For discrete quantum walks with Grover coins on unmarked vertices and negative identity coins on marked vertices, the paper derives closed-form expressions and tight bounds for the average vertex mixing matrix.
Khosrovshah i, and Hamidreza Maimani, The kernels of the incidence matrices of graphs revisited, Linear Algebra and its Applications 414 (2006), no
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Discrete Quantum Walks with Marked Vertices and Their Average Vertex Mixing Matrices
For discrete quantum walks with Grover coins on unmarked vertices and negative identity coins on marked vertices, the paper derives closed-form expressions and tight bounds for the average vertex mixing matrix.