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We consider positive operator valued measures whose image is the bounded operators acting on an infinite-dimensional Hilbert space, and we relax, when possible, the usual assumption of positivity of the operator valued measure seen in the…
A complex conjugation of unitary quantum map is a second-order map (supermap) that maps a unitary operator $U$ to its complex conjugate $U^*$. First, we present a deterministic quantum protocol that universally implements the complex…
Many fundamental and key objects in quantum mechanics are linear mappings between particular affine/linear spaces. This structure includes basic quantum elements such as states, measurements, channels, instruments, non-signalling channels…
A quantum set is defined to be simply a set of nonzero finite-dimensional Hilbert spaces. Together with binary relations, essentially the quantum relations of Weaver, quantum sets form a dagger compact category. Functions between quantum…
A classical (or quantum) superintegrable system on an n-dimensional Riemannian manifold is an integrable Hamiltonian system with potential that admits 2n-1 functionally independent constants of the motion that are polynomial in the momenta,…
We study the two dual quantum information effects to manipulate the amount of information in quantum computation: hiding and allocation. The resulting type-and-effect system is fully expressive for irreversible quantum computing, including…
This paper is an introduction to diagrammatic methods for representing quantum processes and quantum computing. We review basic notions for quantum information and quantum computing. We discuss topological diagrams and some issues about…
Joint measurability of sharp quantum observables is determined pairwise, and so can be captured in a graph. We prove the converse: any graph, whose vertices represent sharp observables, and whose edges represent joint measurability, is…
We develop number theoretic tools that allow to perform computations relevant for the quantum mechanics over finite fields of arbitrary, odd size, with the same speedup that is enjoyed by the Fast Fourier Transform.
Encoding classical data into quantum states is considered a quantum feature map to map classical data into a quantum Hilbert space. This feature map provides opportunities to incorporate quantum advantages into machine learning algorithms…
Axiomatic approach to measurement theory is developed. All the possible statistical properties of apparatuses measuring an observable with nondegenerate spectrum allowed in standard quantum mechanics are characterized.
Quantum computing is a promising new area of computing with quantum algorithms offering a potential speedup over classical algorithms if fault tolerant quantum computers can be built. One of the first applications of the classical computer…
This paper studies the nature of fractional linear transformations in a general relativity context as well as in a quantum theoretical framework. Two features are found to deserve special attention: the first is the possibility of…
We develop elements of a general dilation theory for operator-valued measures and bounded linear maps between operator algebras that are not necessarily completely-bounded. We prove our main results by extending and generalizing some known…
We introduce a family of operations in quantum mechanics that one can regard as "universal quantum measurements" (UQMs). These measurements are applicable to all finite-dimensional quantum systems and entail the specification of only a…
We propose a generalization of the model of classical baker map on the torus, in which the images of two parts of the phase space do overlap. This transformation is irreversible and cannot be quantized by means of a unitary Floquet…
Affine transformations (dilatations and translations) are used to define a deformation of one-dimensional $N=2$ supersymmetric quantum mechanics. Resulting physical systems do not have conserved charges and degeneracies in the spectra.…
Motivated by Cuntz-Krieger-Toeplitz systems associated to undirected graphs and representations of groupoids, we obtain a generalisation of the Sz-Nagy's Dilation Theorem for operator valued partially positive semidefinite maps on…
The interplay between supersymmetry and classical and quantum computation is discussed. First, it is shown that the problem of computing the Witten index of $\mathcal N \leq 2$ quantum mechanical systems is $\#P$-complete and therefore…
A new functional calculus, developed recently for a fully non-perturbative treatment of quantum gravity, is used to begin a systematic construction of a quantum theory of geometry. Regulated operators corresponding to areas of 2-surfaces…