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Nonlocal games and quantum permutation groups
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 theExpand
Everything You Always Wanted to Know About LOCC (But Were Afraid to Ask)
TLDR
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
Graph Homomorphisms for Quantum Players
TLDR
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
Quantum and non-signalling graph isomorphisms
TLDR
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
Quantum homomorphisms
TLDR
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
Quantum Random Access Codes with Shared Randomness
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 mustExpand
Multidimensional quantum entanglement with large-scale integrated optics
TLDR
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
Shortcuts to quantum network routing
TLDR
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
Complexity Classification of Two-Qubit Commuting Hamiltonians
TLDR
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
Oddities of Quantum Colorings
TLDR
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
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