Related papers: The Finite Geometry of Breaking Quantum Secrets
In this paper, we will establish a general method of studying finite-dimensional normed spaces, and apply this method to classifying $3$-dimensional and $4$-dimensional normed spaces over a non-spherically complete field. For this purpose,…
The basic elements of the geometric approach to a consistent quantization formalism are summarized, with reference to the methods of the old quantum mechanics and the induced representations theory of Lie groups. A possible relationship…
Classification of entanglement in multipartite quantum systems is an open problem solved so far only for bipartite systems and for systems composed of three and four qubits. We propose here a coarse-grained classification of entanglement in…
A quantum algorithm for general combinatorial search that uses the underlying structure of the search space to increase the probability of finding a solution is presented. This algorithm shows how coherent quantum systems can be matched to…
In quantum information processing it may be possible to have efficient computation and secure communication beyond the limitations of classical systems. In a fundamental point of view, however, evolution of quantum systems by the laws of…
Qubit-efficient optimization studies how large combinatorial problems can be addressed with quantum circuits whose width is far smaller than the number of logical variables. In quadratic unconstrained binary optimization (QUBO), objective…
We introduce a general approach to realize quantum states with holographic entanglement structure via monitored dynamics. Starting from random unitary circuits in $1+1$ dimensions, we introduce measurements with a spatiotemporally-modulated…
The quadrature of cut elements is crucial for all Finite Element Methods that do not apply boundary-fitted meshes. It should be efficient, accurate, and robust. Various approaches balancing these requirements have been published, with some…
We give an example of a wide class of problems for which quantum information protocols based on multi-system entanglement can be mapped into much simpler ones involving one system. Secret sharing is a cryptographic primitive which plays a…
We study the noncommutative geometrical structures of quantum entangled states. We show that the space of a pure entangled state is a noncommutative space. In particular we show that by rewritten the conifold or the Segre variety we can get…
We offer a systematic account of decomposition of quantum systems into parts. Different decompositions (structures) are mutually linked via the proper linear canonical transformations. Different kinds of structures, as well as their…
In topological quantum computing, information is encoded in "knotted" quantum states of topological phases of matter, thus being locked into topology to prevent decay. Topological precision has been confirmed in quantum Hall liquids by…
The study of free-space quantum communications requires tools from quantum information theory, optics and turbulence theory. Here we combine these tools to bound the ultimate rates for key and entanglement distribution through a free-space…
The quantum phase diagram for a finite $3$-level system in the $\Lambda$ configuration, interacting with a two-mode electromagnetic field in a cavity, is determined by means of information measures such as fidelity, fidelity susceptibility…
We investigate in this work a quantum error correction on a five-qubits graph state used for secret sharing through five noisy channels. We describe the procedure for the five, seven and nine qubits codes. It is known that the three codes…
Studying the geometry of sets appearing in various problems of quantum information helps in understanding different parts of the theory. It is thus worthwhile to approach quantum mechanics from the angle of geometry -- this has already…
Subsystem symmetry has emerged as a powerful organizing principle for unconventional quantum phases of matter, most prominently fracton topological orders. Here, we focus on a special subclass of such symmetries, known as higher-form…
In this paper we analyze the (im)possibility of the exact distinguishability of orthogonal multipartite entangled states under {\em restricted local operation and classical communication}. Based on this local distinguishability analysis we…
We present a framework to study the entanglement structure of a quantum field theory inspired by the formalism of particle detectors in relativistic quantum information. This framework can in principle be used to faithfully capture…
We remark the importance of adding suitable pre-geometric content to tensor models, obtaining what has recently been called tensorial group field theories, to have a formalism that could describe the structure and dynamics of quantum…