Quantum Fractional Revival on Graphs
arXiv:1801.09654
Abstract
Fractional revival is a quantum transport phenomenon important for entanglement generation in spin networks. This takes place whenever a continuous-time quantum walk maps the characteristic vector of a vertex to a superposition of the characteristic vectors of a subset of vertices containing the initial vertex. A main focus will be on the case when the subset has two vertices. We explore necessary and sufficient spectral conditions for graphs to exhibit fractional revival. This provides a characterization of fractional revival in paths and cycles. Our work builds upon the algebraic machinery developed for related quantum transport phenomena such as state transfer and mixing, and it reveals a fundamental connection between them.
arXiv comment21 pages, 5 figures
References in corpus (14)
- Quantum Communication Through an Unmodulated Spin Chain
- Quantum Computation and Decision Trees
- Perfect state transfer in quantum spin networks
- Exponential algorithmic speedup by quantum walk
- On the relationship between continuous- and discrete-time quantum walk
- A Review of Perfect State Transfer and its Application as a Constructive Tool
- Number-Theoretic Nature of Communication in Quantum Spin Systems
- The Basics of Perfect Communication through Quantum Networks
- Almost perfect state transfer in quantum spin chains
- Quantum spin chains with fractional revival
- Analytic next-to-nearest neighbour XX models with perfect state transfer and fractional revival
- Perfect wave-packet splitting and reconstruction in a one-dimensional lattice
- Complex Hadamard Matrices, Instantaneous Uniform Mixing and Cubes
- Linear independence of trigonometric numbers