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According to quantum theory, the outcomes of future measurements cannot (in general) be predicted with certainty. In some cases, even with a complete physical description of the system to be measured and the measurement apparatus, the…
It was argued [1] that there can be no extension of quantum mechanics with improved predictive power on a measurement freely chosen, independently of any event that is not in its future light cone. The assumption of measurement choice was…
Kempf et al. in Ref. [1] have formulated a Hilbert space representation of quantum mechanics with a minimal measurable length. Recently it has been revealed, in the context of doubly special relativity, that a test particles' momentum…
There are two powerful arguments against the possibility of extending quantum mechanics, the violation of Bell inequalities and the Kochen-Specker theorem, but the connection between the two remains confused. Following the distinctive…
We introduce novel upper bounds on the Hilbert space dimensions required to realize quantum correlations in Bell scenarios. We start by considering bipartite cases wherein one of the two parties has two settings and two outcomes. Regardless…
Recently, it has been argued that no extension of quantum theory can have improved predictive power under a strong assumption of free choice of the experimental settings and validity of quantum mechanics. Here, under a different free choice…
In this paper, a modified formulation of generalized probabilistic theories that will always give rise to the structure of Hilbert space of quantum mechanics, in any finite outcome space, is presented and the guidelines to how to extend…
Characterizing high-dimensional entangled states is of crucial importance in quantum information science and technology. Recent theoretical progress has been made to extend the Hardy's paradox into a general scenario with multisetting…
In three papers Colbeck and Renner (Nature Communications 2:411, (2011); Phys. Rev. Lett. 108, 150402 (2012); arXiv:1208.4123) argued that "no alternative theory compatible with quantum theory and satisfying the freedom of choice assumption…
The laws of quantum mechanics place fundamental limits on the accuracy of measurements and therefore on the estimation of unknown parameters of a quantum system. In this work, we prove lower bounds on the size of confidence regions reported…
Ontological theories of quantum mechanics describe a single system by means of well-defined classical variables and attribute the quantum uncertainties to our ignorance about the underlying reality represented by these variables. We…
Unextendibility of quantum states and channels is inextricably linked to the no-cloning theorem of quantum mechanics, it has played an important role in understanding and quantifying entanglement, and more recently it has found applications…
Quantum gates are essential for the realization of quantum computer and have been implemented in various types of two-level systems. However, high-dimensional quantum gates are rarely investigated both theoretically and experimentally even…
Quantum mechanics is widely regarded as a complete theory, yet we argue it is a tractable projection of a deeper, computationally-inaccessible classical variational structure. By analyzing the coupled partial differential equations of the…
According to quantum theory, measurements generate random outcomes, in stark contrast with classical mechanics. This raises the question of whether there could exist an extension of the theory which removes this indeterminism, as suspected…
Reaching ultimate performance of quantum technologies requires the use of detection at quantum limits and access to all resources of the underlying physical system. We establish a full quantum analogy between the pair of angular momentum…
A basic theoretical framework is developed in which elementary particles have a component of their wave function extending into higher spatial dimensions. This model postulates an extension of the Schrodinger equation to include a 4th and…
We propose a quantum mechanics of extended objects that accounts for the finite extent of a particle defined via its Compton wavelength. The Hilbert space representation theory of such a quantum mechanics is presented and this…
The expectation values of operators drawn from a single quantum state cannot be outside of a particular region, called their allowed region or the joint numerical range of the operators. Basically, the allowed region is an image of the…
By considering (non-relativistic) quantum mechanics as it is done in practice in particular in condensed-matter physics, it is argued that a deterministic, unitary time evolution within a chosen Hilbert space always has a limited scope,…