Related papers: Complementary observables in quantum mechanics
According to Bohr's complementarity principle, a particle possesses wave-like properties only when the different paths the particle may take are indistinguishable. In a canonical example of a two-path interferometer with a which-path…
The concept of complementability is extended from bounded operators to densely defined operators on Hilbert spaces. By introducing appropriate projections and decomposition techniques, a framework is developed for analyzing…
Quantum measurement and quantum operation theory is developed here by taking the relational properties among quantum systems, instead of the independent properties of a quantum system, as the most fundamental elements. By studying how the…
The minimal-length paradigm is a cornerstone of quantum gravity phenomenology. Recently, it has been demonstrated that minimal-length quantum mechanics can alternatively be described as an undeformed theory set on a nontrivial momentum…
Small corrections to the uncertainty relations, with effects in the ultraviolet and/or infrared, have been discussed in the context of string theory and quantum gravity. Such corrections lead to small but finite minimal uncertainties in…
Complementarity plays a pivotal role in understanding a diverse range of quantum phenomena. Here, we show how the tradeoff between quantities of a complete complementarity relation is modified in an arbitrary spacetime for a particle with…
Developments in the foundations of quantum mechanics have identified several attributes and tests associated with the "quantumness" of systems, including entanglement, nonlocality, quantum erasure, Bell test, etc. Here we introduce and…
For a pair of observables, they are called "incompatible", if and only if the commutator between them does not vanish, which represents one of the key features in quantum mechanics. The question is, how can we characterize the…
This paper is a programmatic article presenting an outline of a new view of the foundations of quantum mechanics and quantum field theory. In short, the proposed foundations are given by the following statements: * Coherent quantum physics…
The paper is devoted to quantization of polynomial momentum observables in the cotangent bundle of a smooth manifold. A quantization procedure is proposed allowing to quantize a wide class of functions which are polynomials of any order in…
Complementarity principle is one of the central concepts in quantum mechanics which restricts joint measurement for certain observables. Of course, later development shows that joint measurement could be possible for such observables with…
In this contribution I review rigorous formulations of a variety of limitations of measurability in quantum mechanics. To this end I begin with a brief presentation of the conceptual tools of modern measurement theory. I will make precise…
In [11], Newton da Costa together with the author of this paper argued in favor of the possibility to consider quantum superpositions in terms of a paraconsistent approach. We claimed that, even though most interpretations of quantum…
The mathematical notion of incompleteness (eg of rational numbers, Turing-computable functions, and arithmetic proof) does not play a key role in conventional physics. Here, a reformulation of the kinematics of quantum theory is attempted,…
Using tools from quantum information theory, we present a general theory of indistinguishability of identical bosons in experiments consisting of passive linear optics followed by particle number detection. Our results do neither rely on…
We second quantize the Fermi Lagrangian in the Lorenz gauge to obtain a covariant theory of photon quantum mechanics. Number density is real so it is interpreted as position probability density. The Hilbert space is the vector space of…
Whereas complementarity manifests itself via two incompatible observables, quantum contextuality can only be revealed via the joint measurements among at least three observables. By incorporating unsharp measurements and joint measurements…
The superposition of quantum states lies at the heart of physics and has been recently found to serve as a versatile resource for quantum information protocols, defining the notion of quantum coherence. In this contribution, we report on…
We study various optimality criteria for quantum observables. Observables are represented as covariant positive operator valued measures and we consider the case when the symmetry group is compact. Phase observables are examined as an…
We propose an experimentally accessible, objective measure for the macroscopicity of superposition states in mechanical quantum systems. Based on the observable consequences of a minimal, macrorealist extension of quantum mechanics, it…