Related papers: A note on the Relationship between Localization an…
A quantum probability measure is a function on a sigma-algebra of subsets of a (locally compact and Hausdorff) sample space that satisfies the formal requirements for a measure, but whose values are positive operators acting on a complex…
In this article, we show that in the level of quantum mechanics, a photon position operator with commuting components can be obtained in a more natural way; in the level of quantum field theory, the photon position operator corresponds to…
The notion of probability plays a crucial role in quantum mechanics. It appears in quantum mechanics as the Born rule. In modern mathematics which describes quantum mechanics, however, probability theory means nothing other than measure…
We propose a measurement strategy which can, probabilistically, reproduce the statistics of any observable for spatially encoded photonic qubits. It comprises the implementation of a two-outcome positive operator-valued measure followed by…
Localization properties of scalar single particle states are analyzed by explicit calculational examples with a focus on the massless case. Problems arising from the non-existence of relativistic particle position operators respecting the…
The quantum mechanical measurement problem does not arise in the quantum real number approach to quantum measurements of the first kind. The attributes of individual microscopic systems in the experimental ensemble always have qr-number…
This paper presents an overview of close parallels that exist between the theory of positive operator-valued measures (POVMs) associated with a separable Hilbert space and the theory of frames on that space, including its most important…
Projective quantum measurement is a theoretically accepted process in modern quantum mechanics. However, its projection hypothesis is widely regarded as an experimentally established empirical law. In this paper, we combine a previous…
A universal framework for the joint measurement of multiple localized observables in quantum field theory satisfying spacetime locality and compositionality is still lacking. We present an approach to the problem that is based on the one…
Photonic quantum metrology harnesses quantum states of light, such as NOON or Twin-Fock states, to measure unknown parameters beyond classical precision limits. Current protocols suffer from two severe limitations that preclude their…
This paper gives a brief introduction to Positive-Operator Valued Measure (POVM) of quantum communications. The Projection-Valued Measure (PVM) is first introduced and then the POVM. The relation between POVM and PVM is discussed and an…
Does the measurement of a quantum system necessarily break Lorentz invariance? We present a simple model of a detector that measures the spacetime localization of a relativistic particle in a Lorentz invariant manner. The detector does not…
This paper completes a previous work by constructing a class of positive-energy relativistic spatial localization observables in Minkowski spacetime within quantum field theory, using the stress-energy-momentum tensor smeared with suitable…
It is well-known in quantum information theory that a positive operator valued measure (POVM) is the most general kind of quantum measurement. Mathematically, a quantum probability is a normalised POVM, namely a function on certain subsets…
We discuss the problem of implementing generalized measurements (POVMs) with linear optics, either based upon a static linear array or including conditional dynamics. In our approach, a given POVM shall be identified as a solution to an…
Identifying phase transition points is a fundamental challenge in condensed matter physics, particularly for transitions driven by quantum interference effects, such as Anderson and many-body localization. Recent studies have demonstrated…
The quantum reference frames program is based on the idea that reference frames should be treated as quantum physical systems. In this work, we combine these insights with the emphasis on operationality, understood as refraining from…
A relation expressing the covariant transformation properties of a relativistic position operator is derived. This relation differs from the one existing in the literature expressing manifest covariance by some factor ordering. The relation…
We explore the notion of spatial extent and structure, already alluded to in earlier literature, within the formulation of quantum mechanics on the noncommutative plane. Introducing the notion of average position and its measurement, we…
Quantum measurements of physical quantities are usually described as ideal measurements. However, only a few measurements fulfil the conditions of ideal measurements. The aim of the present work is to describe real position measurements…