Related papers: Small k-pairable states
The group of local unitary transformations acts on the space of n-qubit pure states, decomposing it into orbits. In a previous paper we proved that a product of singlet states (together with an unentangled qubit for a system with an odd…
We consider the minimal k-grouping problem: given a graph G=(V,E) and a constant k, partition G into subgraphs of diameter no greater than k, such that the union of any two subgraphs has diameter greater than k. We give a silent…
We analyze composed quantum systems consisting of $k$ subsystems, each described by states in the $n$-dimensional Hilbert space. Interaction between subsystems can be represented by a graph, with vertices corresponding to individual…
An $s$-pair state in a graph is a quantum state of the form $\mathbf{e}_u+s\mathbf{e}_v$, where $u$ and $v$ are vertices in the graph and $s$ is a non-zero complex number. If $s=-1$ (resp., $s=1$), then such a state is called a pair state…
Graph states (or cluster states) are the entanglement resource that enables one-way quantum computing. They can be grown by projective measurements on the component qubits. Such measurements typically carry a significant failure…
In Quantum Information theory, graph states are quantum states defined by graphs. In this work we exhibit a correspondence between graph states and the variety of binary symmetric principal minors, in particular their corresponding orbits…
Provided a complete set of putative $k$-body reductions of a multipartite quantum state, can one determine if a joint state exists? We derive necessary conditions for this to be true. In contrast to what is known as the quantum marginal…
Entanglement has evolved from an enigmatic concept of quantum physics to a key ingredient of quantum technology. It explains correlations between measurement outcomes that contradict classical physics, and has been widely explored with…
Let $d,n\in \mathbb{N}$ be such that $d=\omega(1)$, and $d\le n^{1-a}$ for some constant $a>0$. Consider a $d$-regular graph $G=(V, E)$ and the random graph process that starts with the empty graph $G(0)$ and at each step $G(i)$ is obtained…
Deciding if a given family of quantum states is topologically ordered is an important but nontrivial problem in condensed matter physics and quantum information theory. We derive necessary and sufficient conditions for a family of graph…
Measurement based quantum computing is preformed by adding non-Clifford measurements to a prepared stabilizer states. Entangling gates like CZ are likely to have lower fidelities due to the nature of interacting qubits, so when preparing a…
Graph states, and the entanglement they posses, are central to modern quantum computing and communications architectures. Local complementation---the graph operation that links all local-Clifford equivalent graph states---allows us to…
A set $D$ of vertices of a graph is a \emph{defensive alliance} if, for each element of $D$, the majority of its neighbours are in $D$. We consider the notion of local minimality in this paper. We are interested in finding a locally minimal…
Quantum networks with bipartite resources and shared randomness present the simplest infrastructure for implementing a future quantum internet. Here, we shall investigate which kinds of entanglement can or cannot be generated from this kind…
We investigate multiple qubit Pauli groups and the quantum states/rays arising from their maximal bases. Remarkably, the real rays are carried by a Barnes-Wall lattice $BW_n$ ($n=2^m$). We focus on the smallest subsets of rays allowing a…
Verifying quantum states is central to certifying the correct operation of various quantum information processing tasks. In particular, in measurement-based quantum computing, checking whether correct graph states are generated is essential…
The concept of generalized $k$-connectivity $\kappa_{k}(G)$ of a graph $G$ was introduced by Chartrand et al. in recent years. In our early paper, extremal theory for this graph parameter was started. We determined the minimal number of…
Highly entangled multipartite states such as k-uniform (k-UNI) and absolutely maximally entangled (AME) states serve as critical resources in quantum networking and other quantum information applications. However, there does not yet exist a…
Statistical verification of a quantum state aims to certify whether a given unknown state is close to the target state with confidence. So far, sample-optimal verification protocols based on local measurements have been found only for…
Let $G=(V,E)$ be a connected undirected graph with $k$ vertices. Suppose that on each vertex of the graph there is a player having an $n$-bit string. Each player is allowed to communicate with its neighbors according to an agreed…