arXiv:2210.17448 · Journal of Physics Communications

Geometry of phase-covariant qubit channels

Katarzyna Siudzińska

Published Jun 24, 2023• 3 citations

Abstract

Abstract We analyze the geometry on the space of non-unital phase-covariant qubit maps. Using the corresponding Choi-Jamiołkowski states, we derive the Hilbert-Schmidt line and volume elements using the channel eigenvalues together with the parameter that characterizes non-unitality. We find the shapes and analytically compute the volumes of phase-covariant channels, in particular entanglement breaking and obtainable with time-local generators.

DOI: 10.1088/2399-6528/ace0f4

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arXiv:2210.17448 · Journal of Physics Communications

Geometry of phase-covariant qubit channels

Katarzyna Siudzińska

Published Jun 24, 2023• 3 citations

arXiv HTML PDF

Abstract

DOI: 10.1088/2399-6528/ace0f4

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\mathrm{P}

- and

\mathrm{CP}

-divisible, which is related to the notion of Markovianity.

n

), and their associated Cartan involution provides a route to exactly compute the eigenspectrum of their Choi states and the partial transpose for any

n\in \mathbb{N}

. These channels include previously studied SO

(n)

-covariant channels, and further include Sp

(\frac{n}{2})

-covariant channels (when

n

is even) and S(U(

p

)

\times

q

))-covariant channels (where

n\!=\!p\!+\!q

). We show that all Cartan-covariant channels satisfy the PPT

^{2}

-conjecture and further demonstrate the nontrivial nature of this result for the class of Sp

(\frac{n}{2})

-covariant and

{\rm S}({\rm U}(p) \!\times\!{\rm U}(q))

-covariant channels