Related papers: The Finite Geometry of Breaking Quantum Secrets
In this paper, we present explicit expressions for conforming finite element function spaces, basis functions, and degrees of freedom on the pentatope and tetrahedral prism elements. More generally, our objective is to construct finite…
Compact categories have lately seen renewed interest via applications to quantum physics. Being essentially finite-dimensional, they cannot accomodate (co)limit-based constructions. For example, they cannot capture protocols such as quantum…
In this paper we investigate the use of quantum information to share classical secrets. While every quantum secret sharing scheme is a quantum error correcting code, the converse is not true. Motivated by this we sought to find quantum…
An active area of investigation in the search for quantum advantage is Quantum Machine Learning. Quantum Machine Learning, and Parameterized Quantum Circuits in a hybrid quantum-classical setup in particular, could bring advancements in…
Entanglement is a key resource of quantum science for tasks that require it to be shared among participants. Within atomic, condensed matter and photonic many-body systems the distribution and sharing of entanglement is of particular…
This paper investigates the construction of efficient quantum secret sharing schemes for quantum access structures based on hypergraphs with three hyperedges. We prove that hypercycles with three hyperedges are quantum access structures if…
Any single system whose space of states is given by a separable Hilbert space is automatically equipped with infinitely many hidden tensor-like structures. This includes all quantum mechanical systems as well as classical field theories and…
In this work, we study position-based cryptography in the quantum setting. The aim is to use the geographical position of a party as its only credential. On the negative side, we show that if adversaries are allowed to share an arbitrarily…
How do symmetries induce natural and useful quantum structures? This question is investigated in the context of models of three interacting particles in one-dimension. Such models display a wide spectrum of possibilities for dynamical…
We introduce new rounding methods to improve the accuracy of finite precision quantum arithmetic. These quantum rounding methods are applicable when multiple samples are being taken from a quantum program. We show how to use multiple…
Quantum secret sharing is an encryption technique based on quantum mechanics, which utilizes uncertainty principle to achieve security in transmission. Most protocols focus on the study of quantum ($n,n$) or ($t,n$) threshold single secret…
We work out the phase-space structure for a system of $n$ qubits. We replace the field of real numbers that label the axes of the continuous phase space by the finite field $\Gal{2^n}$ and investigate the geometrical structures compatible…
We construct quantum error-correcting codes that embed a finite-dimensional code space in the infinite-dimensional Hilbert state space of rotational states of a rigid body. These codes, which protect against both drift in the body's…
The need for secrecy and security is essential in communication. Secret sharing is a conventional protocol to distribute a secret message to a group of parties, who cannot access it individually but need to cooperate in order to decode it.…
Ever since entanglement was identified as a computational and cryptographic resource, effort has been made to find an efficient way to tell whether a given density matrix represents an unentangled, or separable, state. Essentially, this is…
The notion of an orthogonality space was recently rediscovered as an effective means to characterise the essential properties of quantum logic. The approach can be considered as minimalistic; solely the aspect of mutual exclusiveness is…
The aim of the paper is to propose geometric descriptions of multipartite entangled states using algebraic geometry. In the context of this paper, geometric means each stratum of the Hilbert space, corresponding to an entangled state, is an…
Quantum entanglement is a defining signature and resource of quantum theory, but its standard definition presupposes a globally fixed decomposition into subsystems. We develop a geometric framework that detects when such a decomposition…
The aim of this thesis is to investigate quantum entanglement and quantum nonlocality of bipartite finite-dimensional systems (bipartite qudits). Entanglement is one of the most fascinating non-classical features of quantum theory, and…
These notes review a description of quantum mechanics in terms of the topology of spaces, basing on the axioms of Topological Quantum Field Theory and path integral formalism. In this description quantum states and operators are encoded by…