phys. Rev. A {\bf 69}, 022118 (2004)]} that all quantum observables in a hidden-variable model for quantum events must commute simultaneously. In this comment, we discuss that Malley's theorem is indeed valid for the…

Heisenberg's uncertainty relations for measurement quantify how well we can jointly measure two complementary observables and have attracted much experimental and theoretical attention recently. Here we provide an exact tradeoff between the…

In a previous paper (arXiv:1008.3661v1[quant-ph] 21 Aug 2010), we have given a purely logical proof of the Conway and Kochen Free Will theorem in QM: the freedom of the observer implies the freedom of the observed particle. Here we show…

We give an explicit axiomatic formulation of the quantum measurement theory which is free of the projection postulate. It is based on the generalized nondemolition principle applicable also to the unsharp, continuous-spectrum and…

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…

We propose a new measure of relative incompatibility for a quantum system with respect to two non-commuting observables, and call it quantumness of relative incompatibility. In case of a classical state, order of observation is…

In the framework of local thermodynamic equilibrium by Buchholz, Ojima and Roos, a class S_x of observables, whose members are supposed to model idealized measurements of thermal properties of given states at spacetime points x, plays a…

We study bipartite spin-singlet correlations when rotational symmetry is described by a quantum group rather than an ordinary Lie group. We show that, even though the single-spin observables act as in the undeformed theory, the non-trivial…

Uncertainty relations are usually formulated as trade-off relations between two or more observables. Here we show that the uncertainty of a single observable already has a nontrivial lower bound originating from the noncommutativity between…

We show that if points of supports of two discrete "not very thick" Fourier transformable measures on LCA groups tend to one another at infinity and the same is true for the masses at these points, then these measures coincide. The result…

One of the central features of quantum theory is that there are pairs of quantum observables that cannot be measured simultaneously. This incompatibility of quantum observables is a necessary ingredient in several quantum phenomena, such as…

The influence theorem for product measures on the discrete space {0,1}^N may be extended to probability measures with the property of monotonicity (which is equivalent to `strong positive-association'). Corresponding results are valid for…

Let $(X,d)$ be a compact metric space. We consider the behavior of probability measures $\mu$ with the property that $$ \int_{X} d(x, y) d\mu(y) \qquad \mbox{is independent of}~x \in X.$$ It appears that such measures, when they exist,…

We study the problem of performing orthogonal qubit measurements simultaneously. Since these measurements are incompatible, one has to accept additional imprecision. An optimal joint measurement is the one with the least possible…

Uncertainty principle is one of the fundamental principles of quantum mechanics. In this work, we derive two uncertainty equalities, which hold for all pairs of incompatible observables. We also obtain an uncertainty relation in weak…

Hardy's theorem states that the hidden variables of any realistic theory of quantum measurement, whose predictions agree with ordinary quantum theory, must have a preferred Lorentz frame. This presents the conflict between special…

Most of the fundamental characteristics of quantum mechanics, such as non-locality and contextuality, are manifest in discrete, finite-dimensional systems. However, many quantum information tasks that exploit these properties cannot be…

Efficiently extracting information from pure quantum states using minimal observables on the main system is a longstanding and fundamental issue in quantum information theory. Despite the inability of probability distributions of position…

We study the dynamics of smooth interval maps with non-flat critical points. For every such a map that is topologically exact, we establish the full (level-2) Large Deviation Principle for empirical means. In particular, the Large Deviation…