Abstract
A complete analysis of multi-mode bosonic Gaussian channels (BGCs) is proposed. We clarify the structure of unitary dilations of general Gaussian channels involving any number of bosonic modes and present a normal form. The maximum number of auxiliary modes that is needed is identified, including all rank deficient cases, and the specific role of additive classical noise is highlighted. By using this analysis, we derive a canonical matrix form of the noisy evolution of n-mode BGCs and of their weak complementary counterparts, based on a recent generalization of the normal mode decomposition for non-symmetric or locality constrained situations. This allows us to simplify the weak-degradability classification. Moreover, we investigate the structure of some singular multi-mode channels, like the additive classical noise channel that can be used to decompose a noisy channel in terms of a less noisy one in order to find new sets of maps with zero quantum capacity. Finally, the two-mode case is analyzed in detail. By exploiting the composition rules of two-mode maps and the fact that anti-degradable channels cannot be used to transfer quantum information, we identify sets of two-mode bosonic channels with zero capacity.
Highlights
E The ideal-like quantum channelThey arise whenever a harmonic system interacts linearly with a number of bosonic modes which are inaccessible in principle or in practice [1, 2, 3, 4, 5, 6, 7]
Bosonic Gaussian channels are ubiquitous in physics
We investigate the structure of some singular multi-mode channels, like the additive classical noise channel that can be used to decompose a noisy channel in terms of a less noisy one in order to find new sets of maps with zero quantum capacity
Summary
They arise whenever a harmonic system interacts linearly with a number of bosonic modes which are inaccessible in principle or in practice [1, 2, 3, 4, 5, 6, 7] They provide realistic noise models for a variety of quantum optical and solid state systems when treated as open quantum systems, including models for wave guides and quantum condensates. Significant progress has been made in this respect in recent years, for some important cases, like the thermal noise channel modelling a realistic fiber with offset noise, the quantum capacity is still not yet known In this context, the degradability properties represent a powerful tool to simplify the quantum capacity issue of such Gaussian channels. They can be characterized as CPT maps that transform Gaussian states into Gaussian states [21, 22]
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