Related papers: Defining quantumness via the Jordan product
Quantum theory is traditionally formulated using complex numbers. This imaginarity of quantum theory has been quantified as a resource with applications in discrimination tasks, pseudorandomness generation, and quantum metrology. Here we…
Coherence is a fundamental resource in quantum information processing, which can be certified by a coherence witness. In order to detect all the coherent states, we introduce a useful concept of coherence witness and structure the set of…
We argue that the ordinary commutative-and-associative algebra of spacetime coordinates (familiar from general relativity) should perhaps be replaced, not by a noncommutative algebra (as in noncommutative geometry), but rather by a Jordan…
We present the quantum computation of nuclear observables where the operators of interest are first decomposed in terms of the linear combination of unitaries. Then we utilise the Hadamard test and the linear combination of unitaries (LCU)…
The classification, up to isomorphism, of two-dimensional (not necessarily commutative) Jordan algebras over algebraically closed fields and $\mathbb{R}$ is presented in terms of their matrices of structure constants.
The questions of describing observables and observation in quantum gravity appear to be centrally important to its physics. A relational approach holds significant promise, and a classification of different types of relational observables…
We introduce a measure of ''quantumness'' for any quantum state in a finite dimensional Hilbert space, based on the distance between the state and the convex set of classical states. The latter are defined as states that can be written as a…
It is proposed the scheme of quantum mechanics, in which a Hilbert space and the linear operators are not primary elements of the theory. Instead of it certain variant of the algebraic approach is considered. The elements of noncommutative…
The dimension of a quantum state is traditionally seen as the number of superposed distinguishable states in a given basis. We propose an absolute, i.e.~basis-independent, notion of dimensionality for ensembles of quantum states. It is…
This paper examines whether unitary evolution alone is sufficient to explain emergence of the classical world from the perspective of computability theory. Specifically, it looks at the problem of how the choice related to the measurement…
Let $G$ be a classical group with natural module $V$ over an algebraically closed field of good characteristic. For every unipotent element $u$ of $G$, we describe the Jordan block sizes of $u$ on the irreducible $G$-modules which occur as…
We introduce an algebraic framework for interacting quantum systems that enables studying complex phenomena, characterized by the coexistence and competition of various broken symmetry states of matter. The approach unveils the hidden unity…
Uncertainty and entanglement are both profound and key concepts in quantum theory. For three observables, the tightest uncertainty constants for both product and summation forms are revealed. In this work, we give an alternative proof for…
This article points out that observables and instruments can be combined in many ways that have natural and physical interpretations. We shall mainly concentrate on the mathematical properties of these combinations. Section~1 reviews the…
In this work we discuss the notion of observable - both quantum and classical - from a new point of view. In classical mechanics, an observable is represented as a function (measurable, continuous or smooth), whereas in (von Neumann's…
We introduce a natural notion of determinant in matrix JB$^*$-algebras, i.e., for hermitian matrices of biquaternions and for hermitian $3\times 3$ matrices of complex octonions. We establish several properties of these determinants which…
Any quantum theory of gravity which treats the gravitational constant as a dynamical variable has to address the issue of superpositions of states corresponding to different eigenvalues. We show how the unobservability of such…
Starting from a generalized Hamilton-Jacobi formalism, we develop a new framework for constructing observables and their evolution in theories invariant under global time reparametrizations. Our proposal relaxes the usual Dirac prescription…
Quantifying coherence is an essential endeavour for both quantum foundations and quantum technologies. Here the robustness of coherence is defined and proven a full monotone in the context of the recently introduced resource theories of…
We give a criterion of classicality for mixed states in terms of expectation values of a quantum observable. Using group representation theory we identify all cases when the criterion can be computed exactly in terms of the spectrum of a…