Posted

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 dd-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)O(d^2/\delta) upper bound and an Ω(d/δ)\Omega(d/\delta) lower bound for the query complexity of constructing a quantum channel that is δ\delta-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 qq-th singular value moments of unknown quantum channels for arbitrary q>2,q∈Rq>2, q\in \mathbb{R}, which has implications for testing if a quantum channel is entanglement breaking.

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