Ryotaro Niwa, Zane Marius Rossi, Philip Taranto, Mio Murao (Jul 01 2025).
Abstract: Given the ability to apply an unknown quantum channel acting on a
d-dimensional system, we develop a quantum algorithm for transforming its singular values. The spectrum of a quantum channel as a superoperator is naturally tied to its Liouville representation, which is in general non-Hermitian. Our key contribution is an approximate block-encoding scheme for this representation in a Hermitized form, given only black-box access to the channel; this immediately allows us to apply polynomial transformations to the channel's singular values by quantum singular value transformation (QSVT). We then demonstrate an
O(d2/δ) upper bound and an
Ω(d/δ) lower bound for the query complexity of constructing a quantum channel that is
δ-close in diamond norm to a block-encoding of the Hermitized Liouville representation. We show our method applies practically to the problem of learning the
q-th singular value moments of unknown quantum channels for arbitrary
q>2,q∈R, which has implications for testing if a quantum channel is entanglement breaking.