On State Distinguishing Without Inverse Queries

Abstract:In the quantum state distinguishing problem, an algorithm is given copies of a state $|\psi\rangle$ or $|\phi\rangle$ separated by trace distance $\varepsilon$, and tasked with deciding which is the case. It is a standard result that $\Theta(\varepsilon^{-2})$ copies are required, while having access to a unitary state preparation oracle and its inverse improves this to $\Theta(\varepsilon^{-1})$ queries. We study the intermediate case with forward-only access, capturing scenarios where the oracle is a physical process that cannot be reversed. Tang and Wright recently showed that distinguishing a known state from an \emph{unknown} close state requires $\Omega(\varepsilon^{-2})$ forward queries in high dimension; we strengthen this result by proving the same bound even when both states are known, as in the state distinguishing setting. Moreover, our lower bound uses a direct hybrid argument, avoiding advanced compressed oracle techniques used in the prior work. In contrast, we give a dimension-independent algorithm solving a continuous-time variant of state distinguishing with only $O(\varepsilon^{-1})$ total forward evolution time. The algorithm uses quantum Zeno dynamics to confine evolution to a known two-dimensional subspace. Thus, a quadratic advantage survives without inverse access for a natural continuous-time analogue of state distinguishing.

arXiv:2610.05389 [quant-ph]

(or arXiv:2610.05389v1 [quant-ph] for this version)

https://doi.org/10.48550/arXiv.2610.05389 Focus to learn more arXiv-issued DOI via DataCite (pending registration)

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