A1 Vertaisarvioitu alkuperäisartikkeli tieteellisessä lehdessä
Geometry on the manifold of Gaussian quantum channels
Tekijät: Siudzinska K, Luoma K, Strunz WT
Kustantaja: AMER PHYSICAL SOC
Julkaisuvuosi: 2019
Journal: Physical Review A
Tietokannassa oleva lehden nimi: PHYSICAL REVIEW A
Lehden akronyymi: PHYS REV A
Artikkelin numero: ARTN 062308
Vuosikerta: 100
Numero: 6
Sivujen määrä: 8
ISSN: 2469-9926
DOI: https://doi.org/10.1103/PhysRevA.100.062308
Tiivistelmä
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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