A1 Refereed original research article in a scientific journal
Geometry on the manifold of Gaussian quantum channels
Authors: Siudzinska K, Luoma K, Strunz WT
Publisher: AMER PHYSICAL SOC
Publication year: 2019
Journal: Physical Review A
Journal name in source: PHYSICAL REVIEW A
Journal acronym: PHYS REV A
Article number: ARTN 062308
Volume: 100
Issue: 6
Number of pages: 8
ISSN: 2469-9926
DOI: https://doi.org/10.1103/PhysRevA.100.062308(external)
Abstract
In the space of quantum channels, we establish the geometry that allows us to make statistical predictions about relative volumes of entanglement breaking channels among all the Gaussian quantum channels. The underlying metric is constructed using the Choi-Jamiolkowski isomorphism between the continuous-variable Gaussian states and channels. This construction involves the Hilbert-Schmidt distance in quantum state space. The volume element of the one-mode Gaussian channels can be expressed in terms of local symplectic invariants. We analytically compute the relative volumes of the one-mode Gaussian entanglement breaking and incompatibility breaking channels. Finally, we show that, when given the purities of the Choi-Jamiolkowski state of the channel, one can determine whether or not such channel is incompatibility breaking.
In the space of quantum channels, we establish the geometry that allows us to make statistical predictions about relative volumes of entanglement breaking channels among all the Gaussian quantum channels. The underlying metric is constructed using the Choi-Jamiolkowski isomorphism between the continuous-variable Gaussian states and channels. This construction involves the Hilbert-Schmidt distance in quantum state space. The volume element of the one-mode Gaussian channels can be expressed in terms of local symplectic invariants. We analytically compute the relative volumes of the one-mode Gaussian entanglement breaking and incompatibility breaking channels. Finally, we show that, when given the purities of the Choi-Jamiolkowski state of the channel, one can determine whether or not such channel is incompatibility breaking.
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