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Abstract: A generalized depolarizing channel acts on an N-dimensional quantum system tocompress the ``Bloch ball- in N^2-1 directions; it has a correspondingcompression vector. We investigate the geometry of these compression vectorsand prove a conjecture of Dixit and Sudarshan 1, namely that when N=2^d i.e.the system consists of d qubits and we work in the Pauli basis then the set ofall compression vectors forms a simplex. We extend this result by investigatingthe geometry in other bases; in particular we find precisely when the set ofall compression vectors forms a simplex.



Author: Christian K. Burrell

Source: https://arxiv.org/







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