Related papers: Uncertainties in Successive Measurements
We propose a class of incompatibility measures for quantum observables based on quantifying the effect of a measurement of one observable on the statistics of the outcomes of another. Specifically, for a pair of observables $A$ and $B$ with…
The problem of measurement in quantum mechanics is reanalyzed within a general, strictly probabilistic framework (without reduction postulate). Based on a novel comprehensive definition of measurement the natural emergence of objective…
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…
The quantification of the "measurement uncertainty" aspect of Heisenberg's Uncertainty Principle---that is, the study of trade-offs between accuracy and disturbance, or between accuracies in an approximate joint measurement on two…
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…
Quantum metrology uses small changes in the output probabilities of a quantum measurement to estimate the magnitude of a weak interaction with the system. The sensitivity of this procedure depends on the relation between the input state,…
The concept of quantum coherence, including various ways to quantify the degree of coherence with respect to the prescribed basis, is currently the subject of active research. The complementarity of quantum coherence in different bases was…
The uncertainty principle sets limit on our ability to predict the values of two incompatible observables measured on a quantum particle simultaneously. This principle can be stated in various forms. In quantum information theory, it is…
Consecutive quantum measurements performed on the same system can reveal fundamental insights into quantum theory's causal structure, and probe different aspects of the quantum measurement problem. According to the Copenhagen…
We derive an optimal bound on the sum of entropic uncertainties of two or more observables when they are sequentially measured on the same ensemble of systems. This optimal bound is shown to be greater than or equal to the bounds derived in…
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…
Obtaining information from a quantum system through a measurement typically disturbs its state. The postmeasurement states for a given measurement, however, are not unique and highly rely on the chosen measurement model, complicating the…
In standard formulations of the uncertainty principle, two fundamental features are typically cast as impossibility statements: two noncommuting observables cannot in general both be sharply defined (for the same state), nor can they be…
In general, it is difficult to evaluate measurement errors when the initial and final conditions of the measurement make it impossible to identify the correct value of the target observable. Ozawa proposed a solution based on the operator…
We give a bound to the precision in the estimation of a parameter in terms of the expectation value of an observable. It is an extension of the Cramer-Rao inequality and of the Heisenberg uncertainty relation, where the estimation precision…
We prove an uncertainty relation, which imposes a bound on any joint measurement of position and momentum. It is of the form $(\Delta P)(\Delta Q)\geq C\hbar$, where the `uncertainties' quantify the difference between the marginals of the…
Uncertainty relations are one of the fundamental principles in physics. It began as a fundamental limitation in quantum mechanics, and today the word {\it uncertainty relation} is a generic term for various trade-off relations in nature. In…
We prove a new sum uncertainty relation in quantum theory which states that the uncertainty in the sum of two or more observables is always less than or equal to the sum of the uncertainties in corresponding observables. This shows that the…
The quantum mechanical measurement problem is the difficulty of dealing with the indefiniteness of the pointer observable at the conclusion of a measurement process governed by unitary quantum dynamics. There has been hope to solve this…
Uncertainty relation lies at the heart of quantum mechanics, characterizing the incompatibility of non-commuting observables in the preparation of quantum states. An important question is how to improve the lower bound of uncertainty…