相关论文: Bounding the joint numerical range of Pauli string…
A set of Pauli stings is well characterized by the graph that encodes its commutatitivity structure, i.e., by its frustration graph. This graph provides a natural interface between graph theory and quantum information, which we explore in…
The incompatibility of measurements is the key feature of quantum theory that distinguishes it from the classical description of nature. Here, we consider groups of d-outcome quantum observables with prime d represented by non-Hermitian…
Measurement incompatibility--the impossibility of jointly measuring certain quantum observables--is a fundamental resource for quantum information processing. We develop a graph-theoretic framework for quantifying this resource for large…
The commutation relations between the generalized Pauli operators of N-qudits (i. e., N p-level quantum systems), and the structure of their maximal sets of commuting bases, follow a nice graph theoretical/geometrical pattern. One may…
In this work, we present a comprehensive exploration of the entanglement and graph connectivity properties of graph states. We quantify the entanglement in pseudo graph states using the entanglement distance, a recently introduced measure…
We introduce a notion of commutativity between operators on a tensor product space, nominally Pauli strings on qubits, that interpolates between qubit-wise commutativity and (full) commutativity. We apply this notion, which we call…
Graph-theoretic structures play a central role in the description and analysis of quantum systems. In this work, we introduce a new class of quantum states, called $A_\alpha$-graph states, which are constructed from either unweighted or…
Broad claims about whether adaptivity helps in quantum state tomography can be misleading unless the state family, measurement architecture, and error metric are specified carefully. We study a restricted but physically important regime:…
Topological quantum field theory (TQFT) provides a unifying framework for describing topological phases of matter and for constructing quantum error-correcting codes, playing a central role across high-energy physics, condensed matter, and…
We use random matrix theory to study the spectrum of random geometric graphs, a fundamental model of spatial networks. Considering ensembles of random geometric graphs we look at short range correlations in the level spacings of the…
In this article we consider the graph alignment problem from the perspective of high-dimensional statistics: we aim to estimate an unknown permutation $\pi^*$ from the observation of two correlated random adjacency matrices $A_1$, $A_2$. We…
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…
It has been conjectured that the Pauli exclusion principle alone may be responsible for a particular geometric arrangement of confined systems of identical fermions even when there is no interaction between them. These geometric structures,…
Geometrically frustrated assemblies where building blocks misfit have been shown to generate intriguing phenomena from self-limited growth, fiber formation, to structural complexity. We introduce a graph theory formulation of geometrically…
A graph is an instrument which is extensively utilized to model various problems in different fields. Up to date, many graphs have been developed to represent algebraic structures, particularly rings in order to study their properties. In…
We have generalised the concept of graph states to what we have called mixed graph states, which we define in terms of mixed graphs, that is graphs with both directed and undirected edges, as the density matrix stabilized by the associated…
We propose a communication-assisted local-hidden-variable model that yields the correct outcome for the measurement of any product of Pauli operators on an arbitrary graph state, i.e., that yields the correct global correlation among the…
For various purposes and, in particular, in the context of data compression, a graph can be examined at three levels. Its structure can be described as the unlabeled version of the graph; then the labeling of its structure can be added; and…
Graph states are multi-particle entangled states that correspond to mathematical graphs, where the vertices of the graph take the role of quantum spin systems and edges represent Ising interactions. They are many-body spin states of…
Pauli matrices and Pauli strings are widely used in quantum computing. These mathematical objects are useful to describe or manipulate the quantum state of qubits. They offer a convenient basis to express operators and observables used in…