Amplitude damping channels in multilevel systems: there's more than you think

The amplitude damping channel (ADC) is one of the stantdard textbook instances of noise affecting 2-dimensional quantum systems (qubits). It can describe effectively ubiquitous relaxation processes affecting quantum devices such as superconducting circuits or losses in optical fibers. Many of its information theoretic properties, notably its quantum capacity, are understood.

Here we discuss the possible generalizations of these relaxation processes in multilevel systems (qudits).

We firstly introduce the class of multilevel amplitude damping (MAD) channels by generalizing the Kraus representation of the qubit ADC. We analyze the degradability/antidegradability properties of this new class of channels and provide explicit evaluations of their quantum capacities, also in non-degradable parameter regions.

Secondly we show that, by inspection of the Stinespring representation of MAD channels (i.e. their interpretation as an interaction system-environment), if we assume reasonable constraints on the environment we obtain a new kind of channels, physically different from MAD channels. In particular, for instance, if we assume a bosonic environment with equally spaced (resonant) levels, we get a new class of amplitude damping channels that we call resonant multilevel amplitude damping (ReMAD) channels. We show how these channels behave on multilevel systems, in particular how they can't be mapped onto "regular" MAD, exhibiting different and new properties. We provide a degradability/antidegradability analysis and compute the quantum capacity, again showing that also this class can have computable quantum capacity in non-degradable parameter regions.