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Everything You Always Wanted to Know About LOCC (But Were Afraid to Ask)
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.
Nonlocal games and quantum permutation groups
Graph Homomorphisms for Quantum Players
Quantum Random Access Codes with Shared Randomness
An optimal construction for such codes is given and it is found that their success probability exactly--it is less than in the quantum case.
Quantum and non-signalling graph isomorphisms
Multidimensional quantum entanglement with large-scale integrated optics
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.
Shortcuts to quantum network routing
- E. Schoute, L. Mančinska, Tanvirul Islam, Iordanis Kerenidis, S. Wehner
- Computer ScienceArXiv
- 26 August 2015
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.
Quantum isomorphism is equivalent to equality of homomorphism counts from planar graphs
- L. Mančinska, D. Roberson
- MathematicsIEEE Annual Symposium on Foundations of Computer…
- 15 October 2019
This combinatorial proof leverages the quantum automorphism group of a graph, a notion from noncommutative mathematics, and shows that homomorphism counts from graphs of bounded treewidth do not determine a graph up to isomorphism.
Oddities of Quantum Colorings
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.