Core Concepts
Subset states can be utilized to create pseudorandom states, resolving a conjecture and showcasing a pseudoentanglement phenomenon. The main thesis is the construction of pseudorandom and pseudoentangled states using subset states.
Abstract
The content explores the use of subset states to generate pseudorandom quantum states, highlighting their importance in quantum cryptography. It delves into the construction of these states, their applications, and the implications for security. The analysis includes technical details, proofs, and comparisons with existing constructions.
Stats
A random subset state is information-theoretically indistinguishable from a Haar random state.
For any function t(n) = ω(poly(n)) and t(n) ≤ s ≤ 2n/t(n), the distance between copies of different types of quantum states is negligible.
The family of states constructed based on PRPs forms a pseudorandom state on n qubits for specific subset sizes.
The entanglement entropy across all cuts plays a crucial role in distinguishing different types of quantum states.
Quotes
"A closely related notion to the PRSs is that of pseudoentangled states studied recently by [1]."
"Our main insight lies in making the connection to the study of graph spectra."
"Concurrent work by Giurgica-Tiron and Bouland proved a similar result."