Related papers: Bennett and Stinespring, Together at Last
Nielsen's approach to quantum state complexity relates the minimal number of quantum gates required to prepare a state to the length of geodesics computed with a certain norm on the manifold of unitary transformations. For a bipartite…
We develop a generic method to compute the dynamics induced by quenches in completely connected quantum systems. These models are expected to provide a mean-field description at least of the short time dynamics of finite dimensional system.…
It is noted that the Schrodinger equation with any self-adjoint Hamiltonian is unitary equivalent to a set of non-interacting classical harmonic oscillators and in this sense any quantum dynamics is completely integrable. Higher order…
We develop a novel formal theory of finite structures, based on a view of finite structures as a fundamental artifact of computing and programming, forming a common platform for computing both within particular finite structures, and in the…
We show that the classical mechanics of an algebraic model are implied by its quantizations. An algebraic model is defined, and the corresponding classical and quantum realizations are given in terms of a spectrum generating algebra.…
The effective approach to quantum dynamics allows a reformulation of the Dirac quantization procedure for constrained systems in terms of an infinite-dimensional constrained system of classical type. For semiclassical approximations, the…
This paper introduces the concept of distorted monoidal categories, a generalization of monoidal and braided monoidal categories that supports non-reversible and direction-sensitive tensor structures. Unlike the classical setting, where the…
We improve on our version of the second law of thermodynamics as a deterministic theorem for quantum spin systems in two basic aspects. The first concerns the general statement of the second law: spontaneous changes in an adiabatically…
We present a unified categorical framework that connects the syntactic Henkin construction for the first-order Completeness Theorem with Lawvere's Fixed-Point Theorem. Concretely, we define two canonical functors from the category of…
The question of how irreversibility can emerge as a generic phenomena when the underlying mechanical theory is reversible has been a long-standing fundamental problem for both classical and quantum mechanics. We describe a mechanism for the…
Within the framework of the individuality interpretation of quantum theory (QT), the basic equations of QT cannot be derived from the basic equations of classical mechanics (CM). The unbridgeable gap between CM and QT is given by the fact…
In this paper, we present an infinity-categorical version of the theory of monoidal categories. We show that the infinity category of spectra admits an essentially unique monoidal structure (such that the tensor product preserves colimits…
We generalise clones, which are sets of functions $f:A^n \rightarrow A$, to sets of mappings $f:A^n \rightarrow A^m$. We formalise this and develop language that we can use to speak about it. We then look at bijective mappings, which have…
Universal Drinfeld twists are inner automorphisms which relate the coproduct of a quantum enveloping algebra to the coproduct of the undeformed enveloping algebra. Even though they govern the deformation theory of classical symmetries and…
It is shown in the paper that the unitary quantum dynamics in quantum mechanics is the universal quantum driving force to speed up a quantum computation. This assertion supports strongly in theory that the unitary quantum dynamics is the…
We propose a categorical foundation for the connection between pure and mixed states in quantum information and quantum computation. The foundation is based on distributive monoidal categories. First, we prove that the category of all…
We provide a new foundation for combinatorial commutative algebra and Stanley-Reisner theory using the partition complex introduced in [Adi18]. One of the main advantages is that it is entirely self-contained, using only a minimal knowledge…
Quantum mechanics exhibits a wide range of nonclassical features, of which entanglement in multipartite systems takes a central place. In several specific settings, it is well known that nonclassicality (e.g., squeezing, spin squeezing,…
In classical dynamical systems, stochastic feedback can stabilize otherwise unstable periodic orbits, giving rise to distinct controlled and uncontrolled phases as the rate of control application is varied. In this work, we apply these…
This thesis develops exact analytical tools to study strongly correlated stochastic systems, with a focus on extreme value statistics, gap statistics, and full counting statistics in multi-particle processes. A central contribution is the…