Related papers: Quantum Errors and Disturbances: Response to Busch…
We show that the theory of operator quantum error correction can be naturally generalized by allowing constraints not only on states but also on observables. The resulting theory describes the correction of algebras of observables (and may…
Until recently Jeffrey Bub and Itamar Pitowsky, in the framework of an information theoretic view of quantum mechanics, claimed first that to the measurement problem in its ordinary formulation there correspond in effect two measurement…
The problem of time in quantum mechanics concerns the fact that in the Schr\"odinger equation time is a parameter, not an operator. Pauli's objection to a time-energy uncertainty relation analogue to the position-momentum one, conjectured…
In recent years, novel quantifications of measurement error in quantum mechanics have for the first time enabled precise formulations of Heisenberg's famous but often challenged measurement uncertainty relation. These relations take the…
The indeterminacy inherent in quantum measurement is an outstanding character of quantum theory, which manifests itself typically in Heisenberg's error-disturbance uncertainty relation. In the last decade, Heisenberg's relation has been…
By invoking quantum estimation theory we formulate bounds of errors in quantum measurement for arbitrary quantum states and observables in a finite-dimensional Hilbert space. We prove that the measurement errors of two observables satisfy…
The discussion of the foundations of quantum mechanics is complicated by the fact that a number of different issues are closely entangled. Three of these issues are i) the interpretation of probability, ii) the choice between realist and…
We reconsider some important foundational problems of quantum mechanics. After reviewing the measurement problem and discussing its unavoidability, we analyze some proposals to overcome it. This analysis leads us to reconsider the current…
About twenty years ago, we proposed the mathematical formulation of Heisenberg's uncertainty principle, and further, we concluded that Heisenberg's uncertainty principle and EPR-paradox are not contradictory. This is true, however we now…
A short foreword has been added for the archive version of this article, which otherwise appears as originally published in 1990, except for the updating of references. The original abstract follows. This is a critical review of the…
Heisenberg's uncertainty principle was originally formulated in 1927 as a quantitative relation between the "mean error" of a measurement of one observable and the disturbance thereby caused on another observable. Heisenberg derived this…
The quantum theory of measurement has been a matter of debate for over eighty years. Most of the discussion has focused on theoretical issues with the consequence that operational prescriptions, which are integral to experimental physics,…
In this letter we show that the field of Operator Space Theory provides a general and powerful mathematical framework for arbitrary Bell inequalities, in particular regarding the scaling of their violation within quantum mechanics. We…
In this work we analyze the deep link between the 20th Century positivist re-foundation of physics and the famous measurement problem of quantum mechanics. We attempt to show why this is not an "obvious" nor "self evident" problem for the…
In general, classical measurement statistics of a quantum measurement is disturbed by performing an additional incompatible quantum measurement beforehand. Using this observation, we introduce a state-independent definition of disturbance…
We revisit the definitions of error and disturbance recently used in error-disturbance inequalities derived by Ozawa and others by expressing them in the reduced system space. The interpretation of the definitions as mean-squared deviations…
Some of the so-called imponderables and counterintuitive puzzles associated with the Copenhagen interpretation of quantum mechanics appear to have alternate, parallel explanations in terms of nonlinear dynamics and chaos. These include the…
The usual conjectures of quantum measurements approaches, inspired from the traditional interpretation of Heisenberg's ("uncertainty") relations, are proved as being incorrect. A group of reconsidered conjectures and a corresponding new…
Objections to pilot-wave theory frequently come in three mutually-contradictory categories: that the theory is too bizarrely different from ordinary physics, that the theory is not radically different enough, and that the physics of…
Bell's theorem depends crucially on counterfactual reasoning, and is mistakenly interpreted as ruling out a local explanation for the correlations which can be observed between the results of measurements performed on spatially-separated…