Related papers: Complementary observables in quantum mechanics
We study the physical content of the PT-symmetric complex extension of quantum mechanics as proposed in Bender et al, Phys. Rev. Lett. 80, 5243 (1998) and 89, 270401 (2002), and show that as a fundamental probabilistic physical theory it is…
Some recent works have introduced a quantum twist to the concept of complementarity, exemplified by a setup in which the which-way detector is in a superposition of being present and absent. It has been argued that such experiments allow…
The notion of incompressible momentum observables is introduced. It is shown that when the metric in a manifold has a certain form, a set of canonically conjugate variables Xk and Pk in which Pk are incompressible, can be constructed. Based…
Generalised observables (POM observables) are necessary for representing all possible measurements on a quantum system. Useful algebraic operations such as addition and multiplication are defined for these observables, recovering many…
We point out a possible complementation of the basic equations of quantum mechanics in the presence of gravity. This complementation is suggested by the well-known fact that quantum mechanics can be equivalently formulated in the position…
In this work, we give rigorous operational meaning to superposition of causal orders. This fits within a recent effort to understand how the standard operational perspective on quantum theory could be extended to include indefinite…
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…
What Niels Bohr called the `epistemological lesson' of `complementarity' was the result of reasoning analogically from the classical conception of a mechanical state to a new quantum mechanical conception of an `object' in a mechanical…
Quantum mechanics predicts the joint probability distribution of the outcomes of simultaneous measurements of commuting observables, but, in the state of the art, has lacked the operational definition of simultaneous measurements. The…
Quantum operators of coordinates and momentum components of a particle in Minkowski space-time belong to a noncommutative algebra and give rise to a quantum phase space. Under some constraints, in particular, the Lorentz invariance…
Observables and instruments have played significant roles in recent studies on the foundations of quantum mechanics. Sequential products of effects and conditioned observables have also been introduced. After an introduction in Section~1,…
We introduce the concept of degree of quantumness in quantum synchronization, a measure of the quantum nature of synchronization in quantum systems. Following techniques from quantum information, we propose the number of non-commuting…
We investigate the problem of coexistence of position and momentum observables. We characterize those pairs of position and momentum observables which have a joint observable.
The physical meaning of the operators is not reducible to the intrinsic relations of the quantum system, since unitary transformations can find other operators satisfying the exact same relations. The physical meaning is determined…
Complementarity and nonlocality are two characteristic traits of quantum physics that distinguishes it from classical physics. In this paper, we prove that the complementarity between global and local observables in Bell's experiment sets…
The description of relativistic effects requires a preliminary definition of events localised in space-time while the clocks used for time definition and the fields used in synchronisation or localisation procedures are necessarily quantum…
Under the principle that quantum mechanical observables are invariant under relevant symmetry transformations, we explore how the usual, non-invariant quantities may capture measurement statistics. Using a relativisation mapping, viewed as…
We propose a formal framework for understanding and unifying the concept of observers across physics, computer science, philosophy, and related fields. Building on cybernetic feedback models, we introduce an operational definition of…
A very simple illustration of the Bell-Kochen-Specker contradiction is presented using continuous observables in infinite dimensional Hilbert space. It is shown that the assumption of the \emph{existence} of putative values for position and…
The quantitative formulation of Bohr's complementarity proposed by Greenberger and Yasin is applied to some physical situations for which analytical expressions are available. This includes a variety of conventional double-slit experiments,…