We present a strong connection between quantum information and quantum permutation groups. Specifically, we define a notion of quantum isomorphisms of graphs based on quantum automorphisms from the… Expand

This paper provides a precise description of LOCC and related operational classes in terms of quantum instruments that captures both finite round protocols as well as those that utilize an unbounded number of communication rounds.Expand

This work considers a nonlocal game in which Alice and Bob are trying to convince a verifier with certainty that a graph X admits a homomorphism to Y, and shows that quantum homomorphisms closely relate to zero-error channel capacity.Expand

It is shown that quantum isomorphic graphs are necessarily cospectral, and a construction for reducing linear binary constraint system games to isomorphism games is provided, related to the FGLSS reduction from inapproximability literature, as well as the CFI construction.Expand

This work considers a nonlocal game in which Alice and Bob are trying to convince a verifier with certainty that a graph X admits a homomorphism to Y, and shows that quantum homomorphisms closely relate to zero-error channel capacity.Expand

We consider a communication method, where the sender encodes n classical bits into 1 qubit and sends it to the receiver who performs a certain measurement depending on which of the initial bits must… Expand

A multidimensional integrated quantum photonic platform able to generate, control, and analyze high-dimensional entanglement is demonstrated, and a programmable bipartite entangled system is realized with dimensions up to 15 × 15 on a large-scale silicon photonics quantum circuit.Expand

This work considers a simplified model where each satellite can perform quantum communication with its immediate neighbours, and can create quantum virtual links that form shortcuts through the network, and gives a routing algorithm for finding the shortest path on this network structure that only uses local information at each vertex to route.Expand

This work proves a dichotomy theorem, which shows that generic two-qubit commuting Hamiltonians can be used to perform computational tasks which are intractable for classical computers under plausible assumptions.Expand

The limitations of the quantum analogs of graph colorings are shown by exhibiting, for the first time, a graph with a 3-dimensional orthogonal representation which cannot be quantum 3-colored, and a graph that can be quantum3-colored but has no3-dimensional Orthogonal representations.Expand