Related papers: Some Nearly Quantum Theories
Quantum computers provide a super-exponential speedup for performing a Fourier transform over the symmetric group, an ability for which practical use cases have remained elusive so far. In this work, we leverage this ability to unlock…
There are 13 equivalence classes of 2D second order quantum and classical superintegrable systems with nontrivial potential, each associated with a quadratic algebra of hidden symmetries. We study the finite and infinite irreducible…
Recently, substantial amount of activity in Quantum General Relativity (QGR) has focussed on the semiclassical analysis of the theory. In this paper we want to comment on two such developments: 1) Polymer-like states for Maxwell theory and…
Quantum theory does not provide a unique definition for the joint probability of two non-commuting observables, which is the next important question after the Born's probability for a single observable. Instead, various definitions were…
We prove that the vast majority of symmetric states of qubits can be decomposed in a unique way into a superposition of spin 1/2 coherent states. For the case of two qubits, the proposed decomposition reproduces the Schmidt decomposition…
We extend the usual process-theoretic view on locality and causality in subsystems (based on the tensor product case) to general quantum systems (i.e.\ possibly non-factor, finite-dimensional von Neumann algebras). To do so, we introduce a…
The paper is concerned with the extension of the classical study of probability measures on a compact group which are square roots of the Haar measure, due to Diaconis and Shahshahani, to the context of compact quantum groups. We provide a…
I explore several related routes to deriving the Jordan-algebraic structure of finite-dimensional quantum theory from more transparent operational or physical principles, mainly involving ideas about the symmetries of, and the correlations…
This paper presents a novel way to use the algebra of unit quaternions to express arbitrary roots or fractional powers of single-qubit gates, and to use such fractional powers as generators for algebras that combine these fractional input…
We introduce new families of pure quantum states that are constructed on top of the well-known Gilmore-Perelomov group-theoretic coherent states. We do this by constructing unitaries as the exponential of operators quadratic in Cartan…
The no-cloning principle tells us that non-orthogonal quantum states cannot be cloned, but it does not tell us that orthogonal states can always be cloned. We suggest a situation where the cloning transformations are restricted, leading to…
Understanding the complexity of quantum states and circuits is a central challenge in quantum information science, with broad implications in many-body physics, high-energy physics and quantum learning theory. A common way to model the…
Recently, it has been argued that quantum mechanics is a complete theory, and that different quantum states do necessarily correspond to different elements of reality, under the assumptions that quantum mechanics is correct and that…
A non-Boolean extension of the classical probability model is proposed. The non-Boolean probabilities reproduce typical quantum phenomena. The proposed model is more general and more abstract, but easier to interpret, than the quantum…
We realise non-unitary fusion categories using subfactor-like methods, and compute their quantum doubles and modular data. For concreteness we focus on generalising the Haagerup-Izumi family of Q-systems. For example, we construct…
There have been several propositions for a geometric and essentially non-linear formulation of quantum mechanics. From a purely mathematical point of view, the point of view of Jordan algebra theory might give new strength to such…
We generalize the notion of weakly mixing unitary representations to locally compact quantum groups, introducing suitable extensions of all standard characterizations of weak mixing to this setting. These results are used to complement the…
Interest in combinatorial interpretations of mathematical entities stems from the convenience of the concrete models they provide. Finding a bijective proof of a seemingly obscure identity can reveal unsuspected significance to it. Finding…
The matrix models attached to real symmetric matrices and the complex/quaternionic Hermitian matrices have been studied by many authors. These models correspond to three of the simple formally real Jordan algebras over R. Such algebras were…
Jordan operator algebras are norm-closed spaces of operators on a Hilbert space which are closed under the Jordan product. The discovery of the present paper is that there exists a huge and tractable theory of possibly nonselfadjoint Jordan…