← 研踪 PaperTrailarXiv:2609.40278 · v2
Computational Bounds for $f$-Routing
首次提交 2026-10-01 01:46
版本更新 2026-11-02 23:44
雷达观测 2026-11-04 23:41
摘要
The $f$-routing protocol is a leading candidate for quantum position verification (Kent, Munro, and Spiller, Physical Review A, 2011), but security guarantees for explicit functions remain limited. We prove unconditional resource lower bounds for uniform attackers. Our techniques bypass communication-complexity bounds central to previous works, which are inherently at most linear in the input length. We show that, for input length $n$ and a sufficiently small constant $ε>0$, a uniform strategy running in time $T$ and succeeding with probability at least $1-ε$ on every input implies the following computational bounds on $f$. 1. If the strategies are arbitrary quantum channels, then $f\in \mathrm{QSZK}(\mathrm{poly}(T))$, where $\mathrm{QSZK}(T)$ is the class of languages having quantum statistical zero-knowledge proofs in which the verifier runs in time $T$ and the simulator in time $\mathrm{poly}(T)$. 2. If the strategies are Clifford+T circuits using at most $t$ magic gates, then $f\in \mathrm{DTIME}(\mathrm{poly}(T2^t))$. 3. If the strategies are explicit Pauli-sparse unitaries acting on at most $T$ qubits and having at most $s$ nonzero Pauli coefficients, then $f\in \mathrm{DTIME}(\mathrm{poly}(Ts))$. Time and space hierarchies then yield explicit functions secure against superlinear and even all polynomial-time adversaries under our computational restrictions. These bounds exceed the bounded-storage qubit bound $q\leq\log n$ of Bluhm, Christandl, and Speelman (Nature Physics, 2022) for the inner product function $f=\mathrm{IP}$, at the cost of restricting adversarial computation and increasing honest evaluation complexity.
作者备注：Improved writing and exposition
观测到的版本
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v2 · 2026-11-02 23:44 · 最新观测版本
Computational Bounds for $f$-Routing
The $f$-routing protocol is a leading candidate for quantum position verification (Kent, Munro, and Spiller, Physical Review A, 2011), but security guarantees for explicit functions remain limited. We prove unconditional resource lower bounds for uniform attackers. Our techniques bypass communication-complexity bounds central to previous works, which are inherently at most linear in the input length. We show that, for input length $n$ and a sufficiently small constant $ε>0$, a uniform strategy running in time $T$ and succeeding with probability at least $1-ε$ on every input implies the following computational bounds on $f$. 1. If the strategies are arbitrary quantum channels, then $f\in \mathrm{QSZK}(\mathrm{poly}(T))$, where $\mathrm{QSZK}(T)$ is the class of languages having quantum statistical zero-knowledge proofs in which the verifier runs in time $T$ and the simulator in time $\mathrm{poly}(T)$. 2. If the strategies are Clifford+T circuits using at most $t$ magic gates, then $f\in \mathrm{DTIME}(\mathrm{poly}(T2^t))$. 3. If the strategies are explicit Pauli-sparse unitaries acting on at most $T$ qubits and having at most $s$ nonzero Pauli coefficients, then $f\in \mathrm{DTIME}(\mathrm{poly}(Ts))$. Time and space hierarchies then yield explicit functions secure against superlinear and even all polynomial-time adversaries under our computational restrictions. These bounds exceed the bounded-storage qubit bound $q\leq\log n$ of Bluhm, Christandl, and Speelman (Nature Physics, 2022) for the inner product function $f=\mathrm{IP}$, at the cost of restricting adversarial computation and increasing honest evaluation complexity.
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