On State Distinguishing Without Inverse Queries
Abstract
In the quantum state distinguishing problem, an algorithm is given copies of a state |ψ⟩ or |ϕ⟩ separated by trace distance ε, and tasked with deciding which is the case. It is a standard result that Θ(ε−2) copies are required, while having access to a unitary state preparation oracle and its inverse improves this to Θ(ε−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 Ω(ε−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(ε−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.
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BibTeX
@misc{wang2026state,
title = {{On State Distinguishing Without Inverse Queries}},
author = {Emma Wang and Joseph Carolan and Andrew M. Childs},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.05389},
eprint = {2610.05389},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.05389},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - On State Distinguishing Without Inverse Queries
AU - Emma Wang
AU - Joseph Carolan
AU - Andrew M. Childs
PY - 2026
DA - 2026/10/04
PB - arXiv
DO - 10.48550/arxiv.2610.05389
UR - https://arxiv.org/abs/2610.05389
AB - In the quantum state distinguishing problem, an algorithm is given copies of a state |ψ⟩ or |ϕ⟩ separated by trace distance ε, and tasked with deciding which is the case. It is a standard result that Θ(ε^−2) copies are required, while having access to a unitary state preparation oracle and its inverse improves this to Θ(ε^−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 Ω(ε^−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(ε^−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.
ER -