Related papers: The Finite Geometry of Breaking Quantum Secrets
We provide a complete geometric description of the set of synchronous quantum correlations for the three experiment two outcome scenario. We show that these correlations form a closed set. Moreover, every correlation in this set can be…
Finite projective geometries, especially the Fano plane, have been observed to arise in the context of certain quantum gate operators. We use Clifford algebras to explain why these geometries, both planar and higher dimensional, appear in…
This thesis, explores the quantum entanglement and evolution through both a geometric and dynamical perspective. The first part focuses on classical phase space and its central role in Hamiltonian mechanics, emphasizing the importance of…
When analysing quantum information processing protocols one has to deal with large entangled systems, each consisting of many subsystems. To make this analysis feasible, it is often necessary to identify some additional structure. de…
We extend the formalism of cluster state quantum secret sharing, as presented in Markham and Sanders [Phys. Rev. A 78, 042309 (2008)] and Keet et al. [Phy. Rev. A 82, 062315 (2010)], to the continuous-variable regime. We show that both…
We develop a systematic approach to determine and measure numerically the geometry of generic quantum or "fuzzy" geometries realized by a set of finite-dimensional hermitian matrices. The method is designed to recover the semi-classical…
The main purpose of this article is to facilitate the implementation of space-time finite element methods in four-dimensional space. In order to develop a finite element method in this setting, it is necessary to create a numerical…
We study the quantum entanglement structure of integer quantum Hall states via the reduced density matrix of spatial subregions. In particular, we examine the eigenstates, spectrum and entanglement entropy (EE) of the density matrix for…
Surface codes describe quantum memory stored as a global property of interacting spins on a surface. The state space is fixed by a complete set of quasi-local stabilizer operators and the code dimension depends on the first homology group…
In this paper we propose a practical quantum key distribution protocol based on geometrically uniform states and a standard decoy state technique. The protocol extends the ideas used in SARG04 to the limit where the core quantum…
In perturbative quantum field theory one encounters certain, very specific geometries over the integers. These perturbative quantum geometries determine the number contents of the amplitude considered. In the article `Modular forms in…
Prepare-and-measure (P&M) quantum networks are the basic building blocks of quantum communication and cryptography. These networks crucially rely on non-orthogonal quantum encodings to distribute quantum correlations, thus enabling superior…
The compression of geometric structures is a relatively new field of data compression. Since about 1995, several articles have dealt with the coding of meshes, using for most of them the following approach: the vertices of the mesh are…
Wheeler emphasized the study of Superspace - the space of 3-geometries on a spatial manifold of fixed topology. This is a configuration space for GR; knowledge of configuration spaces is useful as regards dynamics and QM.In this Article I…
Multipartite entanglement is a crucial resource for a wide range of quantum information processing tasks, including quantum metrology, quantum computing, and quantum communication. The verification of multipartite entanglement, along with…
In several approaches towards a quantum theory of gravity, such as group field theory and loop quantum gravity, quantum states and histories of the geometric degrees of freedom turn out to be based on discrete spacetime. The most pressing…
Most quantum computing architectures can be realized as two-dimensional lattices of qubits that interact with each other. We take transmon qubits and transmission line resonators as promising candidates for qubits and couplers; we use them…
Quantum cryptographic protocols solve the longstanding problem of distributing a shared secret string to two distant users by typically making use of one-way quantum channel. However, alternative protocols exploiting two-way quantum channel…
This paper is one of a series of papers on coherent spaces and their applications, defined in the recent book 'Coherent Quantum Mechanics' by the first author. The paper studies coherent quantization -- the way operators in the quantum…
This paper introduces the Symmetric Extensible Quantum Secret Sharing protocol, which is a novel quantum protocol for secret sharing. At its heart, it is an entanglement based protocol that relies on the use of maximally entangled GHZ…