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Paper 1

A Note on Output Length of One-Way State Generators and EFIs

Minki Hhan, Tomoyuki Morimae, Takashi Yamakawa

Year

2023

Journal

arXiv preprint

DOI

arXiv:2312.16025

arXiv

2312.16025

We study the output length of one-way state generators (OWSGs), their weaker variants, and EFIs. - Standard OWSGs. Recently, Cavalar et al. (arXiv:2312.08363) give OWSGs with $m$-qubit outputs for any $m=ω(\log λ)$, where $λ$ is the security parameter, and conjecture that there do not exist OWSGs with $O(\log \log λ)$-qubit outputs. We prove their conjecture in a stronger manner by showing that there do not exist OWSGs with $O(\log λ)$-qubit outputs. This means that their construction is optimal in terms of output length. - Inverse-polynomial-advantage OWSGs. Let $ε$-OWSGs be a parameterized variant of OWSGs where a quantum polynomial-time adversary's advantage is at most $ε$. For any constant $c\in \mathbb{N}$, we construct $λ^{-c}$-OWSGs with $((c+1)\log λ+O(1))$-qubit outputs assuming the existence of OWFs. We show that this is almost tight by proving that there do not exist $λ^{-c}$-OWSGs with at most $(c\log λ-2)$-qubit outputs. - Constant-advantage OWSGs. For any constant $ε>0$, we construct $ε$-OWSGs with $O(\log \log λ)$-qubit outputs assuming the existence of subexponentially secure OWFs. We show that this is almost tight by proving that there do not exist $O(1)$-OWSGs with $((\log \log λ)/2+O(1))$-qubit outputs. - Weak OWSGs. We refer to $(1-1/\mathsf{poly}(λ))$-OWSGs as weak OWSGs. We construct weak OWSGs with $m$-qubit outputs for any $m=ω(1)$ assuming the existence of exponentially secure OWFs with linear expansion. We show that this is tight by proving that there do not exist weak OWSGs with $O(1)$-qubit outputs. - EFIs. We show that there do not exist $O(\log λ)$-qubit EFIs. We show that this is tight by proving that there exist $ω(\log λ)$-qubit EFIs assuming the existence of exponentially secure PRGs.

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Paper 2

Nonreciprocity-enriched steady phases in open quantum systems

Ding Gu, Zhanpeng Fu, Zhong Wang

Year

2026

Journal

arXiv preprint

DOI

arXiv:2605.00101

arXiv

2605.00101

Nonreciprocity can profoundly alter the spectra and dynamics of open quantum systems, yet its impact on the long-time steady-state phases of matter has remained largely unexplored. Here we show that the interplay of nonreciprocity, symmetry defects, and spatial boundaries can generate phases beyond the standard spontaneous-symmetry-breaking paradigm. We demonstrate this mechanism by showing that sufficiently strong nonreciprocity turns boundaries into sources and drains of symmetry defects, while simultaneously endowing these defects with chiral dynamics in the bulk. As a result, the conventional uniform symmetry-broken state gives way to a domain-wall traveling-wave phase, in which symmetry defects form a persistent chiral wave. We showcase this mechanism in a bosonic model with \(Z_{2}\) symmetry, where periodic boundary conditions support only the conventional symmetric and symmetry-broken phases, whereas open boundary conditions allow the traveling-wave phase. We further show that even in the absence of symmetry breaking, the steady state can exhibit anomalous chiral relaxation: owing to the non-Hermitian skin effect in the stability matrix, local fluctuations are chirally amplified as they approach a boundary, where they eventually decay. Combining mean-field theory with truncated Wigner simulations, we characterize these phases, analyze the order parameter and Goldstone-mode fluctuations of the traveling-wave phase, and confirm its existence in three spatial dimensions.

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