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$k$-Uniform states are fundamental to quantum information and computing, with applications in multipartite entanglement and quantum error-correcting codes (QECCs). Prior work has primarily focused on constructing exact $k$-uniform states or…

Quantum Physics · Physics 2025-08-13 Kaiyi Guo , Fei Shi , You Zhou , Qi Zhao

We study the relationship between notions of pseudorandomness in the quantum and classical worlds. Pseudorandom quantum state generator (PRSG), a pseudorandomness notion in the quantum world, is an efficient circuit that produces states…

Quantum Physics · Physics 2023-09-15 Prabhanjan Ananth , Yao-Ting Lin , Henry Yuen

We study the (quantum) security of pseudorandom generators (PRGs) constructed from random oracles. We prove a "lifting theorem" showing, roughly, that if such a PRG is unconditionally secure against classical adversaries making polynomially…

Cryptography and Security · Computer Science 2025-06-02 Jonathan Katz , Ben Sela

We show how to efficiently generate pseudo-random states suitable for quantum information processing via cluster-state quantum computation. By reformulating pseudo-random algorithms in the cluster-state picture, we identify a strategy for…

Quantum Physics · Physics 2009-11-13 Winton G. Brown , Yaakov S. Weinstein , Lorenza Viola

Unitary designs are unitary ensembles that emulate Haar-random unitary statistics. They provide a vital tool for studying quantum randomness and have found broad applications in quantum technologies. However, existing research has focused…

Quantum Physics · Physics 2026-01-06 Xiaodong Yang , Jiaqing Leng , Jun Li

One-parameter interpolations between any two unitary matrices (e.g., quantum gates) $U_1$ and $U_2$ along efficient paths contained in the unitary group are constructed. Motivated by applications, we propose the continuous unitary path…

Quantum Physics · Physics 2018-10-12 Ramis Movassagh

We show the following hold, unconditionally unless otherwise stated, relative to a random oracle: - There are NP search problems solvable by quantum polynomial-time machines but not classical probabilistic polynomial-time machines. - There…

Quantum Physics · Physics 2024-11-12 Takashi Yamakawa , Mark Zhandry

Efficiently sampling a quantum state that is hard to distinguish from a truly random quantum state is an elementary task in quantum information theory that has both computational and physical uses. This is often referred to as pseudorandom…

Quantum Physics · Physics 2020-04-07 Zvika Brakerski , Omri Shmueli

The applications of random quantum circuits range from quantum computing and quantum many-body systems to the physics of black holes. Many of these applications are related to the generation of quantum pseudorandomness: Random quantum…

Quantum Physics · Physics 2022-09-14 Jonas Haferkamp

Unknown unitary inversion is a fundamental primitive in quantum computing and physics. Although recent work has demonstrated that quantum algorithms can invert arbitrary unknown unitaries without accessing their classical descriptions,…

Quantum Physics · Physics 2025-06-26 Yin Mo , Tengxiang Lin , Xin Wang

There is a large body of work studying what forms of computational hardness are needed to realize classical cryptography. In particular, one-way functions and pseudorandom generators can be built from each other, and thus require equivalent…

Cryptography and Security · Computer Science 2025-04-02 Bruno Cavalar , Eli Goldin , Matthew Gray , Peter Hall , Yanyi Liu , Angelos Pelecanos

Physical unclonable functions (PUFs) are hardware structures in a physical system (e.g. semiconductor, crystals etc.) that are used to enable unique identification of the semiconductor or to secure keys for cryptographic processes. A PUF…

Quantum Physics · Physics 2023-09-19 Vladlen Galetsky , Soham Ghosh , Christian Deppe , Roberto Ferrara

Unitary $t$-designs are the bread and butter of quantum information theory and beyond. An important issue in practice is that of efficiently constructing good approximations of such unitary $t$-designs. Building on results by Aubrun (Comm.…

Quantum Physics · Physics 2020-09-02 Cécilia Lancien , Christian Majenz

Pseudorandom states, introduced by Ji, Liu and Song (Crypto'18), are efficiently-computable quantum states that are computationally indistinguishable from Haar-random states. One-way functions imply the existence of pseudorandom states, but…

Quantum Physics · Physics 2022-03-16 Prabhanjan Ananth , Luowen Qian , Henry Yuen

The efficiency of locally generating unitary designs, which capture statistical notions of quantum pseudorandomness, lies at the heart of wide-ranging areas in physics and quantum information technologies. While there are extensive potent…

Quantum Physics · Physics 2024-12-30 Zimu Li , Han Zheng , Zi-Wen Liu

We investigate the generation of quantum states and unitary operations that are ``random'' in certain respects. We show how to use such states to estimate the average fidelity, an important measure in the study of implementations of quantum…

Quantum Physics · Physics 2007-05-23 Christoph Dankert

Quantum Physical Unclonable Functions (QPUFs) are hardware-based cryptographic primitives with strong theoretical security. This security stems from their modeling as Haar-random unitaries. However, implementing such unitaries on…

Quantum Physics · Physics 2025-11-25 Soham Ghosh , Holger Boche , Marc Geitz

Random circuits giving rise to unitary designs are key tools in quantum information science and many-body physics. In this work, we investigate a class of random quantum circuits with a specific gate structure. Within this framework, we…

We construct a quantum oracle relative to which $\mathsf{BQP} = \mathsf{QMA}$ but cryptographic pseudorandom quantum states and pseudorandom unitary transformations exist, a counterintuitive result in light of the fact that pseudorandom…

Quantum Physics · Physics 2024-09-20 William Kretschmer

Recent active studies have demonstrated that cryptography without one-way functions (OWFs) could be possible in the quantum world. Many fundamental primitives that are natural quantum analogs of OWFs or pseudorandom generators (PRGs) have…

Quantum Physics · Physics 2024-11-06 Minki Hhan , Shogo Yamada